tag:blogger.com,1999:blog-43740484431628828322024-02-08T12:24:29.101+07:00Astronomy Today and BeyondAstronomy Blog for Learning Basic Astronomy and General Knowledge on AstronomyAndri F Martinhttp://www.blogger.com/profile/11669920311565328714noreply@blogger.comBlogger38125tag:blogger.com,1999:blog-4374048443162882832.post-22344120775465809622022-11-14T15:53:00.001+07:002022-11-14T15:53:24.423+07:00MIS2502: Data Analytics Advanced Analytics Using R - ppt download<a href="https://slideplayer.com/slide/16628230/#.Y3IBu11IfSY.blogger">MIS2502: Data Analytics Advanced Analytics Using R - ppt download</a>: The Information Architecture of an Organization Now we’re here… Data entry Transactional Database Data extraction Analytical Data Store Data analysis Stores real-time transactional data Stores historical transactional and summary dataAndri F Martinhttp://www.blogger.com/profile/11669920311565328714noreply@blogger.com0tag:blogger.com,1999:blog-4374048443162882832.post-12058788684557716752012-03-17T09:15:00.000+07:002012-03-17T09:15:31.992+07:00More Precisely 4.1 - The Energy Levels of the Hydrogen Atom<div style="text-align: justify;"><br />
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<tr><td><span style="font-family: 'Times New Roman', Georgia, Times;">By observing the emission spectrum of hydrogen and using the connection between photon energy and color first suggested by Einstein <a href="http://astronomylearn.blogspot.com/2012/02/42-formation-of-spectral-lines.html">(Sec. 4.2)</a>, Niels Bohr determined early in the twentieth century what the energy differences between the various energy levels must be. Using that information, he was then able to infer the actual energies of the excited states of hydrogen.</span><br />
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</div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">A unit of energy often used in atomic physics is the <i>electron volt</i> (eV). Its name derives from the amount of energy gained by an electron when it moves through an electric potential of one volt. For our purposes, however, it is just a convenient quantity of energy, numerically equal to 1.60 x 10<sup>-19</sup>J (joule)—roughly half the energy carried by a single photon of red light. The minimum amount of energy needed to ionize hydrogen from its ground state is 13.6 eV. Bohr numbered the energy levels of hydrogen starting at the ground state, with level 1 the ground state, level 2 the first excited state, and so on. He found that by assigning zero energy to the ground state, the energy of any state (the <i>n</i><sup>th</sup>, say) could be written as follows:</span></div></div><center><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmx5uKiod6QQEII6_VdUeSkvcE1jXRTx_iGqAQHV22H2Yh76DWgjz8Z7b0ke4JnkkRdhEDEKNtcGSHIYp18YulIjZlkoTzivZVelCZWExT9lYUCPLqylHUhZefHBUT4pTJL7xWpPZM2OM/s1600/Bohr+Equation.GIF" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmx5uKiod6QQEII6_VdUeSkvcE1jXRTx_iGqAQHV22H2Yh76DWgjz8Z7b0ke4JnkkRdhEDEKNtcGSHIYp18YulIjZlkoTzivZVelCZWExT9lYUCPLqylHUhZefHBUT4pTJL7xWpPZM2OM/s1600/Bohr+Equation.GIF" /></a> <span style="font-family: 'Times New Roman', Georgia, Times;"><br />
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</div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Thus, the ground state has energy <i>E</i><sub>1</sub> = 0 (by our definition), the first excited state has energy </span> <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEil4CA9FMPFOK7pF5cKYAnv-VS6ofhjiNB-2c3b3_THn0ujmCdH2fTFK44q7c1mknpYl1lrPoX-hl_6h3RlKJtHJVoI8LgRlOM1QzLbpeG4E50b7X6eUHVWkUsANMxWNYambpbS21FUFfU/s1600/energy+2+equation.GIF" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEil4CA9FMPFOK7pF5cKYAnv-VS6ofhjiNB-2c3b3_THn0ujmCdH2fTFK44q7c1mknpYl1lrPoX-hl_6h3RlKJtHJVoI8LgRlOM1QzLbpeG4E50b7X6eUHVWkUsANMxWNYambpbS21FUFfU/s1600/energy+2+equation.GIF" /></a> <span style="font-family: 'Times New Roman', Georgia, Times;"> the second excited state has energy </span> <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghshp-DEyylXk6MY9KbFYofGkNZ8u2y9vclen7SwQAW0Xwmj9BFchJDOzi1GbakjnkT3nkcBOa12Ahk_fw7zTYIfDb1BjjxsDs-Ryh4iYu-IK9LsgRiAZOHg5VmK3hnF6dC6I3duJjphM/s1600/energy+3+equation.GIF" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghshp-DEyylXk6MY9KbFYofGkNZ8u2y9vclen7SwQAW0Xwmj9BFchJDOzi1GbakjnkT3nkcBOa12Ahk_fw7zTYIfDb1BjjxsDs-Ryh4iYu-IK9LsgRiAZOHg5VmK3hnF6dC6I3duJjphM/s1600/energy+3+equation.GIF" /></a> <span style="font-family: 'Times New Roman', Georgia, Times;"> and so on. Notice that there are infinitely many excited states between the ground state and the energy at which the atom is ionized, crowding closer and closer together as<i> n</i> becomes large and <i>E<sub>n</sub></i> approaches 13.6 eV.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
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</div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">EXAMPLE: Using Bohr’s formula for the energy of each electron orbital, we can reverse his reasoning and calculate the energy associated with a transition between any two given states. To boost an electron from the second state to the third, an atom must be supplied with <i>E</i><sub>3</sub> - <i>E</i><sub>2</sub> = 1.89 eV of energy, or 3.03 x 10<sup>-19</sup> J. Using the formula <i>E</i> = <i>hf</i> presented in the text, we find that this corresponds to a photon with a frequency of 4.57 x 10<sup>14</sup> Hz, having a wavelength of 656 nm and lying in the red portion of the spectrum. (A more precise calculation gives the value 656.3 nm reported in the text.) Similarly, the jump from level 3 to level 4 requires </span> <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi173NbCIyE2bhvvT4oaU2M2ewV7cDP4nJTbtE2Jx8DUSzKNa0joPtUAUfkM4nt6L8C42vfc-_1YGhp1M7hzDDP85FCb4EZt5pgMFOwrI56L5fK9Hp2ImIucx78FIloeAJaxaQeQf0hxIE/s1600/energy+4+equation.GIF" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi173NbCIyE2bhvvT4oaU2M2ewV7cDP4nJTbtE2Jx8DUSzKNa0joPtUAUfkM4nt6L8C42vfc-_1YGhp1M7hzDDP85FCb4EZt5pgMFOwrI56L5fK9Hp2ImIucx78FIloeAJaxaQeQf0hxIE/s1600/energy+4+equation.GIF" /></a> <span style="font-family: 'Times New Roman', Georgia, Times;">eV of energy, corresponding to an infrared photon with a wavelength of 1880 nm, and so on. A handy conversion between photon energies <i>E</i> in electron volts and wavelengths </span><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">λ</span><span style="font-family: 'Times New Roman', Georgia, Times;"> in nanometers is</span></div></div><center><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgW75qEiYRmG2KNk4ruRhzhFu9inS_H_QUuIbILbhKA2OQRjanf9WpBqU6McOfvhqZ_-90-rD5LM6hppNGev3yLzwc-yUCW9TjWYZJWoFyYZWA-5xn2JOHN0_4DdcicfD4A6Bou8Bv9uRg/s1600/Photon+equation.GIF" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgW75qEiYRmG2KNk4ruRhzhFu9inS_H_QUuIbILbhKA2OQRjanf9WpBqU6McOfvhqZ_-90-rD5LM6hppNGev3yLzwc-yUCW9TjWYZJWoFyYZWA-5xn2JOHN0_4DdcicfD4A6Bou8Bv9uRg/s1600/Photon+equation.GIF" /></a> <span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></center><div align="left"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">The accompanying diagram summarizes the structure of the hydrogen atom. The various energy levels are depicted as a series of circles of increasing radius, representing increasing energy. The electronic transitions between these levels (indicated by arrows) are conventionally grouped into families, named after their discoverers, that define the terminology used to identify specific spectral lines. (Note that the spacings of the energy levels are not drawn to scale here, to provide room for all labels on the diagram. In reality, the circles should become more and more closely spaced as we move outward.)</span></div><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
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<div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Transitions starting from or ending at the ground state (level 1) form the <i>Lyman series.</i> The first is <i>Lyman alpha</i> (Ly</span><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">α</span><span style="font-family: 'Times New Roman', Georgia, Times;">), corresponding to the transition between the first excited state (level 2) and the ground state. As we have seen, the energy difference is 10.21 eV, and the Ly</span><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">α</span><span style="font-family: 'Times New Roman', Georgia, Times;"> photon has a wavelength of 121.6 nm (1216 Å). The Ly</span><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">β</span><span style="font-family: 'Times New Roman', Georgia, Times;"> (beta) transition, between level 3 (the second excited state) and the ground state, corresponds to an energy change of 12.10 eV and a photon of wavelength 102.6 nm (1026 Å). Ly</span><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">γ</span><span style="font-family: 'Times New Roman', Georgia, Times;"> (gamma) corresponds to a jump from level 4 to level 1, and so on. The accompanying table shows how we can calculate the energies, frequencies, and wavelengths of the photons in the Lyman series using the formulae given previously. All Lyman-series energies lie in the ultraviolet region of the spectrum.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><a href="" name="Anchor-The-5797"></a>The next series of lines, the <i>Balmer series,</i> involves transitions down to (or up from) level 2, the first excited state. All the Balmer series lines lie in or close to the visible portion of the electromagnetic spectrum. Because they form the most easily observable part of the hydrogen spectrum and were the first to be discovered, these lines are often referred to simply as the "Hydrogen" series and denoted by the letter H. As with the Lyman series, the individual transitions are labeled with Greek letters. An H</span><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">α</span><span style="font-family: 'Times New Roman', Georgia, Times;"> photon (level 3 to level 2) has a wavelength of 656.3 nm and is red, Hß (level 4 to level 2) has a wavelength of 486.1 nm (green), H</span><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">γ</span><span style="font-family: 'Times New Roman', Georgia, Times;"> (level 5 to level 2) has a wavelength of 434.1 nm (blue), and so on. The most energetic Balmer series photons have energies that place them just beyond the blue end of the visible spectrum, in the near ultraviolet.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">The classification continues with the <i>Paschen series</i> (transitions down to or up from the second excited state), the <i>Brackett series</i> (third excited state), and the <i>Pfund series</i> (fourth excited state). Beyond that point, infinitely many other families exist, moving farther and farther into the infrared and radio regions of the spectrum, but they are not referred to by any special names. A few of the transitions making up the Lyman and Balmer (Hydrogen) series are marked on the figure. Astronomically, these are the most important sequences.</span></div></div><div class="separator" style="clear: both; text-align: center;"><br />
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</tbody></table></div>Andri F Martinhttp://www.blogger.com/profile/11669920311565328714noreply@blogger.com0tag:blogger.com,1999:blog-4374048443162882832.post-27807661162801924502012-02-18T13:53:00.002+07:002012-02-18T22:14:24.843+07:004.2 The Formation of Spectral Lines<h1 style="text-align: center;">The Formation of Spectral Lines</h1><div style="background-color: white; text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">By the start of the twentieth century, physicists had accumulated substantial evidence that light sometimes behaves in a manner that cannot be explained by the wave theory. As we have just seen, the production of absorption and emission lines involves only certain very specific frequencies or wavelengths of light. This would not be expected if light behaved like a continuous wave and matter always obeyed the laws of Newtonian mechanics. Other experiments conducted around the same time strengthened the conclusion that the notion of radiation as a wave was incomplete. It became clear that when light interacts with matter on very small scales, it does so not in a continuous way but in a discontinuous, "stepwise" manner. The challenge was to find an explanation for this unexpected behavior. The eventual solution revolutionized our view of nature and now forms the foundation for all of physics and astronomy—indeed for virtually all modern science.</span></div><div style="background-color: white; text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div><div style="background-color: white;"><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><b>ATOMIC STRUCTURE</b></span></div><div style="background-color: white;"><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><b><br />
</b></span></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><img height="14" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjro4NwCtC2TCdCM0U8llIjQWPaqnmu4Nt2WLO_hJXMRRt6pjUDNl52NfT4zBngnC52mY9Jyz9gm_C7nhxdDYZ3UdXQFZmOhsitag5SnErKeorWf9nncczB8fnqqR0HGCan4k26Y0kL1QE/s1600/LGICON_3.GIF" width="24" /><a href="" name="Anchor-To-63854"></a>To explain the formation of emission and absorption lines, we must understand not just the nature of light but also the structure of </span><a href="" name="Anchor-atoms-35326"></a><a href="http://astronomylearn.blogspot.com/p/glossary.html#atom"><span style="font-family: 'Times New Roman', Georgia, Times;"><b>atoms</b></span></a><span style="font-family: 'Times New Roman', Georgia, Times;">—the microscopic building blocks from which all matter is constructed. </span><a href="" name="Anchor-35148"></a><span style="font-family: 'Times New Roman', Georgia, Times;">Let's start with the simplest atom of all—hydrogen. </span><a href="" name="Anchor-17848"></a><span style="font-family: 'Times New Roman', Georgia, Times;">A hydrogen atom consists of an electron with a negative electrical charge, orbiting a proton carrying a positive charge. The proton forms the central <a href="" name="Anchor-nucleus-44867"></a><a href="http://astronomylearn.blogspot.com/p/glossary.html#nucleus"><b>nucleus</b></a> (plural: nuclei) of the atom. The hydrogen atom as a whole is electrically neutral. The equal and opposite charges of the proton and the orbiting electron produce an electrical attraction that binds them together within the atom.</span></div></div><div style="background-color: white;"><span style="font-family: 'Times New Roman', Georgia, Times;">How does this picture of the hydrogen atom relate to the characteristic emission and absorption lines associated with hydrogen gas? If an atom emits some energy in the form of radiation, that energy has to come from somewhere within the atom. Similarly, if energy is absorbed, it must cause some internal change. It is reasonable (and correct) to suppose that the energy emitted or absorbed by the atom is associated with changes in the motion of the orbiting electron.</span><br />
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<tr><td></td><td bgcolor="#fffad7"><div style="text-align: justify;"><span style="color: red; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>Figure 4.8</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b> Bohr Atom</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;"> An early-twentieth-century conception of the hydrogen atom pictured its electron orbiting the central proton in a well-defined orbit, rather like a planet orbiting the Sun. Two electron orbits of different energies are shown. (a) The ground state. (b) An excited state.</span></div></td></tr>
</tbody></table><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">The first theory of the atom to provide an explanation of hydrogen's observed spectral lines was set forth by the Danish physicist Niels Bohr in 1912. Now known simply as the <i>Bohr model</i> of the atom, its essential features are as follows. </span><a href="" name="Anchor-First-36123"></a><span style="font-family: 'Times New Roman', Georgia, Times;">First, there is a state of lowest energy—the <a href="" name="Anchor-ground-33869"></a><a href="http://astronomylearn.blogspot.com/p/glossary.html#ground state"><b>ground state</b></a>—which represents the "normal" condition of the electron as it orbits the nucleus. Second, there is a maximum energy that the electron can have and still be part of the atom. <a href="" name="Anchor-Once-6041"></a>Once the electron acquires more than that maximum energy, it is no longer bound to the nucleus, and the atom is said to be<a href="" name="Anchor-ionized-6296"></a> <a href="http://astronomylearn.blogspot.com/p/glossary.html#ionized"><b>ionized</b></a>; an atom missing one or more of its electrons is called an <i>ion.</i> <a href="" name="Anchor-Third-56418"></a>Third, and most important (and also least intuitive), between those two energy levels the electron can exist only in certain sharply defined energy states, often referred to as <i>orbitals.</i></span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><i><br />
</i></span></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">This description of the atom contrasts sharply with the predictions of Newtonian mechanics, which would permit orbits with <i>any</i> energy, not just at certain specific values. In the atomic realm such discontinuous behavior is the norm. <a href="" name="Anchor-In-35441"></a>In the jargon of the field, the orbital energies are said to be <a href="" name="Anchor-quantized-48213"></a><a href="http://astronomylearn.blogspot.com/p/glossary.html#quantized"><b>quantized</b></a>. The rules of <i>quantum mechanics,</i> the branch of physics governing the behavior of atoms and subatomic particles, are far removed from everyday experience.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
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<tr><td><img height="6" src="file:///G:/CHAISSON/COMART/SPACER.GIF" width="6" /><img height="6" src="file:///G:/CHAISSON/COMART/SPACER.GIF" width="6" /><img height="6" src="file:///G:/CHAISSON/COMART/SPACER.GIF" width="6" /></td><td><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjB4McB-WCeTrzjwHHXLelIGbAagYpiA2iHx_htwZSy2nOy6jj4f47Mma_6hGC_YTPZ9ugRv0QMFAmsjqNzse1-vD5X1DKduYAQy3OPNjfFjqX-iuiGwUYq7aMKu-ZhRiT69_UNCcpEb9w/s1600/Modern+Atom+Model.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjB4McB-WCeTrzjwHHXLelIGbAagYpiA2iHx_htwZSy2nOy6jj4f47Mma_6hGC_YTPZ9ugRv0QMFAmsjqNzse1-vD5X1DKduYAQy3OPNjfFjqX-iuiGwUYq7aMKu-ZhRiT69_UNCcpEb9w/s1600/Modern+Atom+Model.JPG" /></a></div></td></tr>
<tr><td></td><td bgcolor="#fffad7"><span style="color: red; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>Figure 4.9</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b> Modern Atom</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"> </span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;">The modern view of the hydrogen atom sees the electron as a "cloud" surrounding the nucleus. The same two energy states are shown as in Figure 4.8.</span></td></tr>
</tbody></table><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">In Bohr's model, each electron orbital was pictured as having a specific radius, much like a planetary orbit in the solar system, as shown in Figure 4.8. <a href="" name="Anchor-However-58495"></a>However, the modern view is not so simple. Although each orbital <i>does</i>have a precise energy, the electron is now envisioned as being smeared out in an "electron cloud" surrounding the nucleus, as illustrated in Figure 4.9. We cannot tell "where" the electron is—we can only speak of the <i>probability</i> of finding it in a certain location within the cloud. It is common to speak of the average distance from the cloud to the nucleus as the "radius" of the electron's orbit. When a hydrogen atom is in its ground state, the radius of the orbit is about 0.05 nm (0.5 Å). As the orbital energy increases, the radius increases, too. For the sake of clarity in the diagrams that follow, we will represent electron orbitals as solid lines, but always bear in mind that Figure 4.9 is a more accurate depiction of reality.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><a href="" name="Anchor-Atoms-44714"></a>Atoms do not always remain in their ground state. An atom is said to be in an <a href="" name="Anchor-excited-37516"></a><a href="http://astronomylearn.blogspot.com/p/glossary.html#excited state"><b>excited state</b></a> when an electron occupies an orbital at a greater than normal distance from its parent nucleus. An atom in such an excited state has a greater than normal amount of energy. The excited state with the lowest energy (that is, the one closest in energy to the ground state) is called the<i> first excited state,</i> that with the second-lowest energy is the <i>second excited state,</i> and so on. An atom can become excited in one of two ways: by absorbing some energy from a source of electromagnetic radiation or by colliding with some other particle—another atom, for example. <a href="" name="Anchor-However-11727"></a>However, the electron cannot stay in a higher orbital forever; the ground state is the only level where it can remain indefinitely. After about 10<sup>-8</sup> s, an excited atom returns to its ground state.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><b style="background-color: white; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;">RADIATION AS PARTICLES</b><br />
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</b></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><i><i><img height="14" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi7BP-072_rJf_a6j879EXh5dxwRChAL8MSSshDxJzWKgCV2cYUdqSRcY23tVUo_GWcFSiHWLjAbp4wfdbu01NHbxUOL9_hspd1du6Q01LTVY6Hhfqhj5EeVEF5rC3DQJpcjtEjA-EjKwI/s1600/LGICON_4.GIF" width="24" /><i><a href="" name="Anchor-Because-9024"></a></i></i></i>Because electrons may exist only in orbitals having specific energies, atoms can absorb only specific amounts of energy as their electrons are boosted into excited states. Likewise, they can emit only specific amounts of energy as their electrons fall back to lower energy states. Thus, the amount of light energy absorbed or emitted in these processes <i>must correspond precisely to the energy difference between two orbitals. <a href="" name="Anchor-The-57478"></a></i>The atom's quantized energy levels require that light must be absorbed and emitted in the form of distinct "packets" of electromagnetic radiation, each carrying a specific amount of energy. We call these packets <a href="" name="Anchor-photons-23522"></a><a href="http://astronomylearn.blogspot.com/p/glossary.html#photon"><b>photons</b></a>. <a href="" name="Anchor-56135"></a>A photon is, in effect, a "particle" of electromagnetic radiation.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><a href="" name="Anchor-The-38762"></a>The idea that light sometimes behaves not as a continuous wave but as a stream of particles was proposed by Albert Einstein in 1905 to explain a number of experimental results then puzzling physicists. Further, Einstein was able to quantify the relationship between the two aspects of light's double nature. <a href="" name="Anchor-He-10152"></a>He found that the energy carried by a photon had to be proportional to the<i>frequency</i> of the radiation:</span></div></div><div class="separator" style="clear: both; text-align: center;"><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;">photon energy </span> <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhtslm_yZ5x5LenBMjHOnKUbQXbENpwLvaLzgmtRgtFnuvmtXWYum33UTNUChr0eSOHMkBHiYEuKTjvyWBAeKeZFPGMuoXSddTf24RsF2ki3lbjO5PRwDwBIG5niO30gZ2CelAUsBmIVcg/s1600/PROPOR.GIF" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhtslm_yZ5x5LenBMjHOnKUbQXbENpwLvaLzgmtRgtFnuvmtXWYum33UTNUChr0eSOHMkBHiYEuKTjvyWBAeKeZFPGMuoXSddTf24RsF2ki3lbjO5PRwDwBIG5niO30gZ2CelAUsBmIVcg/s1600/PROPOR.GIF" /></a> <span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;"> radiation frequency.</span></div><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;">Thus, for example, a "deep red" photon having a frequency of 4 x 10</span><sup style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;">14</sup><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;"> Hz (or a wavelength of approximately 750 nm) has half the energy of a violet photon of frequency of 8 x 10</span><sup style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;">14</sup><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;"> Hz (wavelength = 375 nm), and 500 times the energy of an 8 x 10</span><sup style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;">11</sup><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;"> Hz (wavelength = 375 µm) microwave photon.</span><br />
<div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">The constant of proportionality in the above relation is now known as <i>Planck's constant,</i> in honor of the German physicist Max Planck, who determined its numerical value. It is always denoted by the symbol <i>h</i>, and the equation relating photon energy <i>E</i> to radiation frequency<i> f</i> is usually written</span></div></div><br />
<br />
<center style="background-color: white;"><a href="" name="Anchor-26352"></a><span style="font-family: 'Times New Roman', Georgia, Times;"><i>E</i> =<i> h f</i>.</span></center><br />
<div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Like the gravitational constant <i>G</i> and the speed of light <i>c,</i> Planck's constant is one of the fundamental physical constants of the universe.</span></div><div style="text-align: justify;"><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;"><br />
</span></div><div style="text-align: justify;"><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;">In SI units, the value of Planck's constant is a very small number: </span><i style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;">h =</i><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;"> 6.63 x 10</span><sup style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;">-34</sup><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;"> joule seconds (J. s). Consequently, the energy of a single photon is tiny. Even a very-high-frequency gamma ray (the most energetic type of electromagnetic radiation) with a frequency of 10</span><sup style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;">22</sup><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;"> Hz has an energy of just (6.63 x 10</span><sup style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;">-34</sup><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;">) x</span><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;"> 10</span><sup style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;">22</sup><span style="background-color: white;"> </span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEixOnJ_n3Sqp0N6UQqK0cgkBbIv-2zxDmiiasNa-VP4muk9Me2t5swN-e2fIsnwL5AjhDYp8cngl24K_jV00hJx6suW9RX4F25ekPOGrcaHmx4zmzHXE2XdDodqhnppmvoxH6WKv3EzFis/s1600/APPROX.GIF" imageanchor="1" style="background-color: white; margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEixOnJ_n3Sqp0N6UQqK0cgkBbIv-2zxDmiiasNa-VP4muk9Me2t5swN-e2fIsnwL5AjhDYp8cngl24K_jV00hJx6suW9RX4F25ekPOGrcaHmx4zmzHXE2XdDodqhnppmvoxH6WKv3EzFis/s1600/APPROX.GIF" /></a><span style="background-color: white;"> </span><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;">7 x</span><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;"> 10</span><sup style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;">-12</sup><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;"> J—about the same energy carried by a flying gnat. Nevertheless, this energy is more than enough to damage a living cell. </span><a href="" name="Anchor-The-52971" style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;"></a><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;">The basic reason that gamma rays are so much more dangerous to life than visible light is that each gamma-ray photon typically carries millions, if not billions, of times more energy than a photon of visible radiation.</span></div></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><a href="" name="Anchor-The-53753"></a>The equivalence between photon energy and photon frequency, or wavelength, completes the connection between atomic structure and atomic spectra. <a href="" name="Anchor-Atoms-59425"></a>Atoms absorb and emit radiation at characteristic wavelengths determined by their own particular internal structure. <a href="" name="Anchor-Because-38358"></a>Because this structure is <i>unique</i> to each element, the colors of the absorbed and emitted photons—that is, the spectral lines we observe—are characteristic of that element <i>and only that element. </i>The spectrum we see is thus a unique identifier of the atom involved.</span></div></div><div style="background-color: white;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
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<div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Many people are confused by the idea that light can behave in two such different ways. To be truthful, modern physicists don't yet fully understand <i>why</i> nature displays this wave–particle duality. Nevertheless, there is irrefutable experimental evidence for both of these aspects of radiation. Environmental conditions ultimately determine which description—wave or stream of particles—better fits the behavior of electromagnetic radiation. As a general rule of thumb, in the macroscopic realm of everyday experience, radiation is more usefully described as a wave, whereas in the microscopic domain of atoms it is best characterized as a series of particles.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><b>THE SPECTRUM OF HYDROGEN</b></span><br />
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</b></span></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><a href="" name="Anchor-Figure-17734"></a>Figure 4.10 illustrates schematically the absorption and emission of photons by a hydrogen atom.<a href="" name="Anchor-33782"></a>Figure 4.10(a) shows the atom absorbing a photon and making a transition from the ground state to the first excited state, then emitting a photon of precisely the same energy and dropping back to the ground state. <a href="" name="Anchor-The-51782"></a>The energy difference between the two states corresponds to an ultraviolet photon, of wavelength 121.6 nm (1216 Å).</span></div></div><br />
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<tr><td bgcolor="#fffad7"><div style="text-align: justify;"><span style="color: red; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>Figure 4.10</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b> Atomic Excitation</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;"> (a) Diagram of a photon being absorbed by a hydrogen atom (left), causing the momentary excitation of that atom (center) into its first excited state. After about 10<sup>-8</sup> s, the atom returns to its ground state, accompanied by the emission of a photon of the same energy as the original photon (right). (b) Absorption of a higher-energy photon may also boost the atom into a higher excited state, from which there may be several possible paths back to the ground state. (Remember that the sharp lines used for the orbitals here and in similar figures that follow are intended merely as a schematic representation of the electron energy levels and are not meant to be taken literally. In actuality, electron orbitals are "clouds," as shown in Figure 4.9.) As ultraviolet photons from a hot star pass through surrounding hydrogen gas, many are absorbed by the gas, boosting its atoms into excited states. Electrons in the second excited state can fall to the first excited state on their way back to the ground state (the lower path in part b). This transition produces radiation in the visible region of the spectrum—the 656.3-nm red glow that is characteristic of excited hydrogen gas. The object shown in the inset, designated N81, is an emission nebula: an interstellar cloud consisting largely of hydrogen gas excited by extremely hot star (as seen in white at the center). (Inset:<i>NASA</i>)</span></div></td></tr>
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<div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Absorption may also boost an electron into an excited state higher than the first excited state. Figure 4.10(b) depicts the absorption of a more energetic (higher-frequency, shorter-wavelength) ultraviolet photon, this one having a wavelength of 102.6 nm (1026 Å). Absorption of this photon causes the atom to jump to the <i>second</i> excited state. As before, the atom returns rapidly to the ground state, but this time it can do so in one of two possible ways:</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><span style="font-family: 'Times New Roman', Georgia, Times;"><b>1.</b> It can proceed directly back to the ground state, in the process emitting an ultraviolet photon identical to the one that excited the atom in the first place.</span></div><div style="background-color: white;"><span style="font-family: 'Times New Roman', Georgia, Times;"><b>2.</b> Alternatively, the electron can <i>cascade</i> down one orbital at a time. If this occurs, the atom will emit two photons: one with an energy equal to the difference between the second and first excited states, and the other with an energy equal to the difference between the first excited state and the ground state.</span><br />
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</span></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Either possibility can occur, with roughly equal probability. The second step of this cascade process (2), produces a 121.6-nm ultraviolet photon, just as in Figure 4.10(a). However, the first transition—the one from the second to the first excited state—produces a photon with a wavelength of 656.3 nm (6563 Å), which is in the visible part of the spectrum. This photon is seen as red light. An individual atom—if one could be isolated—would emit a momentary red flash. This is the origin of the red line in the hydrogen spectrum shown in Figure 4.3.</span></div><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">The inset in Figure 4.10 shows an astronomical object whose red coloration is the result of precisely this process. As ultraviolet photons from a young hot star pass through the surrounding cool hydrogen gas out of which the star recently formed, some photons are absorbed by the gas, boosting its atoms into excited states or ionizing them completely. The 656.3-nm red glow characteristic of excited hydrogen gas results as the atoms cascade back to their ground states. This process is called <i>fluorescence.</i></span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><i><br />
</i></span></div></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Absorption of additional energy can boost the electron to even higher orbitals within the atom. As the excited electron cascades back down to the ground state, the atom may emit many photons, each with a different energy and hence a different wavelength, and the resulting spectrum shows many spectral lines. In a sample of heated hydrogen gas, at any instant atomic collisions ensure that atoms are found in many different excited states. The complete emission spectrum therefore consists of wavelengths corresponding to all possible transitions between those states and states of lower energy.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">In the case of hydrogen, all transitions ending at the ground state produce ultraviolet photons. However, downward transitions ending at the <i>first</i> excited state give rise to spectral lines in or near the visible portion of the electromagnetic spectrum (Figure 4.3). The energy levels and spectrum of hydrogen are discussed in more detail in <a href="http://astronomylearn.blogspot.com/"><i>More Precisely 4-1</i></a><i>.</i></span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><i><br />
</i></span></div></div><div style="background-color: white;"><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><b>KIRCHOFF'S LAWS EXPLAINED</b></span><br />
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</b></span></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><img height="14" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMus-VgdsUWlWlS1YspJhgcuMhgoPjXpsJV32E2K0raiDUZWsjwyPqS70qD4vkwVFeTj_6f07XNkjZEOIljMKcxjpmHyXHzfOHxbee8BuVa-ErL6jD2cG9BVSmbdJ3DwcQgR8s27I1mX4/s1600/LGICON_5.GIF" width="24" /><a href="" name="Anchor-21230"></a>Let's reconsider our earlier discussion of emission and absorption lines in terms of the model just presented. In Figure 4.7 a beam of continuous radiation shines through a cloud of hydrogen gas. The beam contains photons of all energies, but most of them cannot interact with the gas—the gas can absorb only those photons having just the right energy to cause a change in an electron's orbit from one state to another. All other photons in the beam—with energies that cannot produce a transition—do not interact with the gas at all but pass through it unhindered. Photons having the right energies are absorbed, excite the gas, and are removed from the beam. This is the cause of the dark absorption lines in the spectrum of Figure 4.7(b). These lines are direct indicators of the energy differences between orbitals in the atoms making up the gas.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">The excited gas atoms return rapidly to their original states, each emitting one or more photons in the process. We might think, then, that although some photons from the beam are absorbed by the gas, they are quickly replaced by reemitted photons, with the result that we could never observe the effects of absorption. In fact, this is not the case, for two reasons. First, while the photons not absorbed by the gas continue on directly to the detector, the reemitted photons can leave in <i>any</i>direction. Most of the reemitted photons leave at angles that do not take them through the slit and on to the detector, and so they are effectively lost from the original beam. Second, as we have just seen, electrons may cascade back to the ground state, emitting several lower-energy photons instead of a single photon equal in energy to the one originally absorbed.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">The net result of these processes is that some of the original energy is channeled into photons of many different colors, moving in many different directions. A second detector looking at the cloud from the side would record the reemitted energy as an emission spectrum, as in Figure 4.7(c). (A spectrum of the object shown in the inset of Figure 4.10, called an <i>emission nebula,</i> would show the same thing.) Like the absorption spectrum, the emission spectrum is characteristic of the gas, not of the original beam.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Absorption and emission spectra are created by the same atomic processes. They correspond to the same atomic transitions. They contain the same information about the composition of the gas cloud. In the laboratory we can move our detector and measure both. In astronomy we cannot change our vantage point, so the type of spectrum we see depends on our chance location with respect to both the source and the intervening gas cloud.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><b>MORE COMPLEX SPECTRA</b></span><br />
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</b></span></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">All hydrogen atoms have basically the same structure—a single electron orbiting a single proton—but, of course, there are many other kinds of atoms, each kind having a unique internal structure.<a href="" name="Anchor-The-56981"></a>The number of protons in the nucleus of an atom determines the <a href="" name="Anchor-element-21683"></a><a href="http://astronomylearn.blogspot.com/p/glossary.html#element"><b>element</b></a> that it represents. Just as all hydrogen atoms have a single proton, all oxygen atoms have eight protons, all iron atoms have 26 protons, and so on.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">The next simplest element after hydrogen is helium. The central nucleus of the most common form of helium is made up of two protons and two <a href="" name="Anchor-neutrons-46919"></a><a href="http://astronomylearn.blogspot.com/p/glossary.html#neutron"><b>neutrons</b></a> (another kind of elementary particle having a mass slightly larger than that of a proton but having no electrical charge). Two electrons orbit this nucleus. As with hydrogen and all other atoms, the "normal" condition for helium is to be electrically neutral, with the negative charge of the orbiting electrons exactly canceling the positive charge of the nucleus (Figure 4.11a).</span></div></div><br />
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<tr><td bgcolor="#fffad7"><div style="text-align: justify;"><span style="color: red; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>Figure 4.11</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b> Helium and Carbon</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;"> (a) A helium atom in its normal ground state. Two electrons occupy the lowest-energy orbital around a nucleus containing two protons and two neutrons. (b) A carbon atom in its normal ground state. Six electrons orbit a six-proton, six-neutron nucleus, two in an inner orbital, with the other four at a greater distance from the center.</span></div></td></tr>
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<div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">More complex atoms contain more protons (and neutrons) in the nucleus and have correspondingly more orbiting electrons. For example, an atom of carbon, shown in Figure 4.11(b), consists of six electrons orbiting a nucleus containing six protons and six neutrons. As we progress to heavier and heavier elements, the number of orbiting electrons increases, and the number of possible electron transitions rises rapidly. The result is that very complicated spectra can be produced. The complexity of atomic spectra generally reflects the complexity of the atoms themselves. A good example is the element iron, which contributes nearly 800 of the Fraunhofer absorption lines seen in the solar spectrum (Figure 4.4).</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Atoms of a single element such as iron can yield many lines for two main reasons. First, the 26 electrons of a normal iron atom can make an enormous number of different transitions among available energy levels. Second, many iron atoms are <i>ionized,</i> with some of their 26 electrons stripped away. The removal of electrons alters an atom's electromagnetic structure, and the energy levels of ionized iron are quite different from those of neutral iron. Each new level of ionization introduces a whole new set of spectral lines. Besides iron, many other elements, also in different stages of excitation and ionization, absorb photons at visible wavelengths. When we observe the entire Sun, all these atoms and ions absorb simultaneously, yielding the rich spectrum we see.</span><br />
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<tr><td><img height="6" src="file:///G:/CHAISSON/COMART/SPACER.GIF" width="6" /><img height="6" src="file:///G:/CHAISSON/COMART/SPACER.GIF" width="6" /></td><td><div class="separator" style="clear: both; text-align: justify;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiqA6nBP0HW1AQhJ2ETyENanDDJ_YTVHiF3jSmIuylAp0EpUo3BUlJ-jGB4lLNdXTOH7wjMq1xG19rIV2ac1ux_l_3OIzEn0PVWBmWpBcfqcwoTIbJ9IJ1Z5wS0w6p_1msoMYNYL0oqy9A/s1600/Emission+Nebula.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiqA6nBP0HW1AQhJ2ETyENanDDJ_YTVHiF3jSmIuylAp0EpUo3BUlJ-jGB4lLNdXTOH7wjMq1xG19rIV2ac1ux_l_3OIzEn0PVWBmWpBcfqcwoTIbJ9IJ1Z5wS0w6p_1msoMYNYL0oqy9A/s1600/Emission+Nebula.JPG" /></a></div></td></tr>
<tr><td></td><td bgcolor="#fffad7"><div style="text-align: justify;"><span style="color: red; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>Figure 4.12</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b> Emission Nebula</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;"> The visible spectrum of the hot gases in a nearby star-forming region known as the Omega nebula (M17). Shining by the light of several very hot stars, the nebula produces a complex spectrum of bright and dark lines (bottom), also shown here as an intensity trace from red to blue (center). <i>(ESO)</i></span></div></td></tr>
</tbody></table><span style="font-family: 'Times New Roman', Georgia, Times; text-align: justify;">The power of spectroscopy is most apparent when many different gases are mixed together because it enables us to study one kind of atom or ion to the exclusion of all others simply by focusing on specific wavelengths of radiation. By identifying the superimposed absorption and emission spectra of many different atoms, we can determine the cloud's composition (and much more—see Section 4.4). Figure 4.12 shows an actual spectrum observed coming from a cosmic object. As in Figure 4.10, the characteristic red glow of this </span><i style="font-family: 'Times New Roman', Georgia, Times; text-align: justify;">emission nebula</i><span style="font-family: 'Times New Roman', Georgia, Times; text-align: justify;"> comes from the </span><span style="font-family: 'Times New Roman', Georgia, Times; text-align: justify;">H</span><img align="absbottom" height="9" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_-fO6dsYEO9EIgIqk_8I__NlRj82qaJZpeU-y91vUzkbP4mJ-wZYEOJXku4cySWZ3Quh6lqJwcc7A9OWNRcAu0E6F-vQZ8BJaExRgKbwpuo17-gD9gzHM6YIC9GEFDgZxdJdx2XsVKg4/s1600/L_ALPHA_2.gif" style="font-family: 'Times New Roman', Georgia, Times; text-align: justify;" width="11" /><span style="font-family: 'Times New Roman', Georgia, Times; text-align: justify;"> transition in hydrogen, the nebula's main constituent. </span><br />
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<span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;">Spectral lines occur throughout the entire electromagnetic spectrum. Usually, electron transitions among the lowest orbitals of the lightest elements, such as hydrogen and helium, produce visible and ultraviolet spectral lines. Transitions among very highly excited states of hydrogen and other elements can produce spectral lines in the infrared and radio parts of the electromagnetic spectrum. Conditions on Earth make it all but impossible to detect these radio and infrared features in the laboratory, but they are routinely observed coming from space. Electron transitions among lower energy levels in heavier, more complex elements produce X-ray spectral lines. These lines have been observed in the laboratory; some have also been observed in stars and other cosmic objects.</span></div>Andri F Martinhttp://www.blogger.com/profile/11669920311565328714noreply@blogger.com0tag:blogger.com,1999:blog-4374048443162882832.post-33901811595554876412012-02-18T12:56:00.001+07:002012-02-18T13:01:42.934+07:004.1 Spectral Lines<h1 style="text-align: center;">Spectral Lines</h1><div style="background-color: white;"><div style="text-align: justify;"><img height="14" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJ54ymVCtThcMHbRD-h84NRSk2OQxJjBmCRuTKfEtRI5KTpQAQ9OXWz6DnCCAofySfOz6QHB3h8Mm8ukOqFqjacEWYuvN_r7Oi06R8IPqXzKkibJbrqPuawkNP_OIlIZV3ppVOb0Cv8Rg/s1600/LGICON_1.GIF" width="24" /><span style="font-family: 'Times New Roman', Georgia, Times;">In Chapter 3 we saw something of how astronomers can analyze electromagnetic radiation received from space to obtain information about distant objects. <a href="" name="Anchor-34280"></a>A vital step in this process is the formation of a <i>spectrum</i>—splitting the incoming radiation into its component wavelengths. But in reality, <i>no</i> cosmic object emits a perfect blackbody spectrum like those discussed earlier. <a href="http://astronomylearn.blogspot.com/2012/02/34-distribution-of-radiation.html">(Sec. 3.4<i>)</i></a> All spectra deviate from this idealized form—some by only a little, others by a lot. Far from invalidating our earlier studies, however, these deviations contain a wealth of detailed information about physical conditions in the source of the radiation. Because spectra are so important, let's examine in more detail how astronomers obtain and interpret them.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Radiation can be analyzed with an instrument known as a </span><a href="" name="Anchor-spectroscope-49575"></a><a href="http://astronomylearn.blogspot.com/p/glossary.html#spectroscope"><span style="font-family: 'Times New Roman', Georgia, Times;"><b>spectroscope</b></span></a><span style="font-family: 'Times New Roman', Georgia, Times;">.<a href="" name="Anchor-35314"></a> In its most basic form, this device consists of an opaque barrier with a slit in it (to define a beam of light),</span><a href="" name="Anchor-42520"></a><span style="font-family: 'Times New Roman', Georgia, Times;"> a prism (to split the beam into its component colors), and an eyepiece or screen (to allow the user to view the resulting spectrum). Figure 4.1 shows such an arrangement. The research instruments called<i>spectrographs,</i> or <i>spectrometers,</i> used by professional astronomers are rather more complex, consisting of a telescope (to capture the radiation), a dispersing device (to spread it out into a spectrum), and a detector (to record the result). Despite their greater sophistication, however, their basic operation is conceptually similar to the simple spectroscope shown in the figure.</span></div></div><br />
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<tr><td><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjBsor-NhXcNldULCLxuCQvRF1rs6Q2v3RYFr2C3_0RnllOeoYsLzaLbc9DPPjkogqIMuPWWG874qnvXBJASCdz0v3P3oYH0awtISvnoEKePVrDn-pm0bE1B8z3dQcTjlchhGVAM4uu3do/s1600/Spectroscope+Diagram.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjBsor-NhXcNldULCLxuCQvRF1rs6Q2v3RYFr2C3_0RnllOeoYsLzaLbc9DPPjkogqIMuPWWG874qnvXBJASCdz0v3P3oYH0awtISvnoEKePVrDn-pm0bE1B8z3dQcTjlchhGVAM4uu3do/s1600/Spectroscope+Diagram.JPG" /></a></div></td></tr>
<tr><td bgcolor="#fffad7"><div style="text-align: justify;"><span style="color: red; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>Figure 4.1</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b> Spectroscope</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;"> Diagram of a simple spectroscope. A small slit in the mask on the left allows a narrow beam of light to pass. The light passes through a prism and is split up into its component colors. The resulting spectrum can be viewed through an eyepiece or simply projected onto a screen.</span></div></td></tr>
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<div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">In many large instruments the prism is replaced by a device called a <i>diffraction grating,</i> consisting of a sheet of transparent material with many closely spaced parallel lines ruled on it. The spacing between the lines is typically a few microns (10<sup>-6</sup></span><span style="font-family: 'Times New Roman', Georgia, Times;"> m), comparable to the wavelength of visible light. The spaces act as many tiny openings, and light is diffracted as it passes through the grating (or is reflected from it, depending on the design of the device). <a href="http://astronomylearn.blogspot.com/2012/02/discovery-31-wave-nature-of-radiation.html"><i>(Discovery 3-1)</i></a> Because different wavelengths of electromagnetic radiation are diffracted by different amounts on encountering the grating, the effect is to split a beam of light into its component colors. You are probably more familiar with diffraction gratings than you think—the "rainbow" of colors seen in light reflected from a compact disk is the result of precisely this process.</span></div></div><h4 style="background-color: white;"><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><b>EMISSION LINES</b></span></h4><div style="background-color: white;"></div><table align="right" border="0" cellpadding="0" cellspacing="2" style="width: 401px;"><tbody>
<tr><td><img height="6" src="file:///G:/CHAISSON/COMART/SPACER.GIF" width="6" /></td><td><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjIGWyXymgZ1J-Utz3B3EgAfK-ZWWp5jI4E9uekLxJTnnAhl-FGVoieHcDheiuMeeIVIXARn6kUzuWKGeFNsmTpHYiBn3fRMTyjOVu6C8j8m5WvFNiuw6vJH0hj8Javd6_VHHidJGo308Q/s1600/Continuous+and+Emission+Spectra.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjIGWyXymgZ1J-Utz3B3EgAfK-ZWWp5jI4E9uekLxJTnnAhl-FGVoieHcDheiuMeeIVIXARn6kUzuWKGeFNsmTpHYiBn3fRMTyjOVu6C8j8m5WvFNiuw6vJH0hj8Javd6_VHHidJGo308Q/s1600/Continuous+and+Emission+Spectra.JPG" /></a></div></td></tr>
<tr><td></td><td bgcolor="#fffad7"><div style="text-align: justify;"><span style="color: red; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>Figure 4.2</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b> Continuous</b></i> <i><b>and Emission Spectra</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;"> When passed through a slit and split up by a prism, light from a source of continuous radiation (a) gives rise to the familiar rainbow of colors. By contrast, the light from excited hydrogen gas (b) consists of a series of distinct bright spectral lines called emission lines. (The focusing lenses have been omitted for clarity.)</span></div></td></tr>
</tbody></table><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><a href="" name="Anchor-The-41312"></a>The spectra we encountered in Chapter 3 are examples of <a href="" name="Anchor-continuous-47857"></a><a href="http://astronomylearn.blogspot.com/p/glossary.html#continuous spectrum"><b>continuous spectra</b></a>. <a href="" name="Anchor-46026"></a>A lightbulb, for example, emits radiation of all wavelengths (mostly in the visible range), with an intensity distribution that is well described by the blackbody curve corresponding to the bulb's temperature. <a href="http://astronomylearn.blogspot.com/2012/02/34-distribution-of-radiation.html">(Sec. 3.4)</a> Viewed through a spectroscope, the spectrum of the light from the bulb would show the familiar rainbow of colors, from red to violet, without interruption, as presented in Figure 4.2(a).</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div><div align="left" style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Not all spectra are continuous, however. For instance, if we took a glass jar containing pure hydrogen gas and passed an electrical discharge through it (a little like a lightning bolt arcing through Earth's atmosphere), the gas would begin to glow—that is, it would emit radiation. If we were to examine that radiation with our spectroscope, we would find that its spectrum consists of only a few bright lines on an otherwise dark background, quite unlike the continuous spectrum described for the incandescent light bulb. Figure 4.2(b) shows this schematically. A more detailed rendering of the spectrum of hydrogen appears in the top panel of Figure 4.3. <a href="" name="Anchor-The-35632"></a>The light produced by the hydrogen in this experiment does <i>not</i> consist of all possible colors but instead includes only a few narrow, well-defined <a href="" name="Anchor-emission-11481"></a><a href="http://astronomylearn.blogspot.com/p/glossary.html#emission lines"><b>emission lines</b></a>—narrow "slices" of the continuous spectrum. The black background represents all the wavelengths <i>not</i>emitted by hydrogen.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><a href="" name="Anchor-After-19136"></a>After some experimentation we would also find that although we could alter the <i>intensity</i> of the lines—for example, by changing the amount of hydrogen in the jar or the strength of the electrical discharge—we could not alter their <i>color</i> (in other words, their frequency or wavelength). The pattern of spectral emission lines is a property of the element hydrogen. Whenever we perform this experiment, the same characteristic colors result.</span></div></div><br />
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<tr><td bgcolor="#fffad7"><div style="text-align: justify;"><span style="color: red; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>Figure 4.3</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b> Elemental Emission</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;"> The emission spectra of some well-known elements. In accordance with the convention adopted throughout this text, frequency increases to the right. <i>(Wabash Instrument Corp.)</i></span></div></td></tr>
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<div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">By the early nineteenth century scientists had carried out similar experiments on many different gases. By vaporizing solids and liquids in a flame, they extended their inquiries to include materials that are not normally found in the gaseous state. <a href="" name="Anchor-Sometimes-16019"></a><a href="" name="Anchor-Sometimes-19996"></a>Sometimes the pattern of lines was fairly simple, sometimes it was very complex, but it was always unique to that element. Even though the origin of the lines was not understood, researchers quickly realized that the lines provided a one-of-a-kind "fingerprint" of the substance under investigation. They could detect the presence of a particular atom or molecule (a group of atoms held together by chemical bonds—see Sec. 4.4) solely through the study of the light it emitted. Scientists have accumulated extensive catalogs of the specific wavelengths at which many different hot gases emit radiation. The particular pattern of the light emitted by a gas of a given chemical composition is known as its <a href="" name="Anchor-emission-35882"></a><a href="http://astronomylearn.blogspot.com/p/glossary.html#emission spectrum"><b>emission spectrum</b></a>. Examples of the emission spectra of some common substances are shown in Figure 4.3.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
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<tr><td><img height="6" src="file:///G:/CHAISSON/COMART/SPACER.GIF" width="6" /><img height="6" src="file:///G:/CHAISSON/COMART/SPACER.GIF" width="6" /></td><td><div align="right"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjUMBFCxXDiLD_KMAwyA9jr2lRJeFkSTutjCH1IvvvLznWh4Gbmfb8Yp9vSn7o-R2gwplVBce7f8WMmTPFJ_nKZ16p0k_U6mNRc0_jRlwZk9HZJkMLwkRY0M_yelfXXPTyo2UUOvAFpiuo/s1600/Solar+Spectrum.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="215" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjUMBFCxXDiLD_KMAwyA9jr2lRJeFkSTutjCH1IvvvLznWh4Gbmfb8Yp9vSn7o-R2gwplVBce7f8WMmTPFJ_nKZ16p0k_U6mNRc0_jRlwZk9HZJkMLwkRY0M_yelfXXPTyo2UUOvAFpiuo/s320/Solar+Spectrum.JPG" width="320" /></a></div></div></td></tr>
<tr><td></td><td bgcolor="#fffad7"><div style="text-align: justify;"><span style="color: red; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>Figure 4.4</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b> Solar Spectrum</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"> </span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;">This visible spectrum of the Sun shows hundreds of dark absorption lines superimposed on a bright continuous spectrum. Here, the scale extends from long wavelengths (red) at the upper left to short wavelengths (blue) at the lower right. <i>(AURA)</i></span></div></td></tr>
</tbody></table><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><b>ABSORPTION LINES</b></span><br />
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</b></span></div></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><a href="" name="Anchor-When-22282"></a>When sunlight is split by a prism, at first glance it appears to produce a continuous spectrum. However, closer scrutiny with a spectroscope shows that the solar spectrum is interrupted vertically by a large number of narrow dark lines, as shown in Figure 4.4. We now know that many of these lines represent wavelengths of light that have been removed (absorbed) by gases present either in the outer layers of the Sun or in Earth's atmosphere. These gaps in the spectrum are called <a href="" name="Anchor-absorption-14210"></a><a href="http://astronomylearn.blogspot.com/p/glossary.html#absorption line"><b>absorption lines</b></a>.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">The English astronomer William Wollaston first noticed the solar absorption lines in 1802. <a href="" name="Anchor-They-49354"></a>They were studied in greater detail about 10 years later by the German physicist Joseph von Fraunhofer, who measured and cataloged over 600 of them. They are now referred to collectively as<i>Fraunhofer lines.</i> Although the Sun is by far the easiest star to study, and so has the most extensive set of observed absorption lines, similar lines are known to exist in the spectra of all stars.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
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<tr><td bgcolor="#fffad7"><div style="text-align: justify;"><span style="color: red; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>Figure 4.5</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b> Absorption Spectrum</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;"> When cool gas is placed between a source of continuous radiation, such as a hot lightbulb, and a detector, the resulting spectrum consists of a continuous spectrum crossed by a series of dark absorption lines. These lines are formed when the intervening gas absorbs certain wavelengths (colors) from the original beam. The absorption lines appear at precisely the same wavelengths as the emission lines that would be produced if the gas were heated to high temperatures.</span></div></td></tr>
</tbody></table><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">At around the same time as the solar absorption lines were discovered, scientists found that absorption lines could also be produced in the laboratory by passing a beam of light from a source that produces a continuous spectrum through a cool gas, as shown in Figure 4.5. <a href="" name="Anchor-They-20715"></a>They quickly observed an intriguing connection between emission and absorption lines: The absorption lines associated with a given gas occur at precisely the <i>same</i> wavelengths as the emission lines produced when the gas is heated.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div><div align="left" style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">As an example, consider the element sodium, whose emission spectrum appears in Figure 4.3. When heated to high temperatures, a sample of sodium vapor emits visible light strongly at just two wavelengths—589.9 nm and 589.6 nm—lying in the yellow part of the spectrum. When a continuous spectrum is passed through some relatively cool sodium vapor, two sharp, dark absorption lines appear at precisely the same wavelengths. The emission and absorption spectra of sodium are compared in Figure 4.6, clearly showing the relation between emission and absorption features.</span></div></div><br />
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<tr><td bgcolor="#fffad7"><div style="text-align: justify;"><span style="color: red; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>Figure 4.6</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b> Sodium Spectrum</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;"> (a) The characteristic emission lines of sodium. The two bright lines in the center appear in the yellow part of the spectrum. (b) The absorption spectrum of sodium. The two dark lines appear at exactly the same wavelengths as the bright lines in the sodium emission spectrum.</span></div></td></tr>
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<span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><b>KIRCHHOFF'S LAWS</b></span><br />
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</b></span></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"> <img align="bottom" height="14" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhyIIQmfEvEcSnN3CVbR2KZeDq56rV0CWlw3kCv-niHq8DSP2AlR8tezxJRzOhvQc7fJVvPUS5f9xjMnFO7YCmVo6N0CS5ir15tGO6kE7d9ZmgAODnQK7pmF0Tt3z_-8Sij99rArgJlv_M/s1600/LGICON_2.GIF" width="24" /><a href="" name="Anchor-The-43760"></a>The analysis of the ways in which matter emits and absorbs radiation is called <a href="" name="Anchor-spectroscopy-23240"></a><a href="http://astronomylearn.blogspot.com/p/glossary.html#spectroscopy"><b>spectroscopy</b></a>.<a href="" name="Anchor-One-54189"></a>One early spectroscopist, the German physicist Gustav Kirchhoff, summarized the observed relationships among the three types of spectra—continuous, emission line, and absorption line—in 1859. He formulated three spectroscopic rules, now known as <a href="" name="Anchor-3800"></a><a href="http://astronomylearn.blogspot.com/p/glossary.html#Kirchhoff's laws"><b>Kirchhoff's laws</b></a>, governing the formation of spectra:</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><b><a href="" name="Anchor-41427"></a>1.</b> A luminous solid or liquid, or a sufficiently dense gas, emits light of all wavelengths and so produces a <i>continuous spectrum</i> of radiation.</span></div></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><b><a href="" name="Anchor-21170"></a>2.</b> A low-density hot gas emits light whose spectrum consists of a series of bright <i>emission lines.</i>These lines are characteristic of the chemical composition of the gas.</span></div></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><b><a href="" name="Anchor-52288"></a>3.</b> A cool thin gas absorbs certain wavelengths from a continuous spectrum, leaving dark<i>absorption lines</i> in their place superimposed on the continuous spectrum. Once again, these lines are characteristic of the composition of the intervening gas—they occur at precisely the same wavelengths as the emission lines produced by that gas at higher temperatures.</span></div></div><br />
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<div style="text-align: justify;"><span style="background-color: white; color: red; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>Figure 4.7</b></i></span><span style="background-color: white; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b> Kirchhoff's Laws</b></i></span><span style="background-color: white; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;"> A source of continuous radiation, here represented by a lightbulb, is used to illustrate Kirchhoff's laws of spectroscopy. (a) The unimpeded beam shows the familiar continuous spectrum of colors.</span></div><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;"></span><br />
<div style="text-align: justify;"><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;"><span style="background-color: white;">(b) When the source is viewed through a cloud of hydrogen gas, a series of dark hydrogen absorption lines appears in the continuous spectrum. These lines are formed when the gas absorbs some of the bulb's radiation and reemits it in random directions. Because most of the reemitted radiation does not go through the slit, the effect is to remove the absorbed radiation from the light that reaches the screen at left. (c) When the gas is viewed from the side, a fainter hydrogen emission spectrum is seen, consisting of reemitted radiation. The absorption lines in (b) and the emission lines in (c) have the same wavelengths.</span></span></div></td></tr>
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<div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><a href="" name="Anchor-Figure-57991"></a>Figure 4.7 illustrates Kirchhoff's laws and the relationship between absorption and emission lines. When viewed directly, the light source, a hot solid (the filament of the bulb), has a continuous (blackbody) spectrum. When the light source is viewed through a cloud of cool hydrogen gas, a series of dark absorption lines appear, superimposed on the spectrum at wavelengths characteristic of hydrogen. The lines appear because the light at those wavelengths is absorbed by the hydrogen. As we will see later in this chapter, the absorbed energy is subsequently reradiated into space, but in all directions, not just the original direction of the beam. Consequently, when the cloud is viewed from the side against an otherwise dark background, a series of faint emission lines is seen. These lines contain the energy lost by the forward beam. If the gas was heated to incandescence, it would produce stronger emission lines at precisely the same wavelengths.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><b>ASTRONOMICAL APPLICATIONS</b></span><br />
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</b></span></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">By the late nineteenth century, spectroscopists had developed a formidable arsenal of techniques for interpreting the radiation received from space. Once astronomers knew that spectral lines were indicators of chemical composition, they set about identifying the observed lines in the solar spectrum. Almost all the lines in light from extraterrestrial sources could be attributed to known elements. For example, many of the Fraunhofer lines in sunlight are associated with the element iron, a fact first recognized by Kirchhoff and coworker Robert Bunsen (of Bunsen burner fame) in 1859. However, some unfamiliar lines also appeared in the solar spectrum. In 1868, astronomers realized that those lines must correspond to a previously unknown element. It was given the name helium, after the Greek word <i>helios,</i> meaning "Sun." Not until 1895, almost three decades after its detection in sunlight, was helium discovered on Earth. (A laboratory spectrum of helium is included in Figure 4.3.)</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Yet for all the information that nineteenth-century astronomers could extract from observations of stellar spectra, they still lacked a theory explaining how the spectra themselves arose. Despite their sophisticated spectroscopic equipment, they knew scarcely any more about the physics of stars than did Galileo or Newton. To understand how spectroscopy can be used to extract detailed information about astronomical objects from the light they emit, we must delve more deeply into the processes that produce line spectra.</span></div></div>Andri F Martinhttp://www.blogger.com/profile/11669920311565328714noreply@blogger.com0tag:blogger.com,1999:blog-4374048443162882832.post-70654907656898449302012-02-17T09:04:00.002+07:002012-02-17T09:10:07.166+07:004. Spectroscopy - The Inner Workings of Atoms<h1 style="text-align: center;">The Inner Workings of Atoms</h1><table border="0" cellpadding="0" cellspacing="2" style="width: 500px;"><tbody>
<tr><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEidSiOW5giYcrtJZeQdfStpq_6RygB70OqBtCehZPFS6Az7kvwm1s0nZclEGHbb7lx13nXKDMQBCIGnldj9kOV19ii4CjKvABXx0tz4L568znzbHDvuv4OFdsTLJ62V0U4tukucCeCsyt0/s1600/visible+spectrum+of+the+giant+star+Arcturus.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEidSiOW5giYcrtJZeQdfStpq_6RygB70OqBtCehZPFS6Az7kvwm1s0nZclEGHbb7lx13nXKDMQBCIGnldj9kOV19ii4CjKvABXx0tz4L568znzbHDvuv4OFdsTLJ62V0U4tukucCeCsyt0/s1600/visible+spectrum+of+the+giant+star+Arcturus.JPG" /></a> </td></tr>
<tr><td><div style="text-align: justify;"><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;">This illustration shows the complete visible spectrum of the giant star Arcturus. By passing the star's light through a prism, the light is spread out into its component colors, displayed here wrapped around row after row from red at top left to blue at bottom right. Each of the 50 rows covers 8 nanometers in wavelength, for complete coverage of the visible spectrum from 300 to 700 microns. The many dark lines are caused by light from the hot star being absorbed by specfic atoms and ions in the star's cooler atmoshpere.</span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;"> </span><i style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: small;">(NOAO)</i><br />
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</i></div><div style="text-align: justify;"><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;"><b>The Big Picture:</b><i> </i>Spectroscopy is a powerful observational technique enabling scientists to infer the nature of matter by the way it emits or absorbs radiation. Not only can spectroscopy reveal the chemical composition of distant stars and yield knowledge of how they shine, it can also provide a wealth of information about the birth, evolution, and death of myriad objects in the Universe.</span></div></td></tr>
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</td><td><h2><span style="color: #0a50a1; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;">LEARNING GOALS</span></h2></td></tr>
<tr><td></td><td></td><td><span style="font-family: 'Times New Roman', Georgia, Times;">Studying this chapter will enable you to:</span></td></tr>
<tr><td align="right" valign="top"><img border="0" height="14" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJ54ymVCtThcMHbRD-h84NRSk2OQxJjBmCRuTKfEtRI5KTpQAQ9OXWz6DnCCAofySfOz6QHB3h8Mm8ukOqFqjacEWYuvN_r7Oi06R8IPqXzKkibJbrqPuawkNP_OIlIZV3ppVOb0Cv8Rg/s1600/LGICON_1.GIF" width="24" /></td><td></td><td><span style="font-family: 'Times New Roman', Georgia, Times;">Describe the characteristics of continuous, emission, and absorption spectra and the conditions under which each is produced.</span></td></tr>
<tr><td align="right" valign="top"><img border="0" height="14" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhyIIQmfEvEcSnN3CVbR2KZeDq56rV0CWlw3kCv-niHq8DSP2AlR8tezxJRzOhvQc7fJVvPUS5f9xjMnFO7YCmVo6N0CS5ir15tGO6kE7d9ZmgAODnQK7pmF0Tt3z_-8Sij99rArgJlv_M/s1600/LGICON_2.GIF" width="24" /></td><td></td><td><span style="font-family: 'Times New Roman', Georgia, Times;">Explain the relation between emission and absorption lines and what we can learn from these lines.</span></td></tr>
<tr><td align="right" valign="top"><img border="0" height="14" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjro4NwCtC2TCdCM0U8llIjQWPaqnmu4Nt2WLO_hJXMRRt6pjUDNl52NfT4zBngnC52mY9Jyz9gm_C7nhxdDYZ3UdXQFZmOhsitag5SnErKeorWf9nncczB8fnqqR0HGCan4k26Y0kL1QE/s1600/LGICON_3.GIF" width="24" /></td><td></td><td><span style="font-family: 'Times New Roman', Georgia, Times;">Specify the basic components of the atom and describe our modern conception of its structure.</span></td></tr>
<tr><td align="right" valign="top"><img border="0" height="14" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi7BP-072_rJf_a6j879EXh5dxwRChAL8MSSshDxJzWKgCV2cYUdqSRcY23tVUo_GWcFSiHWLjAbp4wfdbu01NHbxUOL9_hspd1du6Q01LTVY6Hhfqhj5EeVEF5rC3DQJpcjtEjA-EjKwI/s1600/LGICON_4.GIF" width="24" /></td><td></td><td><span style="font-family: 'Times New Roman', Georgia, Times;">Discuss the observations that led scientists to conclude that light has particle as well as wave properties.</span></td></tr>
<tr><td align="right" valign="top"><img border="0" height="14" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMus-VgdsUWlWlS1YspJhgcuMhgoPjXpsJV32E2K0raiDUZWsjwyPqS70qD4vkwVFeTj_6f07XNkjZEOIljMKcxjpmHyXHzfOHxbee8BuVa-ErL6jD2cG9BVSmbdJ3DwcQgR8s27I1mX4/s1600/LGICON_5.GIF" width="24" /></td><td></td><td><span style="font-family: 'Times New Roman', Georgia, Times;">Explain how electron transitions within atoms produce unique emission and absorption features in the spectra of those atoms.</span></td></tr>
<tr><td><a href="file:///G:/CHAISSON/AT404/HTML/AT40403.htm#Anchor-29092"><span style="font-family: 'Times New Roman', Georgia, Times;"><img align="right" border="0" height="14" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjc_WBzxWewXG7k1TO9vYM8_b3TIS-aiDaHgLcHtwsLZqF-Z7NhewRhAqBJy_5O324WJD_9pIw2NgTPPtoso1LyUgMqWCKc0t7CEAdYnH5NjHYp7z3Qra_AfRr0q06ryoVgTSSKoTKXMlc/s1600/LGICON_6.GIF" width="24" /></span></a></td><td></td><td><span style="font-family: 'Times New Roman', Georgia, Times;">Describe the general features of spectra produced by molecules.</span></td></tr>
<tr><td><a href="file:///G:/CHAISSON/AT404/HTML/AT40404.htm#Anchor-Astronomers-50805"><span style="font-family: 'Times New Roman', Georgia, Times;"><img align="right" border="0" height="14" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEik3-BU1cuvDBK61-D3K3EW1N947Tb03GMll6i_Q8iZk-Cp3NL3JajDlJlSTb7rfDUICguyQiu1LBH2QL-ezAK6Xet9290zUb60eUVZPIkxm6nbXWTh9YPak72ibH-EXf0aMu9llA-VczY/s1600/LGICON_7.GIF" width="24" /></span></a></td><td></td><td><span style="font-family: 'Times New Roman', Georgia, Times;">List and explain the kinds of information that can be obtained by analyzing the spectra of astronomical objects.</span></td></tr>
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<div style="background-color: white;"><div style="text-align: justify;"><span style="color: red; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: large;"><b>T</b></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i>he wave description of radiation allowed nineteenth-century astronomers to begin to decipher the information reaching Earth from the cosmos in the form of visible and invisible light. However, early in the twentieth century, it became clear that the wave theory of electromagnetic phenomena was incomplete—some aspects of light simply could not be explained purely in wave terms. When radiation interacts with matter on atomic scales, it does so not as a continuous wave but in a jerky, discontinuous way—in fact, as a particle. With this discovery, scientists quickly realized that atoms, too, must behave in a discontinuous way, and the stage was set for a scientific revolution that has affected virtually every area of modern life. In astronomy, the observational and theoretical techniques that enable researchers to determine the nature of distant atoms by the way they emit and absorb radiation are now the indispensable foundation of modern astrophysics.</i></span></div></div>Andri F Martinhttp://www.blogger.com/profile/11669920311565328714noreply@blogger.com0tag:blogger.com,1999:blog-4374048443162882832.post-3596035518642553342012-02-16T16:03:00.001+07:002012-02-16T16:04:42.268+07:003.5 The Doppler Effect<h1 style="text-align: center;">The Doppler Effect</h1><div style="text-align: justify;"><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;"><img height="14" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMus-VgdsUWlWlS1YspJhgcuMhgoPjXpsJV32E2K0raiDUZWsjwyPqS70qD4vkwVFeTj_6f07XNkjZEOIljMKcxjpmHyXHzfOHxbee8BuVa-ErL6jD2cG9BVSmbdJ3DwcQgR8s27I1mX4/s1600/LGICON_5.GIF" width="24" /></span><a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=359603551864255334" name="Anchor-Imagine-2563" style="background-color: white;"></a><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;">Imagine a rocket ship launched from Earth with enough fuel to allow it to accelerate to speeds approaching that of light. As the ship’s speed increased, a remarkable thing would happen (Figure 3.14). Passengers would notice that the light from the star system toward which they were traveling seemed to be getting <i>bluer</i>. In fact, <i>all</i> stars in front of the ship would appear bluer than normal, and the greater the ship’s speed, the greater the color change would be. Furthermore, stars behind the vessel would seem <i>redder</i> than normal, while stars to either side would be unchanged in appearance. As the spacecraft slowed down and came to rest relative to Earth, all stars would resume their usual appearance. The travelers would have to conclude that the stars had changed their colors not because of any real change in their physical properties but because of the spacecraft’s own <i>motion.</i></span></div><br />
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<tr><td bgcolor="#fffad7"><div style="text-align: justify;"><span style="color: red; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>Figure 3.13</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b> Astronomical Thermometer</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;"> Comparison of blackbody curves for four cosmic objects. The frequencies and wavelengths corresponding to peak emission are marked. (a) A cool, invisible galactic gas cloud called Rho Ophiuchi. At a temperature of 60 K, it emits mostly low-frequency radio radiation. (b) A dim, young star (shown red in the inset photograph) near the center of the Orion Nebula. The star’s atmosphere, at 600 K, radiates primarily in the infrared. (c) The Sun’s surface, at approximately 6000 K, is brightest in the visible region of the electromagnetic spectrum. (d) Some very bright stars in a cluster called Omega Centauri, as observed by a telescope aboard a space shuttle. At a temperature of 60,000 K, these stars radiate strongly in the ultraviolet. <i>(Harvard College Observatory; J. Moran; AURA; NASA)</i></span></div></td></tr>
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<div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">This phenomenon is not restricted to electromagnetic radiation and fast-moving spacecraft. Waiting at a railroad crossing for an express train to pass, most of us have had the experience of hearing the pitch of a train whistle change from high shrill (high frequency, short wavelength) to low blare (low frequency, long wavelength) as the train approaches and then recedes. </span><a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=359603551864255334" name="Anchor-This-52367"></a><span style="font-family: 'Times New Roman', Georgia, Times;">This motion-induced change in the observed frequency of a wave is known as the </span><a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=359603551864255334" name="Anchor-Doppler-40178"></a><a href="http://astronomylearn.blogspot.com/p/glossary.html#Doppler effect"><span style="font-family: 'Times New Roman', Georgia, Times;"><b>Doppler effect</b></span></a><span style="font-family: 'Times New Roman', Georgia, Times;">, in honor of Christian Doppler, the nineteenth-century Austrian physicist who first explained it in 1842. Applied to cosmic sources of electromagnetic radiation, it has become one of the most important measurement techniques in all of modern astronomy. Here’s how it works:</span></div></div><br />
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<tr><td bgcolor="#fffad7"><div style="text-align: justify;"><span style="color: red; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>Figure 3.14</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b> High-Speed Observers </b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;">Observers in a fast-moving spacecraft will see the stars ahead of them seem bluer than normal, while those behind are reddened. The stars have not changed their properties—the color changes are the result of the observers’ motion relative to the stars.</span></div></td></tr>
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<div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Imagine a wave moving from the place where it is created toward an observer who is not moving with respect to the wave source, as shown in Figure 3.15(a). By noting the distances between successive wave crests, the observer can determine the wavelength of the emitted wave. Now suppose that the wave source is moving. </span><a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=359603551864255334" name="Anchor-As-20677"></a><span style="font-family: 'Times New Roman', Georgia, Times;">As illustrated in Figure 3.15(b), because the source moves between the times of emission of one wave crest and the next, successive wave crests in the direction of motion of the source will be seen to be <i>closer together</i> than normal, whereas crests behind the source will be more widely spaced. An observer in front of the source will therefore measure a <i>shorter</i> wavelength than normal, while one behind will see a <i>longer</i> wavelength. (The numbers indicate successive wave crests emitted by the source and the location of the source at the instant each wave crest was emitted.)</span></div></div><br />
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<tr><td bgcolor="#fffad7"><div style="text-align: justify;"><span style="color: red; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>Figure 3.15</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b> Doppler Effect</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;"> (a) Wave motion from a source toward an observer at rest with respect to the source. The four numbered circles represent successive wave crests emitted by the source. At the instant shown, the fifth wave crest is just about to be emitted. As seen by the observer, the source is not moving, so the wave crests are just concentric spheres (shown here as circles). (b) Waves from a moving source tend to "pile up" in the direction of motion and be "stretched out" on the other side. (The numbered points indicate the location of the source at the instant each wave crest was emitted.) As a result, an observer situated in front of the source measures a shorter-than-normal wavelength—a blueshift—while an observer behind the source sees a redshift. In this diagram the source is shown in motion. However, the same general statements hold whenever there is any relative motion between source and observer.</span></div></td></tr>
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<div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=359603551864255334" name="Anchor-The-23430"></a>The greater the relative speed of source and the observer, the greater the observed shift. If the other velocities involved are not too large compared to the wave speed—less than a few percent, say—we can write down a particularly simple formula for what the observer sees. In terms of the net velocity of <i>recession</i> between source and observer, the apparent wavelength and frequency (measured by the observer) are related to the true quantities (emitted by the source) as follo</span><span style="font-family: 'Times New Roman', Georgia, Times;">ws:</span></div></div><br />
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<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgcnluIALyHf7ZHxAtM_uHQKeQIsZg4_nVpmYCSInLHlcLPAEZx4rhP8GvmzCM9u5lJsl3D-xho6j9U8VycYv1hr4X-xnLxzTFbnNDTL8vFTPE4N8FJNQyFlb_CEjRHMIj_d3oN9pGh03c/s1600/3.5+equation.GIF" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgcnluIALyHf7ZHxAtM_uHQKeQIsZg4_nVpmYCSInLHlcLPAEZx4rhP8GvmzCM9u5lJsl3D-xho6j9U8VycYv1hr4X-xnLxzTFbnNDTL8vFTPE4N8FJNQyFlb_CEjRHMIj_d3oN9pGh03c/s1600/3.5+equation.GIF" /></a> </div><br />
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<div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">A positive recession velocity means that the source and the observer are moving apart; a negative value means that they are approaching. The wave speed is the speed of light <i>c</i> in the case of electromagnetic radiation. For most of this text, the assumption that the recession velocity is small compared to the speed of light will be a good one. Only when we discuss the properties of black holes (Chapter 22) and the structure of the universe on the largest scales (Chapters 25 and 26) will we have to reconsider this formula.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Note that in Figure 3.15 the <i>source</i> is shown in motion (as in our train analogy), whereas in our earlier spaceship example (Figure 3.14) the <i>observers</i> were in motion. <a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=359603551864255334" name="Anchor-For-12727"></a>For electromagnetic radiation, the result is the same in either case—only the <i>relative</i> motion of source and observer matters. Note also that only motion along the line joining source and observer—known as <i>radial</i>motion—appears in the above equation. <a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=359603551864255334" name="Anchor-Motion-44415"></a>Motion <i>transverse</i> (perpendicular) to the line of sight has no significant effect.<a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=359603551864255334" name="Anchor-47857"></a><a href="http://astronomylearn.blogspot.com/2012/02/35-doppler-effect.html#Anchor-49575">*</a></span></div><div style="text-align: justify;"><br />
</div><div style="text-align: justify;"><a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=359603551864255334" name="Anchor-22063"></a><span style="font-family: 'Times New Roman', Georgia, Times;">A wave measured by an observer situated in front of a moving source is said to be <i>blueshifted,</i>because blue light has a shorter wavelength than red light. Similarly, an observer situated behind the source will measure a longer-than-normal wavelength—the radiation is said to be <i>redshifted.</i> This terminology is used even for invisible radiation, for which "red" and "blue" have no meaning. Any shift toward shorter wavelengths is called a blueshift, and any shift toward longer wavelengths is called a redshift. For example, ultraviolet radiation might be blueshifted into the X-ray part of the spectrum or redshifted into the visible; infrared radiation could be redshifted into the microwave range, and so on.</span></div><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
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<div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Because <i>c</i> is so large—300,000 km/s—the Doppler effect is extremely small for everyday terrestrial velocities. For example, consider a source receding from the observer at Earth’s orbital speed of 30 km/s, a velocity much greater than any encountered in day-to-day life. A beam of blue light would be shifted by only 30 km/s/300,000 km/s = 0.01 percent, from 400 nm to 400.04 nm—a very small change indeed, and one that the human eye cannot distinguish. (It is easily detectable with modern instruments, though.)</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">The importance of the Doppler effect to astronomers is that it allows them to determine the speed of any cosmic object along the line of sight simply by determining the extent to which its light is redshifted or blueshifted. Suppose that the beam of blue light just mentioned is observed to have a wavelength of 399 nm instead of the 400 nm with which it was emitted. (Let’s defer to the next chapter the question of <i>how</i> an observer might know the wavelength of the emitted light.) Using the above equation, the observer could calculate the source’s radial velocity to be 399/400 – 1 = – 0.0025 times the speed of light. In other words, the source is <i>approaching</i> the observer at a speed of 0.0025 <i>c</i>, or 750 km/s. The basic reasoning is simple but very powerful. The motions of nearby stars and distant galaxies—even the expansion of the universe itself—have all been measured in this way.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Motorists stopped for speeding on the highway have experienced another, much more down-to-earth, application. Police radar measures speed by means of the Doppler effect, as do the radar guns used to clock the velocity of a pitcher’s fastball or a tennis player’s serve. Notice, incidentally, that the Doppler effect depends only on the relative motion of source and observer; it does not depend on <i>distance</i> in any way.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">In practice, it is hard to measure the Doppler shift of an entire blackbody curve, simply because it is spread over many wavelengths, making small shifts hard to determine with any accuracy. However, if the radiation were more narrowly defined and took up just a narrow "sliver" of the spectrum, then precise measurements of Doppler effect <i>could</i> be made. We will see in the next chapter that in many circumstances this is precisely what does happen, making the Doppler effect one of the observational astronomer’s most powerful tools.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div><span style="font-family: 'Times New Roman', Georgia, Times; font-size: x-small;"><i><a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=359603551864255334" name="Anchor-49575"></a><a href="http://astronomylearn.blogspot.com/2012/02/35-doppler-effect.html#Anchor-47857">*</a>In fact, Einstein’s theory of relativity (see Chapter 22) implies that when the transverse velocity is comparable to the speed of light, a wavelength change, called the transverse Doppler shift, does occur. For most terrestrial and astronomical applications, however, this shift is negligibly small, and we will ignore it here.</i></span></div>Andri F Martinhttp://www.blogger.com/profile/11669920311565328714noreply@blogger.com0tag:blogger.com,1999:blog-4374048443162882832.post-11882841080778566072012-02-16T15:29:00.000+07:002012-02-16T15:29:01.575+07:00More Precisely 3.2 - More About the Radiation Laws<h1>More About the Radiation Laws</h1><span style="background-color: #fef8ee; font-family: 'Times New Roman', Georgia, Times; text-align: justify;">As mentioned in Section 3.4, Wien’s law relates the temperature <i>T</i> of an object to the wavelength </span><span style="background-color: #fef8ee; text-align: justify;">λ</span><span style="background-color: #fef8ee; font-family: 'Times New Roman', Georgia, Times; text-align: justify;"><sub>max</sub> at which it emits the most radiation. (The Greek letter </span><span style="background-color: #fef8ee; text-align: justify;">λ</span><span style="background-color: #fef8ee; font-family: 'Times New Roman', Georgia, Times; text-align: justify;">—lambda—is conventionally used to denote wavelength.) Mathematically, if we measure </span><i style="background-color: #fef8ee; font-family: 'Times New Roman', Georgia, Times; text-align: justify;">T</i><span style="background-color: #fef8ee; font-family: 'Times New Roman', Georgia, Times; text-align: justify;"> in kelvins and </span><span style="background-color: #fef8ee; text-align: justify;">λ</span><sub style="background-color: #fef8ee; font-family: 'Times New Roman', Georgia, Times; text-align: justify;">max </sub><span style="background-color: #fef8ee; font-family: 'Times New Roman', Georgia, Times; text-align: justify;">in centimeters, we find that</span><br />
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<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgsIJKNdB1Iaq3JL09xo9ch1QaYWpBDIQe0KDP5T1YlxZYQeIEcJzM0C_ZAX2GrQskLqvNA_hRp5Yockw0gDhUozRiEzNmNKDM93lFBTlfLGlVj439jcYW47BFd3BjEswC0_jO4tE5vFio/s1600/MP0302PM1.GIF" imageanchor="1" style="background-color: #fef8ee; margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgsIJKNdB1Iaq3JL09xo9ch1QaYWpBDIQe0KDP5T1YlxZYQeIEcJzM0C_ZAX2GrQskLqvNA_hRp5Yockw0gDhUozRiEzNmNKDM93lFBTlfLGlVj439jcYW47BFd3BjEswC0_jO4tE5vFio/s1600/MP0302PM1.GIF" /></a></div><br />
<div style="background-color: #fef8ee;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">We could also convert Wien’s law into an equivalent statement about frequencyƒ, using the relation<i>ƒ</i> = c/</span>λ<span style="font-family: 'Times New Roman', Georgia, Times;">, but the law is most commonly stated in terms of wavelength and is probably easier to remember that way.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: #fef8ee;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">EXAMPLE: For a blackbody with the same temperature as the surface of the Sun, approximately 6000 K, the wavelength of maximum intensity is (0.29/6000) cm, or 480 nm, corresponding to the yellow-green part of the visible spectrum. A cooler star with a temperature of 3000 K has a peak wavelength of (0.29/3000) cm </span>=<span style="font-family: 'Times New Roman', Georgia, Times;"> 970 nm, just longward of the red end of the visible spectrum, in the near infrared. The blackbody curve of a star with a temperature of 12,000 K peaks at 242 nm, in the near ultraviolet, and so on.</span></div></div><div style="background-color: #fef8ee;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Stellar temperatures are typically measured in thousands of kelvins, so it is helpful to rewrite the above equation in more "stellar" units:</span></div></div><br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgkGfD9x1tcbU54Mmx2E4O7wbzh1AilFZfrpHLCHVaI5VEoNd96bdRK59texju0xYm0Hut9a1z3Um5Ynwm_rtHGftsfuzNrzZMt-riGPcYjWvPILwcJZ63rBlcEwvlv9E4PrSi0dEuwpVg/s1600/MP0302PM2.GIF" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgkGfD9x1tcbU54Mmx2E4O7wbzh1AilFZfrpHLCHVaI5VEoNd96bdRK59texju0xYm0Hut9a1z3Um5Ynwm_rtHGftsfuzNrzZMt-riGPcYjWvPILwcJZ63rBlcEwvlv9E4PrSi0dEuwpVg/s1600/MP0302PM2.GIF" /></a> </div><br />
<div style="background-color: #fef8ee;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">We can also give Stefan’s law a more precise mathematical formulation. With <i>T</i> measured in kelvins, the total amount of energy emitted per square meter of its surface per second (a quantity known as the <i>energy flux, F</i>) is given by<a href="http://www.blogger.com/post-create.g?blogID=4374048443162882832" name="Anchor-3500"></a></span></div></div><br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghZ-Bm54PTRqKZ290JpgHC26e82xLBpuf4F4QivYkwbP21A2dx1m3SDfnQ85Fzo6N8u7MgwUT-s0-Oc6vkDaP3AdiygqKErWVV3I9AbddMDxGW7FX0y1GS1n-jr-bxCdWXSXBX2K8GqWA/s1600/MP0302PM3.GIF" imageanchor="1" style="background-color: #fef8ee; margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghZ-Bm54PTRqKZ290JpgHC26e82xLBpuf4F4QivYkwbP21A2dx1m3SDfnQ85Fzo6N8u7MgwUT-s0-Oc6vkDaP3AdiygqKErWVV3I9AbddMDxGW7FX0y1GS1n-jr-bxCdWXSXBX2K8GqWA/s1600/MP0302PM3.GIF" /></a></div><br />
<div style="background-color: #fef8ee;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">The constant </span><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">σ</span><span style="font-family: 'Times New Roman', Georgia, Times;"> (the Greek letter sigma) is known as the <i>Stefan-Boltzmann constant,</i> or often just Stefan’s constant, after Josef Stefan, the Austrian scientist who formulated the equation.</span></div><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div><div style="background-color: #fef8ee;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><a href="http://www.blogger.com/post-create.g?blogID=4374048443162882832" name="Anchor-The-48982"></a>The SI unit of energy is the <i>joule</i> (J). Probably more familiar is the closely related unit called the<i>watt</i> (W), which measures power—the <i>rate</i> at which energy is emitted or expended by an object. One watt is the emission of one joule per second. For example, a 100-W lightbulb emits energy (mostly in the form of infrared and visible light) at a rate of 100 J/s. In these units, the Stefan-Boltzmann constant has the value </span><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">σ</span><span style="font-family: 'Times New Roman', Georgia, Times;"> = 5.67 x 10<sup>-8</sup> W/m<sup>2</sup> • K<sup>4</sup>.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: #fef8ee;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">EXAMPLE: Notice just how rapidly the energy flux increases with increasing temperature. A piece of metal in a furnace, when at a temperature of 3000 K, radiates energy at a rate of about 5.67 x10<sup>-8</sup> W/m<sup>2</sup> • K<sup>4</sup> x (0.01m)<sup>2</sup> x (3000 K) <sup>4</sup> = 460 W for every square centimeter of its surface area. Doubling its temperature to 6000 K, the surface temperature of the Sun (so that it becomes yellow-hot, by Wien’s law) increases the energy emitted by a factor of 16 (four "doublings"), to 7.3<i>kilowatts</i> (7,300 W) per square centimeter.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: #fef8ee;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Notice also that the law relates to energy emitted <i>per unit area.</i> The flame of a blowtorch is considerably hotter than a bonfire, but the bonfire emits far more energy <i>in total,</i> because it is much larger.</span></div></div>Andri F Martinhttp://www.blogger.com/profile/11669920311565328714noreply@blogger.com0tag:blogger.com,1999:blog-4374048443162882832.post-62556356596092763622012-02-16T14:49:00.001+07:002012-02-16T14:50:01.000+07:00More Precisely 3.1 - The Kelvin Temperature Scale<h1 style="text-align: center;">The Kelvin Temperature Scale</h1><div style="background-color: #fef8ee;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">The atoms and molecules that make up any piece of matter are in constant random motion. This motion represents a form of energy known as </span><i style="font-family: 'Times New Roman', Georgia, Times;">thermal energy</i><span style="font-family: 'Times New Roman', Georgia, Times;">—or, more commonly, </span><i style="font-family: 'Times New Roman', Georgia, Times;">heat</i><span style="font-family: 'Times New Roman', Georgia, Times;">. The quantity we call </span><i style="font-family: 'Times New Roman', Georgia, Times;">temperature</i><span style="font-family: 'Times New Roman', Georgia, Times;"> is a direct measure of this internal motion: The higher an object’s temperature, the faster, on average, the random motion of its constituent particles. The temperature of a piece of matter specifies the average thermal energy of the particles it contains.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: #fef8ee;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Our familiar Fahrenheit temperature scale, like the archaic English system in which length is measured in feet and weight in pounds, is of somewhat dubious value. In fact, the "degree Fahrenheit" is now a peculiarity of American society. Most of the world uses the Celsius scale of temperature measurement (also called the centigrade scale). In the Celsius system, water freezes at 0 degrees (0ºC) and boils at 100 degrees (100ºC), as illustrated in the accompanying figure.</span></div><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div><div style="background-color: #fef8ee;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">There are, of course, temperatures below the freezing point of water. Although we know of no matter anywhere in the universe that is actually this cold, temperatures can in theory reach as low as -273.15ºC. This is the temperature at which atomic and molecular motion all but ceases. It is convenient to construct a temperature scale based on this lowest possible temperature, or <i>absolute zero.</i> Scientists commonly use such a scale, called the <i>Kelvin scale</i> in honor of the nineteenth-century British physicist Lord Kelvin. Since it takes absolute zero as its starting point, the Kelvin scale differs from the Celsius scale by 273.15º. In this book, we round off the decimal places and simply use</span></div></div><div style="background-color: #fef8ee;"><span style="font-family: 'Times New Roman', Georgia, Times;">kelvins = degrees Celsius + 273.</span></div><div align="left" style="background-color: #fef8ee;"><span style="font-family: 'Times New Roman', Georgia, Times;">Thus,</span></div><div style="background-color: #fef8ee;"><span style="font-family: 'Times New Roman', Georgia, Times;"><img height="9" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjFIjRiIM4o0ZpeyC-R1f0_fdT2LOGirk_GIHjLXa6bwD7ldAOVbEp6YsbFZuQQxmJa25X2WiwEQq5j6EkIPar5HX0f6bQHsjeXhjjwTLrcCl4y8ULhcsPCUP7OrDBTlSPjLNQ813GADsw/s1600/goldsquare.gif" width="10" /> All thermal motion ceases at 0 kelvins (0 K).</span></div><div style="background-color: #fef8ee;"><span style="font-family: 'Times New Roman', Georgia, Times;"><img height="9" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjFIjRiIM4o0ZpeyC-R1f0_fdT2LOGirk_GIHjLXa6bwD7ldAOVbEp6YsbFZuQQxmJa25X2WiwEQq5j6EkIPar5HX0f6bQHsjeXhjjwTLrcCl4y8ULhcsPCUP7OrDBTlSPjLNQ813GADsw/s1600/goldsquare.gif" width="10" /> Water freezes at 273 kelvins (273 K).</span></div><div style="background-color: #fef8ee;"><span style="font-family: 'Times New Roman', Georgia, Times;"><img height="9" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjFIjRiIM4o0ZpeyC-R1f0_fdT2LOGirk_GIHjLXa6bwD7ldAOVbEp6YsbFZuQQxmJa25X2WiwEQq5j6EkIPar5HX0f6bQHsjeXhjjwTLrcCl4y8ULhcsPCUP7OrDBTlSPjLNQ813GADsw/s1600/goldsquare.gif" width="10" /> Water boils at 373 kelvins (373 K).</span></div><div style="background-color: #fef8ee;"><span style="font-family: 'Times New Roman', Georgia, Times;">Note that the unit is "kelvins," or "K," <i>not</i> "degrees kelvin" or "ºK." (Occasionally, the term "degrees absolute" is used instead.)</span><br />
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<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhcVKruLq6iecn9xk_eWCrqYk-V0xlaS646Lzkuis_j8c4l0uyN72CKdpHiN8K9JuSoPygXQiaVuHc2tfT9tkPnKgIgPOL9t991ZcyKf8Q08X-gcQOO-O34jC-_kT-wMNfNFjEJ1LClrGo/s1600/Temperature+degrees.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhcVKruLq6iecn9xk_eWCrqYk-V0xlaS646Lzkuis_j8c4l0uyN72CKdpHiN8K9JuSoPygXQiaVuHc2tfT9tkPnKgIgPOL9t991ZcyKf8Q08X-gcQOO-O34jC-_kT-wMNfNFjEJ1LClrGo/s400/Temperature+degrees.JPG" width="389" /></a></div><br />
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</span></center>Andri F Martinhttp://www.blogger.com/profile/11669920311565328714noreply@blogger.com0tag:blogger.com,1999:blog-4374048443162882832.post-87586118343030041862012-02-16T14:42:00.000+07:002012-02-16T14:42:25.938+07:00Discovery 3.1 - The Wave Nature of Radiation<h1 style="text-align: center;">The Wave Nature of Radiation</h1><div style="background-color: #fef8ee; text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Until the early nineteenth century, debate raged in scientific circles regarding the true nature of light. On the one hand, the particle, or <i>corpuscular</i>, theory, first expounded in detail by Isaac Newton, held that light consisted of tiny particles moving in straight lines at the speed of light. Different colors were presumed to correspond to different particles. On the other hand, the <i>wave</i> theory, championed by the seventeenth-century Dutch astronomer Christian Huygens, viewed light as a wave phenomenon, in which color was determined by frequency, or wavelength. During the first few decades of the nineteenth century, growing experimental evidence that light displayed three key wave properties—<i>diffraction,</i> <i>interference,</i> and <i>polarization</i>—argued strongly in favor of the wave theory.</span></div><div style="background-color: #fef8ee; text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div><div style="background-color: #fef8ee; text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><a href="http://www.blogger.com/post-create.g?blogID=4374048443162882832" name="Anchor-Diffraction-24394"></a>Diffraction is the deflection, or "bending," of a wave as it passes a corner or moves through a narrow gap. As depicted in the figure below, a sharp-edged hole in a barrier seems at first glance to produce a sharp shadow, as we might expect if radiation were composed of rays or particles moving in perfectly straight lines. Closer inspection, however, reveals that the shadow actually has a "fuzzy" edge, as shown in this photograph at right of the diffraction pattern produced by a small circular opening. We are not normally aware of such effects in everyday life because diffraction is generally very small for visible light. For any wave, the amount of diffraction is proportional to the ratio of the wavelength to the width of the gap. The longer the wavelength and/or the smaller the gap, the greater the angle through which the wave is diffracted. Thus, visible light, with its extremely short wavelengths, shows perceptible diffraction only when passing through very narrow openings. (The effect is much more noticeable for sound waves, however—no one thinks twice about our ability to hear people even when they are around a corner and out of our line of sight.)</span></div><div style="background-color: #fef8ee; text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
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</div><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiUyX5mLaO9DCQ5CuqvheSOvBJiVxK7F1Sroyx96C_3bQsg01jWBYDqoghi4wkjmw3hJ35S9-lqYDVklKt2C0XgbbSMOdcgUN7cmRSMgUDGufiHLs_ovgYV5DpWHYx9MI9tvbJ7SOSvG6g/s1600/Light+as+Wave.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiUyX5mLaO9DCQ5CuqvheSOvBJiVxK7F1Sroyx96C_3bQsg01jWBYDqoghi4wkjmw3hJ35S9-lqYDVklKt2C0XgbbSMOdcgUN7cmRSMgUDGufiHLs_ovgYV5DpWHYx9MI9tvbJ7SOSvG6g/s1600/Light+as+Wave.JPG" /></a> </center><br />
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</i></span></div><div style="background-color: #fef8ee; text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><a href="http://www.blogger.com/post-create.g?blogID=4374048443162882832" name="Anchor-Interference-4176"></a><i>Interference</i> is the ability of two or more waves to reinforce or cancel each other. The second figure shows two identical waves moving through the same region of space. In the first part, the waves are positioned so that their crests and troughs exactly coincide. The net effect is that the two wave motions reinforce each other, resulting in a wave of greater amplitude. This is known as <i>constructive interference.</i> In the second part of the figure, the two waves exactly cancel, so no net motion remains. This is <i>destructive interference.</i> As with diffraction, interference between waves of visible light is not noticeable in everyday experience; however, today it is easily measured in the laboratory (as shown in the diagram).</span></div><div style="background-color: #fef8ee; text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
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<center style="background-color: #fef8ee;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgm7onIOHlT9pTcDpvCELqDsflJyA1xiIKJdda6TGifxiu7jbiWyrueZXDm9NMNdGxuGItlNGXZYVr_ga3FLvdoxJmr0p6VJ8O5GWt8j12Cqhj0eXCIspZt4xl22l2Zg7csk2XwKi1A3K0/s1600/wave+interference.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgm7onIOHlT9pTcDpvCELqDsflJyA1xiIKJdda6TGifxiu7jbiWyrueZXDm9NMNdGxuGItlNGXZYVr_ga3FLvdoxJmr0p6VJ8O5GWt8j12Cqhj0eXCIspZt4xl22l2Zg7csk2XwKi1A3K0/s1600/wave+interference.JPG" /></a></div></center><br />
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</span></div><div style="background-color: #fef8ee; text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Finally, the phenomenon known as <i>polarization</i> of light is also readily understood in terms of the description of electromagnetic waves presented in the text. Normally, light waves are randomly oriented—the electric field in Figure 3.7 may vibrate in any direction perpendicular to the direction of wave motion—and we say the radiation is unpolarized. Most natural objects emit unpolarized radiation. Under some circumstances, however, the electric fields can become aligned—all vibrating in the same plane as the radiation moves through space, and the radiation is said to be polarized. On Earth we can produce polarized light by passing unpolarized light through a Polaroid filter, which has specially aligned elongated molecules that allow the passage of only those waves having electric fields oriented in some specific direction. Reflected light is often polarized, which is why sunglasses constructed with suitably oriented Polaroid filters can be effective in blocking glare.</span></div><div style="background-color: #fef8ee; text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div><div style="background-color: #fef8ee; text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Diffraction and interference play critical roles in many areas of observational astronomy, including telescope design (Chapter 5). The polarization of starlight provides astronomers with an important technique for probing the properties of interstellar gas (Chapter 18). All three phenomena are predicted by the wave theory of light. The particle theory did not predict them; in fact it predicted that they should <i>not</i> occur. Until the early 1800s, the technology was inadequate to resolve the issue. However, by 1830 experimenters had reported unequivocal measurement of each, convincing most scientists that the wave theory was the proper description of electromagnetic radiation. It would be almost a century before the particle description of radiation would resurface, but in radically different form, as we will see in Chapter 4.</span></div>Andri F Martinhttp://www.blogger.com/profile/11669920311565328714noreply@blogger.com0tag:blogger.com,1999:blog-4374048443162882832.post-71230565823895469192012-02-16T09:02:00.004+07:002012-02-16T16:09:22.364+07:003.4 The Distribution of Radiation<h1 style="text-align: center;">The Distribution of Radiation</h1><div style="text-align: justify;"><img height="14" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjro4NwCtC2TCdCM0U8llIjQWPaqnmu4Nt2WLO_hJXMRRt6pjUDNl52NfT4zBngnC52mY9Jyz9gm_C7nhxdDYZ3UdXQFZmOhsitag5SnErKeorWf9nncczB8fnqqR0HGCan4k26Y0kL1QE/s1600/LGICON_3.GIF" style="background-color: white;" width="24" /><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;"><i>All</i> macroscopic objects—fires, ice cubes, people, stars—emit radiation at all times, regardless of their size, shape, or chemical composition. They radiate mainly because the microscopic charged particles they are made up of are in constantly varying random motion, and whenever charges change their state of motion, electromagnetic radiation is emitted. The </span><a href="" name="Anchor-temperature-49640" style="background-color: white;"></a><a href="http://astronomylearn.blogspot.com/p/glossary.html#temperature" style="background-color: white;"><span style="font-family: 'Times New Roman', Georgia, Times;"><b>temperature</b></span></a><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;"> of an object is a direct measure of the amount of microscopic motion within it (see <i><a href="http://astronomylearn.blogspot.com/2012/02/more-precisely-31-kelvin-temperature.html">More Precisely 3-1</a></i>). The hotter the object—that is, the higher its temperature—the faster its constituent particles move and the more energy they radiate.</span></div><div style="text-align: justify;"><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div><div style="background-color: white;"><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><b>THE BLACKBODY SPECTRUM</b></span><br />
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</b></span></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><i>Intensity</i> is a term often used to specify the amount or strength of radiation at any point in space. Like frequency and wavelength, intensity is a basic property of radiation. </span><a href="" name="Anchor-No-15958"></a><span style="font-family: 'Times New Roman', Georgia, Times;">No natural object emits all its radiation at just one frequency. Instead, the energy is generally spread out over a range of frequencies. By studying how the intensity of this radiation is distributed across the electromagnetic spectrum, we can learn much about the object's properties.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><span style="font-family: 'Times New Roman', Georgia, Times;"></span></div><table align="right" border="0" cellpadding="0" cellspacing="2" style="width: 137px;"><tbody>
<tr><td><img height="6" src="file:///G:/CHAISSON/COMART/SPACER.GIF" width="6" /></td><td><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiP0U9b1tKa4rZc1RmAjZWaVVNyK2ewx3Fio3eEowOtTGcrFpF6LI7kvRQtfhXeIW6KTz5A0-fvJJ8KpYf16t-qviZdS1N4KRU12fq4jOYzI2XTDf22PbKY0RlECZOpMsABIUDkMJwRnew/s1600/Ideal+Blackbody+Curve.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiP0U9b1tKa4rZc1RmAjZWaVVNyK2ewx3Fio3eEowOtTGcrFpF6LI7kvRQtfhXeIW6KTz5A0-fvJJ8KpYf16t-qviZdS1N4KRU12fq4jOYzI2XTDf22PbKY0RlECZOpMsABIUDkMJwRnew/s1600/Ideal+Blackbody+Curve.JPG" /></a></div></td></tr>
<tr><td></td><td bgcolor="#fffad7"><span style="color: red; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>Figure 3.10</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b> Ideal Blackbody Curve</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;"> The blackbody, or Planck curve, represents the distribution of the intensity of radiation emitted by any object.</span></td></tr>
</tbody></table><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Figure 3.10 illustrates schematically the distribution of radiation emitted by any object. The curve peaks at a single, well-defined frequency and falls off to lesser values above and below that frequency. Note that the curve is not shaped like a symmetrical bell that declines evenly on either side of the peak. The intensity falls off more slowly from the peak to lower frequencies than it does on the high-frequency side. <a href="" name="Anchor-This-10615"></a>This overall shape is characteristic of the radiation emitted by <i>any</i> object, regardless of its size, shape, composition, or temperature.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div><div style="background-color: white;"><div style="text-align: justify;"><a href="" name="Anchor-The-26904"></a><span style="font-family: 'Times New Roman', Georgia, Times;">The curve drawn in Figure 3.10 is the radiation-distribution curve for a mathematical idealization known as a <i>blackbody</i>—an object that absorbs all radiation falling on it. <a href="" name="Anchor-In-23357"></a>In a steady state, a blackbody must reemit the same amount of energy it absorbs. The<b> <a href="" name="Anchor-blackbody-13861"></a><a href="http://astronomylearn.blogspot.com/p/glossary.html#blackbody curve">blackbody curve</a></b> shown in the figure describes the distribution of that reemitted radiation. (The curve is also known as the <i>Planck curve,</i> after Max Planck, whose mathematical analysis of such thermal emission in 1900 played a key role in modern physics.) No real object absorbs and radiates as a perfect blackbody. However, in many cases, the blackbody curve is a good approximation to reality, and the properties of blackbodies provide important insights into the behavior of real objects.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><b>THE RADIATION LAWS</b></span><br />
<br />
<div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><img height="14" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi7BP-072_rJf_a6j879EXh5dxwRChAL8MSSshDxJzWKgCV2cYUdqSRcY23tVUo_GWcFSiHWLjAbp4wfdbu01NHbxUOL9_hspd1du6Q01LTVY6Hhfqhj5EeVEF5rC3DQJpcjtEjA-EjKwI/s1600/LGICON_4.GIF" width="24" /><a href="" name="Anchor-The-22846"></a>The blackbody curve shifts toward higher frequencies (shorter wavelengths) and greater intensities as an object's temperature increases. Even so, the <i>shape</i> of the curve remains the same. This shifting of radiation's peak frequency with temperature is familiar to us all: Very hot glowing objects, such as toaster filaments or stars, emit visible light. Cooler objects, such as warm rocks or household radiators, produce invisible radiation—warm to the touch but not glowing hot to the eye. These latter objects emit most of their radiation in the lower-frequency infrared part of the electromagnetic spectrum (Figure 3.9).</span></div></div><div style="background-color: white;"><span style="font-family: 'Times New Roman', Georgia, Times;"></span></div><table align="right" border="0" cellpadding="0" cellspacing="2" style="width: 353px;"><tbody>
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</div><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgO3plQmaoXJpK9fygLZ5Er6yZoKEWBQah7fQpwZwTtR47wQDOpyt9mTYg1DZHbl3DqFaJVGI9GX3ebztG1ex9d_sMDrUbCeOB6cHw_11z3uUl948sbzvp-YHVbzE7_wEgBp3Kc1PIs4gI/s1600/Blackbody+Curves.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" height="242" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgO3plQmaoXJpK9fygLZ5Er6yZoKEWBQah7fQpwZwTtR47wQDOpyt9mTYg1DZHbl3DqFaJVGI9GX3ebztG1ex9d_sMDrUbCeOB6cHw_11z3uUl948sbzvp-YHVbzE7_wEgBp3Kc1PIs4gI/s320/Blackbody+Curves.JPG" width="320" /></a></td></tr>
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<tr><td><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.youtube.com/embed/7vR55d80FO0?feature=player_embedded' frameborder='0'></iframe> </div></td></tr>
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<tr><td></td><td bgcolor="#fffad7"><div style="text-align: justify;"><span style="color: red; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>Figure 3.11</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b> Blackbody Curves</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;"> As an object is heated, the radiation it emits peaks at higher and higher frequencies. Shown here are curves corresponding to temperatures of 300 K (room temperature), 1000 K (beginning to glow dull red), 4000 K (red hot), and 7000 K (white hot).</span></div></td></tr>
</tbody></table><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span><br />
<div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><a href="" name="Anchor-Imagine-49575"></a>Imagine a piece of metal placed in a hot furnace. At first, the metal becomes warm, although its visual appearance doesn't change. As it heats up, it begins to glow dull red, then orange, brilliant yellow, and finally white. How do we explain this? As illustrated in Figure 3.11, when the metal is at room temperature (300 K—see <i><a href="http://astronomylearn.blogspot.com/2012/02/more-precisely-31-kelvin-temperature.html">More Precisely 3-1 </a></i>for a discussion of the Kelvin temperature scale), it emits only invisible infrared radiation. As the metal becomes hotter, the peak of its blackbody curve shifts toward higher frequencies. At 1000 K, for instance, most of the emitted radiation is still infrared, but now there is also a small amount of visible (dull red) radiation being emitted (note in Figure 3.11 that the high-frequency portion of the 1000 K curve just overlaps the visible region of the graph).</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">As the temperature continues to rise, the peak of the metal's blackbody curve moves through the visible spectrum, from red (the 4000 K curve) through yellow. The metal eventually becomes white hot because, when its blackbody curve peaks in the blue or violet part of the spectrum (the 7000 K curve), the low-frequency tail of the curve extends through the entire visible spectrum (to the left in Figure 3.11), meaning that substantial amounts of green, yellow, orange, and red light are also emitted. Together, all these colors combine to produce white.</span><br />
<span style="font-family: 'Times New Roman', Georgia, Times;"><br />
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<tr><td><img height="6" src="file:///G:/CHAISSON/COMART/SPACER.GIF" width="6" /></td><td><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjTqIZu7jAuPdczO04hh-n2Iq3O82tmSh8BWXpyJwMJOISWdgwrMM-dszb6ZHHtgbdg3S_EGUKJdldonNJ-tJOt9S9WrpdLEkKrB3CGfyra0__2uR9EobwoRLFtvibEKn8hz40GAEpew1o/s1600/The+Sun+at+Many+Wavelengths.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjTqIZu7jAuPdczO04hh-n2Iq3O82tmSh8BWXpyJwMJOISWdgwrMM-dszb6ZHHtgbdg3S_EGUKJdldonNJ-tJOt9S9WrpdLEkKrB3CGfyra0__2uR9EobwoRLFtvibEKn8hz40GAEpew1o/s1600/The+Sun+at+Many+Wavelengths.JPG" /></a> </div></td></tr>
<tr><td></td><td bgcolor="#fffad7"><div style="text-align: justify;"><span style="color: red; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>Figure 3.12 </b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>The Sun at Many Wavelengths</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;"> Three images of the Sun, made using (a) radio waves, (b) infrared radiation, and (c) visible light, are shown here in false color. By studying the similarities and differences among these views of the same object, acquired on the same day, astronomers can find important clues to its structure, composition, and surface activity. Although most sunlight is emitted in the form of infrared and visible radiation, a wealth of information about our parent star can be obtained by studying it in other regions of the electromagnetic spectrum. (<i>NRAO; AURA</i>)</span></div></td></tr>
</tbody></table><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><a href="" name="Anchor-From-5461"></a>From studies of the precise form of the blackbody curve we obtain a very simple connection between the wavelength at which most radiation is emitted and the absolute temperature (that is, the temperature measured in kelvins) of the emitting object:</span></div><br />
<center style="background-color: white;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjIjlhb0etCL9-qzxyGjEgMWKl1hxpF2BnRUSzVxZNkt71WGK6jXTeTYk15uART8zhjR4dNwGH3k2ovdW0DjwhBGnlf6cqTQR2F0Awo3PXqeVV7QLAAysjaMOaH2ms4fbZIpDuL4ztwyUY/s1600/Wien%E2%80%99s+law.GIF" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjIjlhb0etCL9-qzxyGjEgMWKl1hxpF2BnRUSzVxZNkt71WGK6jXTeTYk15uART8zhjR4dNwGH3k2ovdW0DjwhBGnlf6cqTQR2F0Awo3PXqeVV7QLAAysjaMOaH2ms4fbZIpDuL4ztwyUY/s1600/Wien%E2%80%99s+law.GIF" /></a> </center><br />
<div align="left" style="background-color: white;"><span style="font-family: 'Times New Roman', Georgia, Times;">This relationship, called <a href="" name="Anchor-47234"></a><b>Wien's law,</b> is discussed in more detail in <a href="http://astronomylearn.blogspot.com/2012/02/more-precisely-32-more-about-radiation.html"><i>More Precisely 3-2</i></a><i>.</i></span><br />
<span style="font-family: 'Times New Roman', Georgia, Times;"><i><br />
</i></span><br />
<div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><a href="" name="Anchor-Simply-19819"></a>Simply put, Wien's law tells us that the hotter the object, the bluer its radiation. </span><a href="" name="Anchor-For-30991"></a><span style="font-family: 'Times New Roman', Georgia, Times;">For example (see Figure 3.13), an object with a temperature of 6000 K emits most of its energy in the visible part of the spectrum, with a peak wavelength of 480 nm. At 600 K, the object's emission would peak at a wavelength of 4800 nm, well into the infrared portion of the spectrum. At a temperature of 60,000 K, the peak would move all the way through the visible spectrum to a wavelength of 48 nm, in the ultraviolet range.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><a href="" name="Anchor-It-44766"></a>It is also a matter of everyday experience that, as the temperature of an object increases, the <i>total</i> amount of energy it radiates (summed over all frequencies) increases rapidly. For example, the heat given off by an electric heater increases very sharply as it warms up and begins to emit visible light. Careful experimentation leads to the conclusion that the total amount of energy radiated per unit time is actually proportional to the fourth power of the object's temperature:</span></div></div><br />
<center style="background-color: white;"><span style="font-family: 'Times New Roman', Georgia, Times;">total energy emission </span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEidaRycpO0HF9jZEDfPMZAp8xfbndUqpvArPHD8oiDZuOB7rAEx3hyphenhyphene6Ji8Peozc4BaaEAHTLFXiwbva8ePzHtG_r_2YZUsUFCcSkVCrlAM2YGT17-04NRhK64PRXz67kZcUtFqCZXqVGQ/s1600/PROPOR.GIF" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEidaRycpO0HF9jZEDfPMZAp8xfbndUqpvArPHD8oiDZuOB7rAEx3hyphenhyphene6Ji8Peozc4BaaEAHTLFXiwbva8ePzHtG_r_2YZUsUFCcSkVCrlAM2YGT17-04NRhK64PRXz67kZcUtFqCZXqVGQ/s1600/PROPOR.GIF" /></a> <span style="font-family: 'Times New Roman', Georgia, Times;">temperature<sup>4</sup>.</span></center><br />
<div align="left" style="background-color: white;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span><br />
<div style="text-align: justify;"><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;">This relation is called </span><a href="" name="Anchor-9169" style="background-color: white; font-family: 'Times New Roman', Georgia, Times;"></a><a href="http://astronomylearn.blogspot.com/p/glossary.html#Stefan's law" style="background-color: white; font-family: 'Times New Roman', Georgia, Times;"><b>Stefan's law</b></a><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;">. This is discussed further in</span><i style="background-color: white; font-family: 'Times New Roman', Georgia, Times;">More Precisely 3-2.</i><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;"> From the form of Stefan's law we can see that the energy emitted by a body rises dramatically as its temperature increases. Doubling the temperature causes the total energy radiated to increase by a factor of</span></div><span style="font-family: 'Times New Roman', Georgia, Times;"> 2<sup>4</sup> = 16; tripling the temperature increases the emission by 3<sup>4</sup>= 81, and<br />
so on.</span><br />
<span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span><br />
<span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><b>ASTRONOMICAL APPLICATIONS</b></span><br />
<span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><b><br />
</b></span><br />
<div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><a href="" name="Anchor-No-19341"></a>No known natural terrestrial objects reach temperatures high enough to emit very-high-frequency radiation. Only human-made thermonuclear explosions are hot enough for their spectra to peak in the X-ray or gamma-ray range. (Most human inventions that produce short-wavelength, high-frequency radiation, such as X-ray machines, are designed to emit only a specific range of wavelengths and do not operate at high temperatures. They are said to produce a <i>nonthermal </i>spectrum of radiation.) Many extraterrestrial objects, however, do emit copious quantities of ultraviolet, X-ray, and even gamma-ray radiation. Figure 3.12 shows a familiar object—our Sun—as it appears when viewed using radiation from different parts of the electromagnetic spectrum.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Astronomers often use blackbody curves as thermometers to determine the temperatures of distant objects. For example, study of the solar spectrum makes it possible to measure the temperature of the Sun's surface. Observations of the radiation from the Sun at many frequencies yield a curve shaped somewhat like that shown in Figure 3.10. The Sun's curve peaks in the visible part of the electromagnetic spectrum; the Sun also emits a lot of infrared and a little ultraviolet radiation. Using Wien's law, we find that the temperature of the Sun's surface is approximately 6000 K. (A more precise measurement, applying Wien's law to the blackbody curve that best fits the solar spectrum, yields a temperature of 5800 K.)</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Other cosmic objects have surfaces very much cooler or hotter than the Sun's, emitting most of their radiation in invisible parts of the spectrum (Figure 3.13). For example, the relatively cool surface of a very young star may measure 600 K and emit mostly infrared radiation. Cooler still is the interstellar gas cloud from which the star formed; at a temperature of 60 K, such a cloud emits mainly long-wavelength radiation in the radio and infrared parts of the spectrum. The brightest stars, by contrast, have surface temperatures as high as 60,000 K and hence emit mostly ultraviolet radiation.</span></div></div></div>Andri F Martinhttp://www.blogger.com/profile/11669920311565328714noreply@blogger.com0tag:blogger.com,1999:blog-4374048443162882832.post-9987906951207413642012-02-15T10:51:00.001+07:002012-02-16T06:21:15.519+07:003.3 The Electromagnetic Spectrum<h1 style="text-align: center;">The Electromagnetic Spectrum</h1><div style="text-align: justify;"><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;"><img height="14" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhyIIQmfEvEcSnN3CVbR2KZeDq56rV0CWlw3kCv-niHq8DSP2AlR8tezxJRzOhvQc7fJVvPUS5f9xjMnFO7YCmVo6N0CS5ir15tGO6kE7d9ZmgAODnQK7pmF0Tt3z_-8Sij99rArgJlv_M/s1600/LGICON_2.GIF" width="24" /></span><a name="Anchor-Figure-23013" style="background-color: white;"></a><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;">Figure 3.9 plots the entire range of electromagnetic radiation, illustrating the relationships among the different "types" of electromagnetic radiation listed earlier. </span><a name="Anchor-We-9799" style="background-color: white;"></a><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;">We see that the only characteristic distinguishing one from another is wavelength, or frequency. To the low-frequency, long-wavelength side of visible light lie <i>radio</i> and <i>infrared</i> radiation. Radio frequencies include radar, microwave radiation, and the familiar AM, FM, and TV bands. We perceive infrared radiation as heat. </span><a name="Anchor-At-16583" style="background-color: white;"></a><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;">At higher frequencies (shorter wavelengths) are the domains of <i>ultraviolet, X-ray,</i> and <i>gamma-ray</i> radiation. Ultraviolet radiation, lying just beyond the violet end of the visible spectrum, is responsible for suntans and sunburns. X rays are perhaps best known for their ability to penetrate human tissue and reveal the state of our insides without resorting to surgery. Gamma rays are the shortest-wavelength radiation. They are often associated with radioactivity and are invariably damaging to living cells they encounter.</span></div><div align="left" style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">All these spectral regions, including the visible spectrum, collectively make up the </span><a name="Anchor-electromagnetic-24178"></a><a href="http://astronomylearn.blogspot.com/p/glossary.html#electromagnetic spectrum"><span style="font-family: 'Times New Roman', Georgia, Times;"><b>electromagnetic spectrum.</b></span></a><span style="font-family: 'Times New Roman', Georgia, Times;"> Remember that, despite their greatly differing wavelengths and the different roles they play in everyday life on Earth, all are basically the same phenomenon, and all move at the same speed—the speed of light, <i>c.</i></span></div></div><div style="text-align: center;"><br />
</div><table border="0" cellpadding="0" cellspacing="2" style="text-align: center; width: 75px;"><tbody>
<tr><td><img src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiOoJfWtvwMltYaccE6Afv_sRb99J-UHKLZs-8WBPXKtF7mAj-aq83hqHULVnF-I-nWz7Vy8LehcPLjJb002pqSbE-pm6dd7aSbJUg7EWce52xDmo93R0cV3glPAaHFkLwgkGiSHU9x9xA/s1600/AACHCLA0.JPG" /></td></tr>
<tr><td bgcolor="#fffad7"><span style="color: red; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>Figure 3.9</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b> Electromagnetic Spectrum</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;"> The entire electromagnetic spectrum, running from long-wavelength, low-frequency radio waves, to short-wavelength, high-frequency gamma rays.</span></td></tr>
</tbody></table><div style="text-align: center;"><br />
</div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Figure 3.9 is worth studying carefully, as it contains a great deal of information. Note that wave frequency (in hertz) increases from left to right, and wavelength (in meters) increases from right to left. Scientists often disagree on the "correct" way to display wavelengths and frequencies in diagrams of this type. When picturing wavelengths and frequencies, this book consistently adheres to the convention that frequency increases toward the <i>right.</i></span></div><span style="font-family: 'Times New Roman', Georgia, Times;"><i><br />
</i></span></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Notice also that the wavelength and frequency scales in Figure 3.9 do not increase by equal increments of 10. Instead, successive values marked on the horizontal axis differ by<i> factors of 10</i>—each is 10 times greater than its neighbor. This type of scale, called a <i>logarithmic</i> scale, is often used in science to condense a large range of some quantity into a manageable size. Had we used a linear scale for the wavelength range shown in Figure 3.9, the figure would have been many light-years long! Throughout the text we will often find it convenient to use a logarithmic scale to compress a wide range of some quantity onto a single, easy-to-view plot.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Figure 3.9 shows that wavelengths extend from the size of mountains for radio radiation to the size of an atomic nucleus for gamma-ray radiation. <a name="Anchor-The-41109"></a>The box at the upper right emphasizes how small the visible portion of the electromagnetic spectrum is. Most objects in the universe emit large amounts of invisible radiation. Indeed, many of them emit only a tiny fraction of their total energy in the visible range. A wealth of extra knowledge can be gained by studying the invisible regions of the electromagnetic spectrum. To remind you of this important fact and to identify the region of the electromagnetic spectrum in which a particular observation was made, we have attached a spectrum icon—an idealized version of the wavelength scale in Figure 3.9—to every astronomical image presented in this text.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><a name="Anchor-Only-31612"></a>Only a small fraction of the radiation produced by astronomical objects actually reaches Earth's surface because of the <i>opacity</i> of our planet's atmosphere. Opacity is the extent to which radiation is blocked by the material through which it is passing—in this case, air. The more opaque an object is, the less radiation gets through it: Opacity is just the opposite of transparency. Earth's atmospheric opacity is plotted along the wavelength and frequency scales at the bottom of Figure 3.9. The extent of shading is proportional to the opacity. Where the shading is greatest, no radiation can get in or out. Where there is no shading at all, the atmosphere is almost completely transparent.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">What causes opacity to vary along the spectrum? Certain atmospheric gases absorb radiation very efficiently at some wavelengths. For example, water vapor (H<sub>2</sub>O) and oxygen (O<sub><sup>2</sup></sub>) absorb radio waves having wavelengths less than about a centimeter, while water vapor and carbon dioxide (CO<sub>2</sub>) are strong absorbers of infrared radiation. Ultraviolet, X-ray, and gamma-ray radiation are completely blocked by the <i>ozone layer</i> (O<sub>3</sub>) high in Earth's atmosphere (see Section 7.3). A passing but unpredictable source of atmospheric opacity in the visible part of the spectrum is the blockage of light by atmospheric clouds.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">In addition, the interaction between the Sun's ultraviolet radiation and the upper atmosphere produces a thin, electrically conducting layer at an altitude of about 100 km. The <i>ionosphere,</i> as this layer is known, reflects long-wavelength radio waves (wavelengths greater than about 10 m) as well as a mirror reflects visible light. In this way, extraterrestrial waves are kept out, and terrestrial waves—such as those produced by AM radio stations—are kept in. (That's why it is possible to transmit some radio frequencies beyond the horizon—the broadcast waves bounce off the ionosphere.)</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><div style="text-align: justify;"><a name="Anchor-The-32768"></a><span style="font-family: 'Times New Roman', Georgia, Times;">The effect of atmospheric opacity is that there are only a few <i>spectral windows,</i> at well-defined locations in the electromagnetic spectrum, where Earth's atmosphere is transparent. In much of the radio and in the visible portions of the spectrum, the opacity is low and we can study the universe at those wavelengths from ground level. In parts of the infrared range, the atmosphere is partially transparent, so we can make certain infrared observations from the ground. Moving to the tops of mountains, above as much of the atmosphere as possible, improves observations. In the rest of the spectrum, however, the atmosphere is opaque. Ultraviolet, X-ray, and gamma-ray observations can be made only from above the atmosphere, from orbiting satellites.</span></div></div>Andri F Martinhttp://www.blogger.com/profile/11669920311565328714noreply@blogger.com0tag:blogger.com,1999:blog-4374048443162882832.post-37804549792528929362012-02-15T10:21:00.002+07:002012-02-16T06:24:17.104+07:003.2 Waves in What?<h1 style="text-align: center;">Waves in What?</h1><div style="background-color: white;"><div style="text-align: justify;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJ54ymVCtThcMHbRD-h84NRSk2OQxJjBmCRuTKfEtRI5KTpQAQ9OXWz6DnCCAofySfOz6QHB3h8Mm8ukOqFqjacEWYuvN_r7Oi06R8IPqXzKkibJbrqPuawkNP_OIlIZV3ppVOb0Cv8Rg/s1600/LGICON_1.GIF" imageanchor="1" style="background-color: white; margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJ54ymVCtThcMHbRD-h84NRSk2OQxJjBmCRuTKfEtRI5KTpQAQ9OXWz6DnCCAofySfOz6QHB3h8Mm8ukOqFqjacEWYuvN_r7Oi06R8IPqXzKkibJbrqPuawkNP_OIlIZV3ppVOb0Cv8Rg/s1600/LGICON_1.GIF" /></a><span style="font-family: 'Times New Roman', Georgia, Times;">Waves of radiation differ fundamentally from water waves, sound waves, or any other waves that travel through a material medium. </span><a name="Anchor-Radiation-7322"></a><span style="font-family: 'Times New Roman', Georgia, Times;">Radiation needs <i>no</i> such medium. When light radiation travels from a distant galaxy, or from any other cosmic object, it moves through the virtual vacuum of space. Sound waves, by contrast, cannot do this; if we were to remove all the air from a room, conversation would be impossible. Communication by flashlight or radio, however, would be entirely feasible.</span></div><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">The ability of light to travel through empty space was once a great mystery. The idea that light, or any other kind of radiation, could move as a wave through nothing at all seemed to violate common sense, yet it is now a cornerstone of modern physics.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><b>INTERACTIONS BETWEEN CHARGED PARTICLES</b></span><br />
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</b></span></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">To understand more about the nature of light, consider for a moment an <i>electrically charged </i>particle, such as an </span><a name="Anchor-electron-36459"></a><a href="http://astronomylearn.blogspot.com/p/glossary.html#electron"><span style="font-family: 'Times New Roman', Georgia, Times;"><b>electron</b></span></a><span style="font-family: 'Times New Roman', Georgia, Times;"> or a <a name="Anchor-proton-48415"></a><a href="http://astronomylearn.blogspot.com/p/glossary.html#proton"><b>proton</b></a>. Like mass, electrical charge is a fundamental property of matter. Electrons and protons are elementary particles—"building blocks" of atoms and all matter—that carry the basic unit of charge. Electrons are said to carry a <i>negative</i> charge, whereas protons carry an equal and opposite <i>positive</i> charge.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Just as a massive object exerts a gravitational force on any other massive body (as we saw in <a href="http://astronomylearn.blogspot.com/search/label/2.%20The%20Copernican%20Revolution">Chapter 2</a>), an electrically charged particle exerts an <i>electrical</i> force on every other charged particle in the universe. <a href="http://astronomylearn.blogspot.com/2012/02/27-newtons-laws.html">(Sec. 2.7)</a> Buildup of electrical charge (a net imbalance of positive over negative, or vice versa) is what causes "static cling" on your clothes when you take them out of a hot clothes dryer, or the shock you sometimes feel when you touch a metal door frame on a particularly dry day.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
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<tr><td></td><td bgcolor="#fffad7"><div style="text-align: justify;"><span style="color: red; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>Figure 3.5</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b> Charged Particles</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;"> (a) Particles carrying like electrical charges repel one another, whereas particles carrying unlike charges attract. (b) A charged particle is surrounded by an electric field, which determines the particle's influence on other charged particles. We represent the field by a series of field lines. (c) If a charged particle begins to vibrate back and forth, its electric field changes. The resulting disturbance travels through space as a wave.</span></div></td></tr>
</tbody></table><div style="text-align: justify;"><a name="Anchor-Unlike-42790"></a><span style="font-family: 'Times New Roman', Georgia, Times;">Unlike the gravitational force, which is always attractive, electrical forces can be either attractive or repulsive. As illustrated in Figure 3.5(a), particles with <i>like</i> charges (that is, both negative or both positive—for example, two electrons or two protons) repel one another. Particles with <i>unlike</i> charges (that is, having opposite signs—an electron and a proton, say) attract.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">How is the electrical force transmitted through space? Extending outward in all directions from any charged particle is an <a name="Anchor-electric-15339"></a><a href="http://astronomylearn.blogspot.com/p/glossary.html#electric field"><b>electric field</b></a><b>,</b> which determines the electrical force exerted by the particle on all other charged particles in the universe (Figure 3.5b). The strength of the electric field, like the strength of the gravitational field, decreases with increasing distance from the charge according to an inverse-square law. By means of the electric field, the particle's presence is "felt" by all other charged particles, near and far.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Now suppose our particle begins to vibrate, perhaps because it becomes heated or collides with some other particle. Its changing position causes its associated electric field to change, and this changing field in turn causes the electrical force exerted on other charges to vary (Figure 3.5c). If we measure the change in the force on these other charges, we learn about our original particle. Thus, <i>information about the particle's state of motion is transmitted through space via a changing electric field.</i> This <i>disturbance</i> in the particle's electric field travels through space as a wave.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><b>ELECTROMAGNETIC WAVES</b></span><br />
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</b></span></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">The laws of physics tell us that a <a name="Anchor-magnetic-43598"></a><a href="http://astronomylearn.blogspot.com/p/glossary.html#magnetic field"><b>magnetic field</b></a> must accompany every changing electric field. Magnetic fields govern the influence of <i>magnetized</i> objects on one another, much as electric fields govern interactions between charged particles. The fact that a compass needle always points to magnetic north is the result of the interaction between the magnetized needle and Earth's magnetic field (Figure 3.6). Magnetic fields also exert forces on <i>moving</i> electric charges (that is, electric currents)—electric meters and motors rely on this basic fact. Conversely, moving charges <i>create</i>magnetic fields (electromagnets are a familiar example). In short, electric and magnetic fields are inextricably linked to one another: a change in either one necessarily creates the other.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
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<tr><td></td><td bgcolor="#fffad7"><div style="text-align: justify;"><span style="color: red; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>Figure 3.6 </b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>Magnetism</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;"> Earth's magnetic field interacts with a magnetic compass needle, causing the needle to become aligned with the field—that is, to point toward Earth's north (magnetic) pole. The north magnetic pole lies at latitude 80º N, longitude 107º W, some 1140 km from the geographic North Pole.</span></div></td></tr>
</tbody></table><div style="text-align: justify;"><a name="Anchor-Thus-63642"></a><span style="font-family: 'Times New Roman', Georgia, Times;">Thus, as illustrated in Figure 3.7, the disturbance produced by our moving charge actually consists of vibrating electric <i>and</i> magnetic fields, always oriented perpendicular to one another and moving together through space. These fields do not exist as independent entities; rather, they are different aspects of a single physical phenomenon:<a name="Anchor-electromagnetism-44622"></a><a href="http://astronomylearn.blogspot.com/p/glossary.html#electromagnetism"><b>electromagnetism.</b></a> Together, they constitute an electromagnetic wave that carries energy and information from one part of the universe to another.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Now consider a real cosmic object—a star, say. When some of its charged contents move around, their electric fields change, and we can detect that change. The resulting electromagnetic ripples travel outward in waves, requiring no material medium in which to travel. Small charged particles, either in our eyes or in our experimental equipment, eventually respond to the electromagnetic field changes by vibrating in tune with the received radiation. This response is how we detect the radiation—and how we see. Figure 3.8 shows a more familiar example of information being transferred by electromagnetic radiation. A television transmitter causes electric charges to oscillate up and down a metal rod near the tower's top, thereby generating electromagnetic radiation. This radiation can be detected by rooftop antennas. In the metal rods of the receiving antenna, electric charges respond by vibrating in time with the transmitted wave frequency. The information carried by the pattern of vibrations is then converted into sound and pictures by your TV set.</span></div></div><br />
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<tr><td></td><td bgcolor="#fffad7"><span style="color: red; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>Figure 3.7</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b> Electromagnetic Wave </b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;">Electric and magnetic fields vibrate perpendicular to each other. Together they form an electromagnetic wave that moves through space at the speed of light in the direction perpendicular to both the electric and the magnetic fields comprising it.</span></td></tr>
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<tr><td></td><td bgcolor="#fffad7"><span style="color: red; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>Figure 3.8 </b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>Television Signal</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;"> Charged particles in an ordinary household television antenna vibrate in response to electromagnetic radiation broadcast by a distant transmitter. The radiation is produced when electric charges are made to oscillate in the transmitter's emitting antenna. The vibrations in the receiving antenna "echo" the oscillations in the transmitter, allowing the original information to be retrieved.</span></td></tr>
</tbody></table><div style="text-align: justify;"><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;">How </span><i style="background-color: white; font-family: 'Times New Roman', Georgia, Times;">quickly</i><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;"> does one charge feel the change in the electromagnetic field when another begins to move? This is an important question, because it is equivalent to asking how fast an electromagnetic wave travels. Does it propagate at some measurable speed, or is it instantaneous? </span><a name="Anchor-Both-41350" style="background-color: white; font-family: 'Times New Roman', Georgia, Times;"></a><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;">Both theory and experiment tell us that all electromagnetic waves move at a very specific speed—the </span><a name="Anchor-speed-58267" style="background-color: white; font-family: 'Times New Roman', Georgia, Times;"></a><a href="http://astronomylearn.blogspot.com/p/glossary.html#speed of light" style="background-color: white; font-family: 'Times New Roman', Georgia, Times;"><b>speed of light</b></a><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;"> (always denoted by the letter </span><i style="background-color: white; font-family: 'Times New Roman', Georgia, Times;">c</i><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;">). Its exact value is 299,792.458 km/s in a vacuum (and somewhat less in material substances such as air or water). </span><a name="Anchor-We-17280" style="background-color: white; font-family: 'Times New Roman', Georgia, Times;"></a><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;">We will round this value off to </span><i style="background-color: white; font-family: 'Times New Roman', Georgia, Times;">c</i><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;"> = 3.00 x</span><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;"> 10</span><sup style="background-color: white; font-family: 'Times New Roman', Georgia, Times;">5</sup><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;"> km/s. This is an extremely high speed. In the time needed to snap your fingers (about a tenth of a second) light can travel three-quarters of the way around our planet! If the currently known laws of physics are correct, then the speed of light is the fastest speed possible. (see </span><a href="http://astronomylearn.blogspot.com/p/glossary.html" style="background-color: white; font-family: 'Times New Roman', Georgia, Times;"><i>More Precisely 22-1</i></a><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;">)</span></div><div style="text-align: justify;"><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><a name="Anchor-The-46770"></a>The speed of light is very large, but it is still <i>finite</i>. <a name="Anchor-That-10238"></a>That is, light does not travel instantaneously from place to place. This fact has some interesting consequences for our study of distant objects. It takes time—often lots of time—for light to travel through space. The light we see from the nearest large galaxy—the Andromeda Galaxy, shown in Figure 3.1—left that object about 2.5 million years ago, around the time our first human ancestors appeared on planet</span> <span style="font-family: 'Times New Roman', Georgia, Times;">Earth. We can know nothing about this galaxy as it exists today. For all we know, it may no longer even exist! Only our descendants, 2.5 million years into the future, will know if it exists now. So as we study objects in the cosmos, remember that the light we see left those objects long ago. We can never observe the universe as it is—only as it was.</span></div></div>Andri F Martinhttp://www.blogger.com/profile/11669920311565328714noreply@blogger.com0tag:blogger.com,1999:blog-4374048443162882832.post-76497148027827124872012-02-15T07:24:00.032+07:002012-02-16T16:07:40.263+07:003.1 Information from the Skies<h1 style="text-align: center;">Information from the Skies</h1><div style="text-align: justify;"><span style="background-color: white; color: black; font-family: 'Times New Roman', Georgia, Times;">Figure 3.1 </span><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;">shows a galaxy in the constellation Andromeda. On a dark, clear night, far from cities or other sources of light, the Andromeda Galaxy, as it is generally called, can be seen with the naked eye as a faint, fuzzy patch on the sky, comparable in diameter to the full Moon. Yet the fact that it is visible from Earth belies this galaxy's enormous distance from us. It lies roughly 2.5 million <i>light-years</i> away. An object at such a distance is truly inaccessible in any realistic human sense. Even if a space probe could miraculously travel at the speed of light, it would need 2.5 million years to reach this galaxy and 2.5 million more to return with its findings. Considering that civilization has existed on Earth for fewer than 10,000 years, and its prospects for the next 10,000 are far from certain, even this unattainable technological feat would not provide us with a practical means of exploring other galaxies. Even the farthest reaches of our own galaxy, "only" a few tens of thousands of light-years distant, are effectively off-limits to visitors from Earth, at least for the foreseeable future.</span></div><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;"><br />
</span><br />
<div style="background-color: white;"><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><b>LIGHT AND RADIATION</b></span></div><table align="right" border="0" cellpadding="0" cellspacing="2" style="width: 137px;"><tbody>
<tr><td><img height="6" src="file:///G:/CHAISSON/COMART/SPACER.GIF" width="6" /></td><td><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiBaiYRaR6ae6K7XvZy5ZfhWYcvLuzBoqmAxMFLS_GPtsq2wsMlFrpPs7K2YFBssjPC2v5XdOYV2REDoBlTDQTjM3M-p3oRfxLICUyFkI36wEMHVtReX1aFFlNAiaVCZ1jDvE70tAUKEKM/s1600/AACHCKS0.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="189" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiBaiYRaR6ae6K7XvZy5ZfhWYcvLuzBoqmAxMFLS_GPtsq2wsMlFrpPs7K2YFBssjPC2v5XdOYV2REDoBlTDQTjM3M-p3oRfxLICUyFkI36wEMHVtReX1aFFlNAiaVCZ1jDvE70tAUKEKM/s320/AACHCKS0.JPG" width="320" /></a></div></td></tr>
<tr><td></td><td bgcolor="#fffad7"><div style="text-align: justify;"><span style="color: red; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>Figure 3.1</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b> Andromeda</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;"> The pancake-shaped Andromeda Galaxy lies about 2.5 million light-years away, according to the most recent distance measurements. It contains a few hundred billion stars. (<i>T. Hallas</i>)</span></div></td></tr>
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<div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Given the impossibility of traveling to such remote parts of the universe, how do astronomers know anything about objects far from Earth? How do we obtain detailed information about any planet, star, or galaxy too distant for a personal visit or any kind of controlled experiment? The answer is that we use the laws of physics, as we know them here on Earth, to interpret the </span><a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=7649714802782712487" name="Anchor-electromagnetic-50514"></a><a href="http://astronomylearn.blogspot.com/p/glossary.html#electromagnetic radiation"><span style="font-family: 'Times New Roman', Georgia, Times;"><b>electromagnetic radiation</b></span></a><span style="font-family: 'Times New Roman', Georgia, Times;"> emitted by these objects. <i>Radiation</i> is any way in which energy is transmitted through space from one point to another without the need for any physical connection between those two locations. The term <i>electromagnetic</i> just means that the energy is carried in the form of rapidly fluctuating <i>electric</i> and <i>magnetic</i> fields (to be discussed in more detail later in Section 3.2). Virtually all we know about the universe beyond Earth's atmosphere has been gleaned from painstaking analysis of electromagnetic radiation received from afar.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><div style="text-align: justify;"><a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=7649714802782712487" name="Anchor-Visible-3388"></a><a href="http://astronomylearn.blogspot.com/p/glossary.html#visible light"><span style="font-family: 'Times New Roman', Georgia, Times;"><b>Visible light</b></span></a><span style="font-family: 'Times New Roman', Georgia, Times;"> is the particular type of electromagnetic radiation to which our human eyes happen to be sensitive. As light enters our eye, the cornea and lens focus it onto the retina, whereupon small chemical reactions triggered by the incoming energy send electrical impulses to the brain, producing the sensation of sight. <a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=7649714802782712487" name="Anchor-But-22462"></a>But there is also <i>invisible</i> electromagnetic radiation, which goes completely undetected by our eyes. </span><a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=7649714802782712487" name="Anchor-Radio-30540"></a><a href="http://astronomylearn.blogspot.com/p/glossary.html#radio"><span style="font-family: 'Times New Roman', Georgia, Times;"><b>Radio</b></span></a><b><span style="font-family: 'Times New Roman', Georgia, Times;">, <a href="http://astronomylearn.blogspot.com/p/glossary.html#infrared">infrared</a>,</span></b><span style="font-family: 'Times New Roman', Georgia, Times;"> and <a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=7649714802782712487" name="Anchor-ultraviolet-36058"></a><a href="http://astronomylearn.blogspot.com/p/glossary.html#ultraviolet"><b>ultraviolet</b></a> waves, as well as <a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=7649714802782712487" name="Anchor-46696"></a><a href="http://astronomylearn.blogspot.com/p/glossary.html#X ray"><b>X-rays</b></a> and <a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=7649714802782712487" name="Anchor-gamma-46575"></a><a href="http://astronomylearn.blogspot.com/p/glossary.html#gamma ray"><b>gamma rays,</b></a> all fall into this category. Recognize that, despite the different names, the words <i>light, rays,</i><i>radiation,</i> and <i>waves</i> really refer to the same thing. The names are just historical accidents, reflecting the fact that it took many years for scientists to realize that these apparently very different types of radiation are in reality one and the same physical phenomenon. Throughout this text, we will use the general terms "light" and "electromagnetic radiation" more or less interchangeably.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><b>WAVE MOTION</b></span><br />
<span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><b><br />
</b></span></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Despite the early confusion still reflected in current terminology, scientists now know that all types of electromagnetic radiation travel through space in the form of <i>waves</i>. To understand the behavior of light, then, we must know a little about wave motion.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><div style="text-align: justify;"><a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=7649714802782712487" name="Anchor-Simply-13440"></a><span style="font-family: 'Times New Roman', Georgia, Times;">Simply stated, a <a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=7649714802782712487" name="Anchor-wave-52360"></a><a href="http://astronomylearn.blogspot.com/p/glossary.html#wave"><b>wave</b></a> is a way in which energy is transferred from place to place without physical movement of material from one location to another. In wave motion, the energy is carried by a disturbance of some sort. This <i>disturbance,</i> whatever its nature, occurs in a distinctive repeating pattern. Ripples on the surface of a pond, sound waves in air, and electromagnetic waves in space, despite their many obvious differences, all share this basic defining property.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Imagine a twig floating in a pond. A pebble thrown into the pond at some distance from the twig disturbs the surface of the water, setting it into up-and-down motion. This disturbance will propagate outward from the point of impact in the form of waves. When the waves reach the twig, some of the pebble's energy will be imparted to it, causing the twig to bob up and down. In this way, both energy and <i>information</i>—the fact that the pebble entered the water—are transferred from the place where the pebble landed to the location of the twig. We could tell that a pebble (or, at least, some object) had entered the water just by observing the twig. With a little additional physics, we could even estimate the pebble's energy.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">A wave is not a physical object. No water traveled from the point of impact of the pebble to the twig—at any location on the surface, the water surface simply moved up and down as the wave passed. What, then, <i>did</i> move across the surface of the pond? As illustrated in Figure 3.2, the answer is that the wave was the <i>pattern</i> of up-and-down motion. This pattern was transmitted from one point to the next as the disturbance moved across the water.</span></div></div><center style="background-color: white;"><div style="text-align: -webkit-auto;"><br />
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<tr><td></td><td><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjYnTFnW9cBYLYqsIOgl4FEmeATULTGmdQ5dKZPkraI3aUx3wPXHvrN_6ELSt953auQMaqXXUopo-DzT-0m7CHJnUYRBvltGStoQXeBk0qTWMbLy3RE52ZLHNm2YwSXR_9H8fcpYLdL1ak/s1600/AACHCKT0.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjYnTFnW9cBYLYqsIOgl4FEmeATULTGmdQ5dKZPkraI3aUx3wPXHvrN_6ELSt953auQMaqXXUopo-DzT-0m7CHJnUYRBvltGStoQXeBk0qTWMbLy3RE52ZLHNm2YwSXR_9H8fcpYLdL1ak/s1600/AACHCKT0.JPG" /></a></div></td></tr>
<tr><td></td><td bgcolor="#fffad7"><div style="text-align: justify;"><span style="color: red; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>Figure 3.2 </b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>Water Wave </b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;">The passage of a wave across a pond causes the surface of the water to bob up and down, but there is no movement of water from one part of the pond to another. Here waves ripple out from the point where a pebble has hit the water to the point where a twig is floating. The inset shows schematically a series of "snapshots" of part of the pond surface as the wave passes by. The points numbered 1 through 5 represent nearby particles on the surface.</span></div></td></tr>
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<div style="background-color: white;"><span style="color: black; font-family: 'Times New Roman', Georgia, Times;"><br />
</span><br />
<div style="text-align: justify;"><span style="color: black; font-family: 'Times New Roman', Georgia, Times;">Figure 3.3</span><span style="font-family: 'Times New Roman', Georgia, Times;"> shows how wave properties are quantified and illustrates some standard terminology.<a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=7649714802782712487" name="Anchor-The-50585"></a>The <i>wave period</i> is the number of seconds needed for the wave to repeat itself at some point in space. </span><a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=7649714802782712487" name="Anchor-The-10572"></a><span style="font-family: 'Times New Roman', Georgia, Times;">The <a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=7649714802782712487" name="Anchor-wavelength-44601"></a><a href="http://astronomylearn.blogspot.com/p/glossary.html#wavelength"><b>wavelength</b></a> is the number of meters needed for the wave to repeat itself at a given moment in time. It can be measured as the distance between two adjacent wave <i>crests,</i> two adjacent wave <i>troughs,</i> or any other two similar points on adjacent wave cycles (for example, the points marked <img height="7" src="file:///G:/CHAISSON/COMART/MULTIP.GIF" width="7" /> in the figure). The maximum departure of the wave from the undisturbed state—still air, say, or a flat pond surface—is called its <b><a href="http://astronomylearn.blogspot.com/p/glossary.html#amplitude">amplitude.</a></b></span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=7649714802782712487" name="Anchor-The-20480"></a>The number of wave crests passing any given point per unit time is called the wave's <a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=7649714802782712487" name="Anchor-frequency-37417"></a><a href="http://astronomylearn.blogspot.com/p/glossary.html#frequency"><b>frequency</b></a>. If a wave of a given wavelength moves at high speed, then many crests pass per second and the frequency is high. Conversely, if the same wave moves slowly, then its frequency will be low. The frequency of a wave is just one divided by the wave's period:</span></div></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgApL7JZirnD7E1L-FG_r_L8qLvwieETQhK8qVPXtzybjrtktU5UtoioRZhxMGp74QB9MF8y5GUb9ah2ztEhllyflckyQzVmUVmqa3NdPMHNj_l6UEmrwq9IFbdqQlPor_vmAHqK2tX5O4/s1600/wave+frequency.GIF" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgApL7JZirnD7E1L-FG_r_L8qLvwieETQhK8qVPXtzybjrtktU5UtoioRZhxMGp74QB9MF8y5GUb9ah2ztEhllyflckyQzVmUVmqa3NdPMHNj_l6UEmrwq9IFbdqQlPor_vmAHqK2tX5O4/s1600/wave+frequency.GIF" /></a> </div><div style="text-align: justify;"><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div><div style="text-align: justify;"><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;">Frequency is expressed in units of inverse time (cycles per second), called hertz (Hz) in honor of the nineteenth-century German scientist Heinrich Hertz, who studied the properties of radio waves. Thus a wave with a period of 5 s has a frequency of (1/5) cycles/s = 0.2 Hz, meaning that one wave crest passes a given point in space every five seconds.</span></div><div style="background-color: white; text-align: left;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">A wave moves a distance equal to one wavelength in one wave period. <a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=7649714802782712487" name="Anchor-The-11516"></a>The product of wavelength and frequency therefore equals the <i>wave velocity:</i></span></div></div><br />
<center style="background-color: white;"><a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=7649714802782712487" name="Anchor-wavelength-11484"></a><span style="font-family: 'Times New Roman', Georgia, Times;">wavelength x frequency = velocity.</span></center><br />
<div style="background-color: white;"><div style="text-align: justify;"><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;">Thus, if the wave in our earlier example had a wavelength of 0.5 m, its velocity is (0.5 m) x (0.2 Hz) = 0.1 m/s. Wavelength and wave frequency are </span><i style="background-color: white; font-family: 'Times New Roman', Georgia, Times;">inversely</i><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;"> related—doubling one halves the other.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Before about 1800, scientists were divided in their opinions about the nature of light. Some believed that light was a wave phenomenon, while others maintained that light was in reality a stream of particles that moved in straight lines. Given the experimental apparatus available at the time, neither camp could find conclusive evidence to disprove the other theory. <i><a href="http://astronomylearn.blogspot.com/2012/02/discovery-31-wave-nature-of-radiation.html">Discovery 3-1</a> </i>discusses some more wave properties of importance to modern astronomers, and describes how their detection in experiments using visible light early in the nineteenth century finally tilted the balance of scientific opinion in favor of the wave theory.</span></div><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div><div style="background-color: white;"><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><b>THE COMPONENTS OF VISIBLE LIGHT</b></span><br />
<span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><b><br />
</b></span></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=7649714802782712487" name="Anchor-White-34172"></a>White light is a mixture of colors, which we conventionally divide into six major hues—red, orange, yellow, green, blue, and violet. As shown in Figure 3.4, we can separate a beam of white light into a rainbow of these basic colors—called a <i>spectrum</i> (plural, <i>spectra</i>)—by passing it through a prism. This experiment was first reported by Isaac Newton over 300 years ago. In principle, the original beam of white light could be recovered by passing the spectrum through a second prism to recombine the colored beams.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div align="left" style="background-color: white;"><div style="text-align: justify;"><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;">What determines the color of a beam of light? The answer is its frequency (or equivalently, its wavelength). We see different colors because our eyes react differently to electromagnetic waves of different frequencies. A prism splits a beam of light </span><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;">up into separate colors because light rays of different frequencies are bent, or </span><i style="background-color: white; font-family: 'Times New Roman', Georgia, Times;">refracted, </i><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;">slightly differently as they pass through the prism—red light the least, violet light the most. </span><a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=7649714802782712487" name="Anchor-Red-11970" style="background-color: white; font-family: 'Times New Roman', Georgia, Times;"></a><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;">Red light has a frequency of roughly 4.3 x</span><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;"> 10</span><sub style="background-color: white; font-family: 'Times New Roman', Georgia, Times;"><sup>14</sup> </sub><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;">Hz, corresponding to a wavelength of about 7.0 x</span><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;"> 10</span><sub style="background-color: white; font-family: 'Times New Roman', Georgia, Times;"><sup>-7</sup></sub><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;"> m. Violet light, at the other end of the visible range, has nearly double </span><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;">the frequency—7.5 x 10</span><sub style="background-color: white; font-family: 'Times New Roman', Georgia, Times;"><sup>14</sup></sub><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;"> Hz—and (since the speed of light is the same in either case) just over half the wavelength—</span><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;">4.0 x 10</span><sup style="background-color: white; font-family: 'Times New Roman', Georgia, Times;">-7</sup><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;"> m. The other colors we see have frequencies and wavelengths intermediate between these two extremes, spanning the entire </span><i style="background-color: white; font-family: 'Times New Roman', Georgia, Times;">visible spectrum</i><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;"> shown in Figure 3.4. Radiation outside this range is invisible to human eyes.</span></div></div><center style="background-color: white;"><table border="0" cellpadding="0" cellspacing="2" style="width: 137px;"><tbody>
<tr><td></td><td><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhl7NaKw7wDBlmdxeAX4j9sKbMCXTOqrN-EMMX-teMr5x_2_ETh75H-RTAtlI-66UowQtCHr_vSt_TkgW8kWhjNocEGYBhB8IVjOrFHnRUK_nUCb37xmmVBzW89Qet3I8GsUVir7CoR7is/s1600/AACHCKU0.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhl7NaKw7wDBlmdxeAX4j9sKbMCXTOqrN-EMMX-teMr5x_2_ETh75H-RTAtlI-66UowQtCHr_vSt_TkgW8kWhjNocEGYBhB8IVjOrFHnRUK_nUCb37xmmVBzW89Qet3I8GsUVir7CoR7is/s1600/AACHCKU0.JPG" /></a></div></td></tr>
<tr><td></td><td bgcolor="#fffad7"><div style="text-align: justify;"><span style="color: red; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>Figure 3.3</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b> Wave Properties</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;"> Representation of a typical wave, showing its direction of motion, wavelength, and amplitude. In one wave period, the entire pattern shown here moves one wavelength to the right.</span></div></td></tr>
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<div align="left" style="background-color: white;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span><br />
<div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Scientists often use a unit called the <i>nanometer</i> (nm) when describing the wavelength of light (see Appendix 2). There are 10<sup>9</sup> nanometers in one meter. An older unit called the <i>angstrom</i> (1 Å = 10<sup>-10</sup> m = 0.1 nm) is also widely used. (The unit is named after the nineteenth-century Swedish physicist Anders Ångstrom—pronounced "ong.strem.") However, in SI units, the nanometer is preferred. <a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=7649714802782712487" name="Anchor-Thus-25615"></a>Thus, the visible spectrum covers the wavelength range from 400 nm to 700 nm (4000 Å to 7000 Å). The radiation to which our eyes are most sensitive has a wavelength near the middle of this range, at about 550 nm (5500 Å), in the yellow-green region of the spectrum. It is no coincidence that this wavelength falls within the range of wavelengths at which the Sun emits most of its electromagnetic energy—our eyes have evolved to take greatest advantage of the available light.</span></div></div><br />
<center style="background-color: white;"> <table border="0" cellpadding="0" cellspacing="2" style="width: 137px;"><tbody>
<tr><td></td><td><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhobAQlUQBt9ysjvU-vPneVC5ShfFiLmnNSt58OmYtqM4biduQDe_hAAMSvk-dqyr_3ydsXnpGCh-aHyiOGKfDKShhGeAbHGtA6ZGnBN0ZlnxXBGjfEMQ7lXIQ6_fIEOyYWaVkpOdwig5A/s1600/AACHCKV0.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhobAQlUQBt9ysjvU-vPneVC5ShfFiLmnNSt58OmYtqM4biduQDe_hAAMSvk-dqyr_3ydsXnpGCh-aHyiOGKfDKShhGeAbHGtA6ZGnBN0ZlnxXBGjfEMQ7lXIQ6_fIEOyYWaVkpOdwig5A/s1600/AACHCKV0.JPG" /></a></div></td></tr>
<tr><td></td><td bgcolor="#fffad7"><div style="text-align: justify;"><span style="color: red; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>Figure 3.4 </b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>Visible Spectrum</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;"> While passing through a prism, white light splits into its component colors, spanning red to violet in the visible part of the electromagnetic spectrum. The slit narrows the beam of radiation. The image on the screen is just a series of different-colored images of the slit. Human eyes are insensitive to radiation of wavelength shorter than 400 nm or longer than 700 nm, but radiation outside the visible range is easily detected by other means.</span></div></td></tr>
</tbody></table></center>Andri F Martinhttp://www.blogger.com/profile/11669920311565328714noreply@blogger.com0tag:blogger.com,1999:blog-4374048443162882832.post-37539640569097601362012-02-14T16:15:00.004+07:002012-02-17T06:38:21.945+07:003. Radiation - Information From The Cosmos<h1 style="text-align: center;">Information From The Cosmos</h1><div style="text-align: center;"><br />
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</div><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhTJg098LOABrQEe1tnniZD5C4jtv3s23olY7I7-ZOLfykuysrMa-2bKn2n9vJrfRnqeUjTtqQT5Nzy-8cRRc5Wx5hiNBVf3R79R-lpMhaGKQUKXKWKo9b2F6SSuLdwrK6eFkyINCnYqOg/s1600/AACHCKR0.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhTJg098LOABrQEe1tnniZD5C4jtv3s23olY7I7-ZOLfykuysrMa-2bKn2n9vJrfRnqeUjTtqQT5Nzy-8cRRc5Wx5hiNBVf3R79R-lpMhaGKQUKXKWKo9b2F6SSuLdwrK6eFkyINCnYqOg/s1600/AACHCKR0.JPG" /></a> </div></td></tr>
<tr><td><div style="text-align: justify;"><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;">The Ring Nebula in the constellation Lyra is one of the most magnificent objects in our galaxy. Seen here glowing in the light of its own fading radiation, the nebula is actually the expanding atmosphere of a nearly dead star. That dying dwarf star can be seen at the center of the ring of hydrogen-rich gas, shown here in true color. Owing to the nebula's distance of some 5000 light-years, its apparent size is just 1/100<sup>th</sup> that of the full Moon. It is too dim to see with the naked eye. <i>(STScI)</i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;"><b>The Big Picture:</b> Stars evolve from birth to maturity to death, much like living things, but on vastly longer timescales. Our own star, the Sun, is about Mid-way through its evolution. In another 5 billion years, the Sun will swell late in life to resemble the object shown here. By that time, humanity will be long gone from Earth—either voluntarily, as our descendants move out into the wider Universe, or involuntarily, having perished in the atmosphere of our dying parent star. (<i>Astronomical Society of the Pacific</i>)</span></div></td></tr>
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</td><td><h2><span style="color: #0a50a1; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;">LEARNING GOALS</span></h2></td></tr>
<tr><td></td><td></td><td><span style="font-family: 'Times New Roman', Georgia, Times;">Studying this chapter will enable you to:</span></td></tr>
<tr><td align="right" valign="top"><a href="http://astronomylearn.blogspot.com/2012/02/32-waves-in-what.html#Anchor-Waves-59146" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJ54ymVCtThcMHbRD-h84NRSk2OQxJjBmCRuTKfEtRI5KTpQAQ9OXWz6DnCCAofySfOz6QHB3h8Mm8ukOqFqjacEWYuvN_r7Oi06R8IPqXzKkibJbrqPuawkNP_OIlIZV3ppVOb0Cv8Rg/s1600/LGICON_1.GIF" /></a> </td><td></td><td><span style="font-family: 'Times New Roman', Georgia, Times;">Discuss the nature of electromagnetic radiation, and tell how that radiation transfers energy and information through interstellar space.</span></td></tr>
<tr><td align="right" valign="top"><a href="http://astronomylearn.blogspot.com/2012/02/33-electromagnetic-spectrum.html#Anchor-Figure-23013" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhyIIQmfEvEcSnN3CVbR2KZeDq56rV0CWlw3kCv-niHq8DSP2AlR8tezxJRzOhvQc7fJVvPUS5f9xjMnFO7YCmVo6N0CS5ir15tGO6kE7d9ZmgAODnQK7pmF0Tt3z_-8Sij99rArgJlv_M/s1600/LGICON_2.GIF" /></a> </td><td></td><td><span style="font-family: 'Times New Roman', Georgia, Times;">Describe the major regions of the electromagnetic spectrum and explain how the properties of Earth's atmosphere affect our ability to make astronomical observations at different wavelengths.</span></td></tr>
<tr><td align="right" valign="top"><a href="http://astronomylearn.blogspot.com/2012/02/34-distribution-of-radiation.html#Anchor-All-12276" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjro4NwCtC2TCdCM0U8llIjQWPaqnmu4Nt2WLO_hJXMRRt6pjUDNl52NfT4zBngnC52mY9Jyz9gm_C7nhxdDYZ3UdXQFZmOhsitag5SnErKeorWf9nncczB8fnqqR0HGCan4k26Y0kL1QE/s1600/LGICON_3.GIF" /></a> </td><td></td><td><span style="font-family: 'Times New Roman', Georgia, Times;">Explain what is meant by the term "blackbody radiation" and describe the basic properties of such radiation.</span></td></tr>
<tr><td align="right" valign="top"><a href="http://astronomylearn.blogspot.com/2012/02/34-distribution-of-radiation.html#Anchor-The-22846" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi7BP-072_rJf_a6j879EXh5dxwRChAL8MSSshDxJzWKgCV2cYUdqSRcY23tVUo_GWcFSiHWLjAbp4wfdbu01NHbxUOL9_hspd1du6Q01LTVY6Hhfqhj5EeVEF5rC3DQJpcjtEjA-EjKwI/s1600/LGICON_4.GIF" /></a> </td><td></td><td><span style="font-family: 'Times New Roman', Georgia, Times;">Tell how we can determine the temperature of an object by observing the radiation that it emits.</span></td></tr>
<tr><td align="right" valign="top"><a href="http://astronomylearn.blogspot.com/2012/02/35-doppler-effect.html#Anchor-Imagine-2563" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMus-VgdsUWlWlS1YspJhgcuMhgoPjXpsJV32E2K0raiDUZWsjwyPqS70qD4vkwVFeTj_6f07XNkjZEOIljMKcxjpmHyXHzfOHxbee8BuVa-ErL6jD2cG9BVSmbdJ3DwcQgR8s27I1mX4/s1600/LGICON_5.GIF" /></a> </td><td></td><td><span style="font-family: 'Times New Roman', Georgia, Times;">Show how the relative motion of a source of radiation and its observer can change the perceived wavelength of the radiation, and explain the importance of this phenomenon to astronomy.</span></td></tr>
</tbody></table><span style="color: #e32e2a; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: large;"><b>A</b></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i>stronomical objects are more than just things of beauty in the night sky. Planets, stars, and galaxies are of vital significance if we are to fully understand our place in the big picture—the "grand design" of the universe. Each object is a source of information about the material aspects of our universe—its state of motion, its temperature, its chemical composition, even its past history. When we look at the stars, the light we see actually began its journey to Earth decades, centuries—even millennia—ago. The faint rays from the most distant galaxies have taken billions of years to reach us. The stars and galaxies in the night sky show us the far away and the long ago. In this chapter we begin our study of how astronomers extract information from the light emitted by astronomical objects. These basic concepts of radiation are central to modern astronomy.</i></span>Andri F Martinhttp://www.blogger.com/profile/11669920311565328714noreply@blogger.com0tag:blogger.com,1999:blog-4374048443162882832.post-50499679569467169322012-02-14T15:45:00.000+07:002012-02-14T15:45:12.207+07:00More Precisely 2.3 - Weighing The Sun<h1 style="text-align: center;">Weighing The Sun</h1><div style="text-align: justify;"><span style="background-color: #f8f8ee; font-family: 'Times New Roman', Georgia, Times;">We can use Newtonian mechanics to calculate some useful formula relating the properties of planetary orbits to the mass of the Sun. Again for simplicity, let’s assume that the orbits are circular (not a bad approximation in most cases, and Newton’s laws easily extend to cover the more general case of eccentric orbits). Consider a planet of mass </span><i style="background-color: #f8f8ee; font-family: 'Times New Roman', Georgia, Times;">m</i><span style="background-color: #f8f8ee; font-family: 'Times New Roman', Georgia, Times;"> moving at speed </span><i style="background-color: #f8f8ee; font-family: 'Times New Roman', Georgia, Times;">v</i><span style="background-color: #f8f8ee; font-family: 'Times New Roman', Georgia, Times;"> in an orbit of radius </span><i style="background-color: #f8f8ee; font-family: 'Times New Roman', Georgia, Times;">r</i><span style="background-color: #f8f8ee; font-family: 'Times New Roman', Georgia, Times;"> around the Sun, of mass M. The planet’s acceleration (see </span><i style="background-color: #f8f8ee; font-family: 'Times New Roman', Georgia, Times;">More Precisely 2-2</i><span style="background-color: #f8f8ee; font-family: 'Times New Roman', Georgia, Times;">) is</span></div><div style="text-align: justify;"><span style="background-color: #f8f8ee;"></span></div><br />
<center style="background-color: #f8f8ee;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh4Zjduv52as09FL7ytU7I76FBM6Q8tX8Kvp0_VopEm2cseZ0LmePe6TFHjcIBqEN-2mgjGzLWzuMibEjmIB4pDflIc-Cqj-Uos0Y8ktPNrN0LblBu7HHHr-SxiFKapobzePn80xm8VXMI/s1600/MP0203_F1.GIF" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh4Zjduv52as09FL7ytU7I76FBM6Q8tX8Kvp0_VopEm2cseZ0LmePe6TFHjcIBqEN-2mgjGzLWzuMibEjmIB4pDflIc-Cqj-Uos0Y8ktPNrN0LblBu7HHHr-SxiFKapobzePn80xm8VXMI/s1600/MP0203_F1.GIF" /></a> </center><br />
<div style="background-color: #f8f8ee;"><span style="font-family: 'Times New Roman', Georgia, Times;">so, by Newton’s second law, the force required to keep it in orbit is</span></div><br />
<center style="background-color: #f8f8ee;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEicDBCiX3AGv_pDDdTO4ObWudePop1SZC3f7HhS5BjW_LrF_JNAMUxiErexvE_cJG0iV1wYu9GvrHEMWjjMfUxRipBUKgLITD-ptq7mwNITmItM_u2Z5fbHIhq19rF-dTKRVRwd3zc9Dj0/s1600/MP0203_F2.GIF" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEicDBCiX3AGv_pDDdTO4ObWudePop1SZC3f7HhS5BjW_LrF_JNAMUxiErexvE_cJG0iV1wYu9GvrHEMWjjMfUxRipBUKgLITD-ptq7mwNITmItM_u2Z5fbHIhq19rF-dTKRVRwd3zc9Dj0/s1600/MP0203_F2.GIF" /></a> </center><br />
<div style="background-color: #f8f8ee;"><span style="font-family: 'Times New Roman', Georgia, Times;">Comparing this with the gravitational force due to the Sun, it follows that</span></div><br />
<center style="background-color: #f8f8ee;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhx3dWojTu1CKCaykK2ADBJ-yIjR31CXlKh977h-W3d8y2td_XwCV5J3MiwrUQ1StpILeG_pqwNgLyZnzk8jBTsgkrXy0mxoMWX5EJB5ryOKN2SXTmpbDhIRgooxIxnyHEp7XozWcl3-Ek/s1600/MP0203_F3.GIF" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhx3dWojTu1CKCaykK2ADBJ-yIjR31CXlKh977h-W3d8y2td_XwCV5J3MiwrUQ1StpILeG_pqwNgLyZnzk8jBTsgkrXy0mxoMWX5EJB5ryOKN2SXTmpbDhIRgooxIxnyHEp7XozWcl3-Ek/s1600/MP0203_F3.GIF" /></a> </center><br />
<div style="background-color: #f8f8ee;"><span style="font-family: 'Times New Roman', Georgia, Times;">so the circular orbit speed is</span></div><br />
<center style="background-color: #f8f8ee;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQTHc032ySJHsSRgjR9TSf2l69AwvC7CK5kw9mlPYCPt_37fJxJ3Vab93HDvFMcE6A4WTa1zfSRT_ilfNvcbk02EWXOn1cuTpaFgXnvRY1tektlFoAfknY8ygTOsBizG2NfwP0yF2RWhQ/s1600/MP0203_F4.GIF" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQTHc032ySJHsSRgjR9TSf2l69AwvC7CK5kw9mlPYCPt_37fJxJ3Vab93HDvFMcE6A4WTa1zfSRT_ilfNvcbk02EWXOn1cuTpaFgXnvRY1tektlFoAfknY8ygTOsBizG2NfwP0yF2RWhQ/s1600/MP0203_F4.GIF" /></a> </center><br />
<div style="background-color: #f8f8ee;"><span style="font-family: 'Times New Roman', Georgia, Times;">Dividing this speed into the circumference of the orbit (2</span>π<i style="font-family: 'Times New Roman', Georgia, Times;">r</i><span style="font-family: 'Times New Roman', Georgia, Times;">), we obtain a form of Kepler’s third law (equivalent to the formula presented in the text):</span></div><br />
<center style="background-color: #f8f8ee;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgHEqxbtnZLtVgfijLlWhpXWXzf4BUpuhvwYglKwGmygam2bedkzLZUeMuXL6qsZGUu8WQmG-xgYakw6e0Nis2j8P4DuiMGMtyshdCvRpIeO3LpTlU4hmY0Yww84zZVaIur8CCvVHQ5ISE/s1600/MP0203_F5.GIF" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgHEqxbtnZLtVgfijLlWhpXWXzf4BUpuhvwYglKwGmygam2bedkzLZUeMuXL6qsZGUu8WQmG-xgYakw6e0Nis2j8P4DuiMGMtyshdCvRpIeO3LpTlU4hmY0Yww84zZVaIur8CCvVHQ5ISE/s1600/MP0203_F5.GIF" /></a> </center><br />
<div align="left" style="background-color: #f8f8ee;"><span style="font-family: 'Times New Roman', Georgia, Times;">where <i>P</i> = 2</span>π<i style="font-family: 'Times New Roman', Georgia, Times;">r</i><span style="font-family: 'Times New Roman', Georgia, Times;">/</span><i style="font-family: 'Times New Roman', Georgia, Times;">v</i><span style="font-family: 'Times New Roman', Georgia, Times;"> is the orbital period.</span></div><div style="background-color: #f8f8ee;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Now we turn the problem around. Because we have measured G in the laboratory on Earth and because we know the length of a year and the size of the astronomical unit, we can use Newtonian mechanics to <i>weigh</i> the Sun. Rearranging the above equation to read</span></div></div><br />
<center style="background-color: #f8f8ee;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEim6RiiwrAJZaICUpvKPb5e3P1Z6SGvbPshaHo-mcHiFH2bQ0Xm4FHfA85Pib8D5wQwj-Nh3BOgBHHIxAmofonhrQKlcfWWQkR_0qt-AMhgqc8mfHCJlzJ_e47HTr2Z1rVKnWf-Ev-TAm4/s1600/MP0203_F6.GIF" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEim6RiiwrAJZaICUpvKPb5e3P1Z6SGvbPshaHo-mcHiFH2bQ0Xm4FHfA85Pib8D5wQwj-Nh3BOgBHHIxAmofonhrQKlcfWWQkR_0qt-AMhgqc8mfHCJlzJ_e47HTr2Z1rVKnWf-Ev-TAm4/s1600/MP0203_F6.GIF" /></a> </center><br />
<div style="background-color: #f8f8ee;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">and substituting the known values of<i> v</i> = 30 km/s, <i>r</i> = 1 A.U. = 1.5 x 10<sup>11</sup> m, and <i>G</i> = 6.7 x10<sup>-11</sup> N m<sup>2</sup>/kg<sup>2</sup>, we calculate the mass of the Sun to be 2.0 x 10<sup>30</sup> kg—an enormous mass by terrestrial standards. Similarly, knowing the distance to the Moon and the length of the (sidereal) month, we can measure the mass of Earth to be 6.0 x 10<sup>24</sup> kg.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: #f8f8ee;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">In fact, this is how basically <i>all</i> masses are measured in astronomy. Because we can’t just go out and attach a scale to an astronomical object when we need to know its mass, we must look for its gravitational influence on something else. This principle applies to planets, stars, galaxies, and even clusters of galaxies—very different objects but all subject to the same physical laws.</span></div></div>Andri F Martinhttp://www.blogger.com/profile/11669920311565328714noreply@blogger.com0tag:blogger.com,1999:blog-4374048443162882832.post-88763722645303433702012-02-14T15:37:00.000+07:002012-02-14T15:37:48.137+07:00More Precisely 2.2 - The Moon Is Falling!<h1 style="text-align: center;">The Moon Is Falling!</h1><span style="background-color: #f8f8ee; font-family: 'Times New Roman', Georgia, Times; text-align: justify;">The story of Isaac Newton seeing an apple fall to the ground and "discovering" gravity is well known, in one form or another, to most high-school students. However, the real importance of Newton’s observation was his realization that, by observing falling bodies on Earth and elsewhere, he could </span><i style="background-color: #f8f8ee; font-family: 'Times New Roman', Georgia, Times; text-align: justify;">quantify</i><span style="background-color: #f8f8ee; font-family: 'Times New Roman', Georgia, Times; text-align: justify;"> the properties of the gravitational force and deduce the mathematical form of his law of gravitation.</span><br />
<div style="text-align: justify;"><span style="background-color: #f8f8ee;"></span></div><div style="text-align: justify;"><span style="background-color: #f8f8ee; font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div><div style="background-color: #f8f8ee;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Galileo Galilei had demonstrated some years earlier, by the simple experiment of dropping different objects from a great height (the top of the Tower of Pisa, according to lore) and noting that they hit the ground at the same time (at least, to the extent that air resistance was unimportant), that gravity causes the <i>same</i> acceleration in all bodies, regardless of mass. Since acceleration is proportional to force divided by mass (Newton’s second law), this meant that the gravitational force on one body due to another had to be directly proportional to the first body’s mass. Applying the same reasoning to the other body and using Newton’s third law, it follows that the force must also be proportional to the mass of the second body, hence the two "mass" terms in the law of gravity. (The experimental finding that the gravitational force is precisely proportional to mass is now known as the <i>equivalence principle.</i> It forms an essential part of the modern theory of gravity; see <a href="http://astronomylearn.blogspot.com/"><i>More Precisely 22-1</i></a>).</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: #f8f8ee;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">What about the "inverse-square" part of Newton’s law? At Earth’s surface, the acceleration due to gravity is approximately 9.80 m/s<sup>2</sup>. It is denoted by the letter <i>g</i>. Where else other than on Earth could a falling body be seen? As illustrated in the accompanying figures, Newton realized that he could tell how gravity varies with distance by studying another object influenced by our planet’s gravity—the Moon. Here’s how he did it.</span></div></div><br />
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<div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Let’s assume for the sake of simplicity that the Moon’s orbit around Earth is circular. As shown in the second figure, even though the Moon’s orbital <i>speed</i> is constant, its <i>velocity</i> (red arrows) is not—the direction of the Moon’s motion is steadily changing. In other words, the Moon is <i>accelerating,</i> constantly falling toward Earth. In fact, the acceleration of any body moving with speed <i>v</i> in a circular orbit of radius <i>r</i> may be shown to be</span></div></div><br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgo3KbAplIbMFWLDW5foZKMdVEvMO6aygieGcEb3NICzDTKNy4mGDVoAvM-agzYxC6nRG5P8ej7v3q_0Ho9g3eMCnlgAvuRm4bAvMb9mTUdcUu6vAUM-ZdsVjWRLVOge90W3BFNrcuFYbc/s1600/MP2-2_Equation.GIF" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgo3KbAplIbMFWLDW5foZKMdVEvMO6aygieGcEb3NICzDTKNy4mGDVoAvM-agzYxC6nRG5P8ej7v3q_0Ho9g3eMCnlgAvuRm4bAvMb9mTUdcUu6vAUM-ZdsVjWRLVOge90W3BFNrcuFYbc/s1600/MP2-2_Equation.GIF" /></a> </div><br />
<div style="background-color: #f8f8ee;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">always directed toward the center of the circle (toward Earth, in the case of the Moon). This acceleration is sometimes called <i>centripetal</i> ("center-seeking") acceleration. You probably already have an intuitive experience for this equation—just think of the acceleration you feel as you take a tight corner (small <i>r</i>) at high speed (large <i>v</i>) in your car.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: #f8f8ee;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Knowing the Moon’s distance <i>r</i> = 384,000 km (measured by triangulation), and the Moon’s sidereal orbit period <i>P</i> = 27.3 days, Newton computed the Moon’s orbital speed <i>v</i> = 2</span>π<i style="font-family: 'Times New Roman', Georgia, Times;">r</i><span style="font-family: 'Times New Roman', Georgia, Times;">/</span><i style="font-family: 'Times New Roman', Georgia, Times;">P</i><span style="font-family: 'Times New Roman', Georgia, Times;"> = 1.02 km/s, and hence determined its acceleration to be a = 0.00272 m/s</span><sup style="font-family: 'Times New Roman', Georgia, Times;">2</sup><span style="font-family: 'Times New Roman', Georgia, Times;">, or 0.000278 g. </span><a href="http://astronomylearn.blogspot.com/2012/02/more-precisely-14-measuring-distances.html" style="font-family: 'Times New Roman', Georgia, Times;"><i>(More Precisely 1-4)</i></a><span style="font-family: 'Times New Roman', Georgia, Times;"> Thus, Newton found, the Moon, lying 60 times farther from Earth’s center than the apple falling from the tree in his garden (taking Earth’s radius to be 6400 km), experiences an acceleration 3600, or 60</span><sup style="font-family: 'Times New Roman', Georgia, Times;">2</sup><span style="font-family: 'Times New Roman', Georgia, Times;">, times smaller. In other words, </span><i style="font-family: 'Times New Roman', Georgia, Times;">the acceleration due to gravity is inversely proportional to the square of the distance.</i><span style="font-family: 'Times New Roman', Georgia, Times;"> Isaac Newton’s application of simple geometric reasoning and some very basic laws of motion resulted in a breakthrough that would revolutionize astronomers’ view of the solar system, and pave the way for humanity’s exploration of the universe.</span></div></div>Andri F Martinhttp://www.blogger.com/profile/11669920311565328714noreply@blogger.com0tag:blogger.com,1999:blog-4374048443162882832.post-61409136156029066362012-02-14T15:11:00.000+07:002012-02-14T15:50:28.842+07:002.7 Newton’s Laws<h1 style="text-align: center;">Newton's Laws</h1><div style="background-color: white;"><span style="font-family: 'Times New Roman', Georgia, Times;"></span></div><table align="right" border="0" cellpadding="0" cellspacing="2" style="width: 137px;"><tbody>
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<tr><td><img height="6" src="file:///G:/CHAISSON/COMART/SPACER.GIF" width="10" /></td><td bgcolor="#fffad7"><div style="text-align: justify;"><span style="color: #e32e3a; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>Figure 2.17</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b> Isaac Newton</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;">(1642–1727). <i>(The Granger Collection)</i></span></div></td></tr>
</tbody></table><div style="text-align: justify;"><a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=6140913615602906636" name="Anchor-30659"></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEik3-BU1cuvDBK61-D3K3EW1N947Tb03GMll6i_Q8iZk-Cp3NL3JajDlJlSTb7rfDUICguyQiu1LBH2QL-ezAK6Xet9290zUb60eUVZPIkxm6nbXWTh9YPak72ibH-EXf0aMu9llA-VczY/s1600/LGICON_7.GIF" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEik3-BU1cuvDBK61-D3K3EW1N947Tb03GMll6i_Q8iZk-Cp3NL3JajDlJlSTb7rfDUICguyQiu1LBH2QL-ezAK6Xet9290zUb60eUVZPIkxm6nbXWTh9YPak72ibH-EXf0aMu9llA-VczY/s1600/LGICON_7.GIF" /></a><span style="font-family: 'Times New Roman', Georgia, Times;">Kepler's three laws, which so simplified the solar system, were discovered <i>empirically.</i> In other words, they resulted solely from the analysis of observational data and were not derived from any theory or mathematical model. Indeed, Kepler did not have any appreciation for the physics underlying his laws. Nor did Copernicus understand the basic reasons <i>why</i> his heliocentric model of the solar system worked. Even Galileo, often called the father of modern physics, failed to understand why the planets orbit the Sun (although Galileo's work laid vital groundwork for Newton's theories—see <a href="http://astronomylearn.blogspot.com/2012/02/more-precisely-22-moon-is-falling.html"><i>More Precisely 2-2</i></a>).</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">What prevents the planets from flying off into space or from falling into the Sun? What causes them to revolve about the Sun, apparently endlessly? To be sure, the motions of the planets obey Kepler's three laws, but only by considering something more fundamental than those laws can we really understand these motions. The heliocentric system was secured when, in the seventeenth century, the British mathematician Isaac Newton (Figure 2.17) developed a deeper understanding of the way <i>all</i> objects move and interact with one another as they do.</span></div></div><h4 style="background-color: white;"><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;">THE LAWS OF MOTION</span></h4><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Isaac Newton was born in Lincolnshire, England, on Christmas Day in 1642, the year Galileo died. Newton studied at Trinity College of Cambridge University, but when the bubonic plague reached Cambridge in 1665, he returned to the relative safety of his home for two years. During that time he made probably the most famous of his discoveries, the law of gravity (although it is but one of the many major scientific advances for which Newton was responsible). However, either because he regarded the theory as incomplete or possibly because he was afraid that he would be attacked or plagiarized by his colleagues, he did not tell anyone of his monumental achievement for almost 20 years. It was not until 1684, when Newton was discussing with Edmund Halley (of Halley's comet fame) the leading astronomical problem of the day—Why do the planets move according to Kepler's laws?—that he astounded his companion by revealing that he had solved the problem in its entirety nearly two decades before!.</span></div><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div><div style="background-color: white;"><div style="text-align: justify;"><a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=6140913615602906636" name="Anchor-Prompted-37241"></a><span style="font-family: 'Times New Roman', Georgia, Times;">Prompted by Halley, Newton published his theories in perhaps the most influential physics book ever written: <i>Philosophiae Naturalis Principia Mathematica</i> (<i>The Mathematical Principles of Natural Philosophy</i>—what we would today call "science"), usually known simply as Newton's<i>Principia.</i> The ideas expressed in that work form the basis for what is now known as <a href="http://astronomylearn.blogspot.com/p/glossary.html#Newtonian mechanics"><b>Newtonian mechanics</b></a>. Three basic laws of motion, the law of gravity, and a little calculus (which Newton also developed) are sufficient to explain and quantify virtually all the complex dynamic behavior we see on Earth and throughout the universe.</span></div></div><blockquote style="background-color: white;"><span style="font-family: 'Times New Roman', Georgia, Times;"><a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=6140913615602906636" name="Anchor-Figure-7671"></a>Figure 2.18 illustrates <i>Newton's</i> <i>first law of motion</i>:</span><br />
<div style="text-align: justify;"><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;">I. Every body continues in a state of rest or in a state of uniform motion in a straight line unless it is compelled to change that state by a force acting on it.</span></div></blockquote><br />
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<tr><td bgcolor="#fffad7"><div style="text-align: justify;"><span style="color: #e32e3a; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>Figure 2.18</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b> Newton's First Law</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;"> An object at rest will remain at rest (a) until some force acts on it (b). It will then remain in that state of uniform motion until another force acts on it. The arrow in (c) shows a second force acting at a direction different from the first, which causes the object to change its direction of motion.</span></div></td></tr>
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<div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=6140913615602906636" name="Anchor-The-56658"></a>The first law simply states that a moving object will move forever in a straight line unless some external <a href="http://astronomylearn.blogspot.com/p/glossary.html#force"><b>force</b></a>—a push or a pull—changes its direction of motion. For example, the object might glance off a brick wall or be hit with a baseball bat; in either case, a force changes the original motion of the object. The tendency of an object to keep moving at the same speed and in the same direction unless acted upon by a force is known as <a href="http://astronomylearn.blogspot.com/p/glossary.html#inertia"><b>inertia</b></a>. A familiar measure of an object's inertia is its <a href="http://astronomylearn.blogspot.com/p/glossary.html#mass"><b>mass</b></a>—loosely speaking, the total amount of matter it contains. The greater an object's mass, the more inertia it has, and the greater is the force needed to change its state of motion.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Newton's first law implies that it requires no force to maintain motion in a straight line with<i>constant velocity</i>—that is, motion with constant speed and constant direction in space. This contrasts sharply with the view of Aristotle, who maintained (incorrectly) that the natural state of an object was to be <i>at rest</i>—most probably an opinion based on Aristotle's observations of the effect of friction. In our discussion we will neglect friction—the force that slows balls rolling along the ground, blocks sliding across tabletops, and baseballs moving through the air. In any case, it is not an issue for the planets because there is no appreciable friction in outer space. The fallacy in Aristotle's argument was first realized and exposed by Galileo, who conceived of the notion of inertia long before Newton formalized it into a law.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=6140913615602906636" name="Anchor-The-61176"></a>The rate of change of the velocity of an object—speeding up, slowing down, or simply changing direction—is called its <a href="http://astronomylearn.blogspot.com/p/glossary.html#acceleration"><b>acceleration</b></a>, and is the subject of <i>Newton's second law,</i> which states that the acceleration of an object is directly proportional to the applied force and inversely proportional to its mass:</span></div></div><blockquote style="background-color: white;"><div style="text-align: justify;"><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;">II. When a force <i>F</i> acts on a body of mass <i>m,</i> it produces in it an acceleration a equal to the force divided by the mass. Thus, <i>a</i> = <i>F/m,</i> or <i>F</i> =<i>ma.</i></span></div></blockquote><div style="background-color: white;"><span style="font-family: 'Times New Roman', Georgia, Times;"></span></div><table align="right" border="0" cellpadding="0" cellspacing="2" style="width: 134px;"><tbody>
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<tr><td><img height="6" src="file:///G:/CHAISSON/COMART/SPACER.GIF" width="10" /></td><td bgcolor="#fffad7"><div style="text-align: justify;"><span style="color: #e32e3a; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>Figure 2.19</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b> Gravity</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;"> A ball thrown up from the surface of a massive object such as a planet is pulled continuously by the gravity of that planet (and, conversely, the gravity of the ball continuously pulls the planet).</span></div></td></tr>
</tbody></table><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Thus, the greater the force acting on the object, or the smaller the mass of the object, the greater its acceleration. If two objects are pulled with the same force, the more massive one will accelerate less; if two identical objects are pulled with different forces, the one experiencing the greater force will accelerate more. In honor of Newton, the SI unit of force is named after him. By definition, 1 newton (N) is the force required to cause a mass of 1 kilogram to accelerate at a rate of one meter per second every second (1 m/s<sup>2</sup>). One newton is approximately 0.22 pounds.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Finally, <i>Newton's third law</i> simply tells us that forces cannot occur in isolation:</span></div></div><blockquote style="background-color: white;"><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;">III. To every action there is an equal and opposite reaction.</span></blockquote><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">In other words, if body A exerts a force on body B, then body B necessarily exerts a force on body A that is equal in magnitude, but oppositely directed.</span></div><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Only in extreme circumstances—when velocities approach the speed of light—do Newton's laws break down, and this fact was not realized until the twentieth century, when Albert Einstein's theories of relativity once again revolutionized our view of the universe (see Chapter 22). Most of the time, however, Newtonian mechanics provides an excellent description of the motion of planets, stars, and galaxies through the cosmos.</span></div></div><h4 style="background-color: white;"><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=6140913615602906636" name="Anchor-GRAVITY-17864"></a>GRAVITY</span></h4><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Forces may act <i>instantaneously</i> or <i>continuously.</i> The force from a baseball bat that hits a home run can be thought of as being instantaneous. A good example of a continuous force is the one that prevents the baseball from zooming off into space—<a href="http://astronomylearn.blogspot.com/p/glossary.html#gravity"><b>gravity</b></a>, the phenomenon that started Newton on the path to the discovery of his laws. Newton hypothesized that any object having mass always exerts an attractive <i>gravitational force</i> on all other massive objects. The more massive an object, the stronger its gravitational pull.</span></div><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=6140913615602906636" name="Anchor-Consider-19041"></a>Consider a baseball thrown upward from Earth's surface, as illustrated in Figure 2.19. In accordance with Newton's first law, the downward force of Earth's gravity continuously modifies the baseball's velocity, slowing the initial upward motion and eventually causing the ball to fall back to the ground. Of course, the baseball, having some mass of its own, also exerts a gravitational pull on Earth. By Newton's third law, this force is equal and opposite to the <i>weight</i> of the ball (the force with which Earth attracts it). But, by Newton's second law, Earth has a much greater effect on the light baseball than the baseball has on the much more massive Earth. The ball and Earth feel the same gravitational force, but Earth's <i>acceleration</i> is much smaller.</span></div></div><div style="background-color: white;"><span style="font-family: 'Times New Roman', Georgia, Times;"></span></div><table align="right" border="0" cellpadding="0" cellspacing="2" style="width: 137px;"><tbody>
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</div><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_vaHWZhQ_lXtfBCPE2Nx80R3nH-XsrT2VQRdLUx-CVzumJZ2tdCsUBudMRT_InMcKPOs5i_bRxQRgZucdxp90ZRK1v-FKFiUgomGTUVGyoV-tXfgD4Sx-YUF4bHZDUCtOYhEaaJKc9wo/s1600/AACHCKI0.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_vaHWZhQ_lXtfBCPE2Nx80R3nH-XsrT2VQRdLUx-CVzumJZ2tdCsUBudMRT_InMcKPOs5i_bRxQRgZucdxp90ZRK1v-FKFiUgomGTUVGyoV-tXfgD4Sx-YUF4bHZDUCtOYhEaaJKc9wo/s1600/AACHCKI0.JPG" /></a></td></tr>
<tr><td><img height="6" src="file:///G:/CHAISSON/COMART/SPACER.GIF" width="10" /></td><td bgcolor="#fffad7"><div style="text-align: justify;"><span style="color: #e32e3a; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>Figure 2.20</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b> Gravitational Force</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;"> (a) The gravitational force between two bodies is proportional to the mass of each and is inversely proportional to the square of the distance between them. (b) Inverse-square forces rapidly weaken with distance from their source. The strength of the gravitational force decreases with the square of the distance from the Sun, but never quite reaches zero, no matter how far away from the Sun.</span></div></td></tr>
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</span><br />
<div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=6140913615602906636" name="Anchor-Now-15330"></a>Now consider the trajectory of the same baseball batted from the surface of the Moon. The pull of gravity is about one-sixth as great on the Moon as on Earth, so the baseball's velocity changes more slowly—a typical home run in a ballpark on Earth would travel nearly half a mile on the Moon. The Moon, less massive than Earth, has less gravitational influence on the baseball. The magnitude of the gravitational force, then, depends on the<i>masses</i> of the attracting bodies. In fact, the force is <i>directly proportional</i> to the product of the two masses.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=6140913615602906636" name="Anchor-Studying-38380"></a>Studying the motions of the planets reveals a second aspect of the gravitational force. At locations equidistant from the Sun's center, the gravitational force has the same strength, and it is always directed toward the Sun. Furthermore, detailed calculation of the planets' accelerations as they orbit the Sun reveals that the strength of the Sun's gravitational pull decreases in proportion to the <i>square</i> of the distance from the Sun. (See also <a href="http://astronomylearn.blogspot.com/2012/02/more-precisely-22-moon-is-falling.html"><i>More Precisely 2-2</i></a> for the line of reasoning that originally led Newton to this conclusion.) The force of gravity is said to obey an <a href="http://astronomylearn.blogspot.com/p/glossary.html#inverse-square law"><b>inverse-square law</b></a>. As shown in Figure 2.20(b), inverse-square forces decrease rapidly with distance from their source. For example, tripling the distance makes the force 3<sup>2</sup> = 9 times weaker, while multiplying the distance by five results in a force that is 5<sup>2</sup> = 25 times weaker. Despite this rapid decrease, the force never quite reaches zero. The gravitational pull of an object having some mass can never be completely extinguished.</span></div></div><div style="background-color: white;"><a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=6140913615602906636" name="Anchor-We-49414"></a><span style="font-family: 'Times New Roman', Georgia, Times;">We can combine the preceding statements about mass and distance to form a law of gravity that dictates the way in which <i>all</i> material objects attract one another:</span></div><blockquote style="background-color: white;"><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;">Every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of the masses of the particles and inversely proportional to the square of the distance between them.</span></blockquote><div style="background-color: white;"><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;">As a proportionality, Newton's law of gravity is</span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxxDKR96yUjv0ymdDNngQinEwRkFDzyqAVrUeqvAYah8Bs4Z2kdFKNAhvy70nBxwDw1QK5NWih4t8LUxGsrbWuJjmkGL3csOq6yBAiF2-3dDx5eAfB4VuxxkGz-t2sX-hmvOZ-xgU3z3s/s1600/07+Equation+1.GIF" imageanchor="1" style="background-color: white; margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxxDKR96yUjv0ymdDNngQinEwRkFDzyqAVrUeqvAYah8Bs4Z2kdFKNAhvy70nBxwDw1QK5NWih4t8LUxGsrbWuJjmkGL3csOq6yBAiF2-3dDx5eAfB4VuxxkGz-t2sX-hmvOZ-xgU3z3s/s1600/07+Equation+1.GIF" /></a></div><div style="background-color: white;"><div class="separator" style="clear: both; text-align: center;"><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;">(The symbol</span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjKeKAe00lzqWmcKTk5UadPLugGJPicRV9YqoaoEoF_UbSxRN-fB5N3VoRlvj2bSnxBL-N9P9LXKGL4Q3zYk5fVpEFxh6r9_O5aHrdRiEUFjrwg1JEesdYYnvhl5d9Qn4HhP_v3jWJBGM0/s1600/INFINITY.GIF" imageanchor="1" style="background-color: white; margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjKeKAe00lzqWmcKTk5UadPLugGJPicRV9YqoaoEoF_UbSxRN-fB5N3VoRlvj2bSnxBL-N9P9LXKGL4Q3zYk5fVpEFxh6r9_O5aHrdRiEUFjrwg1JEesdYYnvhl5d9Qn4HhP_v3jWJBGM0/s1600/INFINITY.GIF" /></a><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;"> here means "is proportional to.") The rule for computing the force <i>F</i> between two bodies of masses <i>m</i><sub>1</sub> and <i>m</i><sub>2</sub>, separated by distance <i>r</i>, is usually written more compactly as</span></div></div><br />
<center style="background-color: white;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhE8ditKdwi78COcn0IohsLiNxEzc7TPj47VlI5wdMCg833qtmRQJGWIRvD2i5ONwhZ4GXfKamzAhHwVFblBeC91jVCOFeRZuSveuskgsN6f19lp2u2Zo8009V_fUhqvrTdMOqWT6WciEY/s1600/07+Equation+2.GIF" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhE8ditKdwi78COcn0IohsLiNxEzc7TPj47VlI5wdMCg833qtmRQJGWIRvD2i5ONwhZ4GXfKamzAhHwVFblBeC91jVCOFeRZuSveuskgsN6f19lp2u2Zo8009V_fUhqvrTdMOqWT6WciEY/s1600/07+Equation+2.GIF" /></a> </center><br />
<div style="background-color: white;"><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;">The quantity </span><i style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;">G</i><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;"> is known as the </span><i style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;">gravitational constant,</i><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;"> or often simply as Newton's constant. It is one of the fundamental constants of the universe. Its value has been measured in extremely delicate laboratory experiments as</span><br />
<span style="font-family: 'Times New Roman', Georgia, Times;"> 6.67 x 10<sup>-11</sup> newton meter<sup>2</sup>/kilogram<sup>2</sup> (N m<sup>2</sup>/kg<sup>2</sup>).</span></div><div style="background-color: white;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span><br />
<div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=6140913615602906636" name="Anchor-To-50504"></a>To Newton, gravity was a force that acted at a distance, with no obvious way in which it was actually transmitted from place to place. Newton was not satisfied with this explanation, but he had none better. To appreciate the modern view of gravity, consider any piece of matter having some mass—it could be smaller than an atom or larger than a galaxy. Extending outward from this object in all directions is a <a href="file:///G:/CHAISSON/GLOSSARY/GLOSS_G.HTM#gravitational field"><b>gravitational field</b></a> produced by the matter. We now regard such a field as a property of space itself—a property that determines the influence of one massive object on another. All other matter "feels" the field as a gravitational force.</span></div></div><h4 style="background-color: white;"><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><table align="right" bgcolor="white" border="0" cellpadding="0" cellspacing="2" style="width: 137px;"><tbody>
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</div><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXTPDxswwL7tVYxlb3PeJ6xQte7yenZYTa6UVPwJKNSTQR6Ls4kNKjheNb54VCrFNm2R0IvncdEOjvpvvITqdFQ6V2xPnLSzAYHUbaX4luXP6gpkhSYcJ_DhBwH7xwY2bul0RUgaqy9J8/s1600/AACHCKJ0.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXTPDxswwL7tVYxlb3PeJ6xQte7yenZYTa6UVPwJKNSTQR6Ls4kNKjheNb54VCrFNm2R0IvncdEOjvpvvITqdFQ6V2xPnLSzAYHUbaX4luXP6gpkhSYcJ_DhBwH7xwY2bul0RUgaqy9J8/s1600/AACHCKJ0.JPG" /></a></td></tr>
<tr><td><img height="6" src="file:///G:/CHAISSON/COMART/SPACER.GIF" width="10" /></td><td bgcolor="#fffad7"><div style="text-align: justify;"><span style="color: #e32e3a; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>Figure 2.21</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b> Solar Gravity</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;"> The Sun's inward pull of gravity on a planet competes with the planet's tendency to continue moving in a straight line. These two effects combine, causing the planet to move smoothly along an intermediate path, which continually "falls around" the Sun. This unending tug-of-war between the Sun's gravity and the planet's inertia results in a stable orbit.</span></div></td></tr>
</tbody></table></span><a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=6140913615602906636" name="Anchor-PLANETARY-2565"></a><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;">PLANETARY MOTION</span></h4><div style="background-color: white;"><div style="text-align: justify;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_DZeSrIDuEyRs8PmJx8eceoykVt4q9O3U_GXyZZ1w_pV7-5XRsmO7mLE2UvufGafIz7v3U7bw_4QoaqSMbaMd251qE_tcOV40pJyUF3eQ9LQtkp0vSey0Uk-rUz1enLfjroGlzYkeYVs/s1600/LGICON_8.GIF" imageanchor="1" style="background-color: white; margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_DZeSrIDuEyRs8PmJx8eceoykVt4q9O3U_GXyZZ1w_pV7-5XRsmO7mLE2UvufGafIz7v3U7bw_4QoaqSMbaMd251qE_tcOV40pJyUF3eQ9LQtkp0vSey0Uk-rUz1enLfjroGlzYkeYVs/s1600/LGICON_8.GIF" /></a><span style="font-family: 'Times New Roman', Georgia, Times;">The mutual gravitational attraction between the Sun and the planets, as expressed by Newton's law of gravity, is responsible for the observed planetary orbits. As depicted in Figure 2.21, this gravitational force continuously pulls each planet toward the Sun, deflecting its forward motion into a curved orbital path. Because the Sun is much more massive than any of the planets, it dominates the interaction. We might say that the Sun "controls" the planets, not the other way around.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">The Sun–planet interaction sketched here is analogous to what occurs when you whirl a rock at the end of a string above your head. The Sun's gravitational field is your hand and the string, and the planet is the rock at the end of that string. The tension in the string provides the force necessary for the rock to move in a circular path. </span><a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=6140913615602906636" name="Anchor-If-11681"></a><span style="font-family: 'Times New Roman', Georgia, Times;">If you were suddenly to release the string—which would be like eliminating the Sun's gravity—the rock would fly away along a tangent to the circle, in accordance with Newton's first law.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">In the solar system, at this very moment, Earth is moving under the combined influence of these two effects: the competition between gravity and inertia. The net result is a stable orbit, despite our continuous rapid motion through space. (In fact, Earth orbits the Sun at a speed of about 30 km/s, or about 70,000 mph. Verify this for yourself by calculating how fast Earth must move to complete a circle of radius 1 A.U.—and hence of circumference 2</span><span style="background-color: white;">π</span><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;"> A.U., or 940 million km—in 1 year, or 3.2 x</span><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;"> 10</span><sup style="background-color: white; font-family: 'Times New Roman', Georgia, Times;">7</sup><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;"> seconds. The answer is 9.4 x</span><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;"> 10</span><sup style="background-color: white; font-family: 'Times New Roman', Georgia, Times;">8</sup><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;"> km/3.2 x</span><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;"> 10</span><sup style="background-color: white; font-family: 'Times New Roman', Georgia, Times;">7 </sup><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;">s, or 29.4 km/s.) </span><i style="background-color: white; font-family: 'Times New Roman', Georgia, Times;"><a href="http://astronomylearn.blogspot.com/2012/02/more-precisely-23-weighing-sun.html">More Precisely 2-3</a> </i><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;">describes how astronomers can use Newtonian mechanics and the law of gravity to quantify planetary motion and measure the masses of Earth, the Sun, and many other astronomical objects by studying the orbits of objects near them.</span></div></div><h4 style="background-color: white;"><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><table align="right" border="0" cellpadding="0" cellspacing="2" style="width: 134px;"><tbody>
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<tr><td><img height="6" src="file:///G:/CHAISSON/COMART/SPACER.GIF" width="10" /></td><td bgcolor="#fffad7"><div style="text-align: justify;"><span style="color: #e32e3a; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>Figure 2.22</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b> Orbits</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;"> (a) The orbits of two bodies (stars, for example) with equal masses, under the influence of their mutual gravity, are identical ellipses with a common focus. That focus is not at the center of either star but instead is located at the center of mass of the pair, midway between them. The positions of the two bodies at three different times are indicated by the pairs of numbers. (Notice that a line joining the bodies always passes through the common focus.) (b) The orbits of two bodies, one of which is twice as massive as the other. Again, the elliptical orbits have a common focus, and the two ellipses have the same eccentricity. However, in accordance with Newton's laws of motion, the more massive body moves more slowly, and in a smaller orbit, staying closer to the center of mass (at the common focus). In this particular case, the larger ellipse is twice the size of the smaller one. (c) In this extreme case of a hypothetical planet orbiting the Sun, the common focus of the two orbits lies inside the Sun.</span></div></td></tr>
</tbody></table><a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=6140913615602906636" name="Anchor-31961"></a>KEPLER'S LAWS RECONSIDERED</span></h4><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=6140913615602906636" name="Anchor-22883"></a>Newton's laws of motion and the law of universal gravitation provided a theoretical explanation for Kepler's empirical laws of planetary motion. Kepler's three laws follow directly from Newtonian mechanics, as solutions to the equations describing the motion of a body moving in response to an inverse-square force. However, just as Kepler modified Copernican model by introducing ellipses rather than circles, so too did Newton make corrections to Kepler's first and third laws. It turns out that a planet does not orbit the exact center of the Sun. Instead, both the planet and the Sun orbit their common <a href="http://astronomylearn.blogspot.com/p/glossary.html#center of mass"><b>center of mass</b></a>. Because the Sun and the planet feel equal and opposite gravitational forces (by Newton's third law), the Sun must also move (by Newton's first law), driven by the gravitational influence of the planet. The Sun is so much more massive than any planet that the center of mass of the planet–Sun system is very close to the center of the Sun, which is why Kepler's laws are so accurate. Thus, Kepler's first law becomes</span></div></div><blockquote style="background-color: white;"><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;">I. The orbit of a planet around the Sun is an ellipse, with the <i>center of mass of the planet–Sun</i> system at one focus.</span></blockquote><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">As shown in Figure 2.22, however, the center of mass for two objects of comparable mass does not lie within either object. For identical masses (Figure 2.22a), the orbits are identical ellipses, with a common focus located midway between the two objects. For unequal masses (as in Figure 2.22b), the elliptical orbits still share a focus and both have the same eccentricity, but the more massive object moves more slowly and on a tighter orbit. (Note that Kepler's second law, as stated earlier, continues to apply without modification to each orbit separately, but the <i>rates</i> at which the two orbits sweep out area are different.) In the extreme case of a planet orbiting the much more massive Sun (see Figure 2.22c), the path traced out by the Sun's center lies entirely within the Sun itself.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">The change to Kepler's third law is also small in the case of a planet orbiting the Sun, but very important in other circumstances, such as the orbital motion of two stars that are gravitationally bound to each other. <a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=6140913615602906636" name="Anchor-Following-12839"></a>Following through the mathematics of Newton's theory, we find that the true relationship between the semi-major axis <i>a</i> (measured in astronomical units) of the planet's orbit relative to the Sun and its orbital period <i>P</i> (in Earth years) is</span></div></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiTwHEyM2a69WX6WBNlXXpoDlIYSGC-YurtSWWKMBQk2l8wkwc01TdCiwuSxf0T2yzyVVXqGTDony2cqAthIjeu9D7cktGT6pbPYBZTA3pUViYFQ6sTuTnXeAnp3TB9Bn_Bdv77EqhQGRs/s1600/07+Equation+3.GIF" imageanchor="1" style="background-color: white; margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiTwHEyM2a69WX6WBNlXXpoDlIYSGC-YurtSWWKMBQk2l8wkwc01TdCiwuSxf0T2yzyVVXqGTDony2cqAthIjeu9D7cktGT6pbPYBZTA3pUViYFQ6sTuTnXeAnp3TB9Bn_Bdv77EqhQGRs/s1600/07+Equation+3.GIF" /></a></div><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;"><br />
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<span style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;">where </span><i style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;">M</i><sub style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;">total</sub><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;"> is the </span><i style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;">combined</i><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;"> mass of the two objects. Notice that Newton's restatement of Kepler's third law preserves the proportionality between </span><i style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;">P</i><sup style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;">2</sup><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;"> and </span><i style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;">a</i><sup style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;">3</sup><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;">, but now the proportionality includes </span><i style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;">M</i><sub style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;">total</sub><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;">, so it is </span><i style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;">not</i><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;"> quite the same for all the planets. The Sun's mass is so great, however, that the differences in </span><i style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;">M</i><sub style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;">total</sub><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;"> among the various combinations of the Sun and the other planets are almost unnoticeable, so Kepler's third law, as originally stated, is a very good approximation. This modified form of Kepler's third law is true in all circumstances, inside or outside the solar system.</span><br />
<h4 style="background-color: white;"><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><table align="right" border="0" cellpadding="0" cellspacing="2" style="width: 137px;"><tbody>
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<tr><td><img height="6" src="file:///G:/CHAISSON/COMART/SPACER.GIF" width="10" /></td><td bgcolor="#fffad7"><span style="color: #e32e3a; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>Figure 2.23</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b> Escape Speed</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;"> The effect of launch speed on the trajectory of a satellite. With too low a speed at point A, the satellite will simply fall back to Earth. Given enough speed, however, the satellite will go into orbit—it "falls around Earth." As the initial speed at point A is increased, the orbit will become more and more elongated. When the initial speed exceeds the escape speed, the satellite will become unbound from Earth and will escape along a hyperbolic trajectory.</span></td></tr>
</tbody></table>ESCAPING FOREVER</span></h4><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">The law of gravity that describes the orbits of planets around the Sun applies equally well to natural moons and artificial satellites orbiting any planet. All our Earth-orbiting, human-made satellites move along paths governed by a combination of the inward pull of Earth's gravity and the forward motion gained during the rocket launch. If the rocket initially imparts enough speed to the satellite, it can go into orbit. Satellites not given enough speed at launch (such as intercontinental ballistic missiles, ICBMs) fail to achieve orbit and fall back to Earth (see Figure 2.23). (Technically, ICBMs actually do orbit Earth's attracting center, but their orbits intersect Earth's surface.) </span><br />
<span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;">Some space vehicles, such as the robot probes that visit other planets, attain enough speed to escape our planet's gravitational field and move away from Earth forever. This speed, known as the <a href="http://astronomylearn.blogspot.com/p/glossary.html#escape speed"><b>escape speed</b></a>, is about 41 percent greater (actually,</span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjYMOpzwptHTCzGGcfwJ9t9NC8lBgMCc7TFmuYcc6YCaaZ2m-SlL1K73RH3MQ4ilNzMSH2Fb3FJp5IozSCLmZLVX7VAjcm20HYEOqqovzva5mZ2khzvDX4nvkb2KGjbUY49iEm2xvCF7e4/s1600/07+Equation+5.GIF" imageanchor="1" style="background-color: white; margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjYMOpzwptHTCzGGcfwJ9t9NC8lBgMCc7TFmuYcc6YCaaZ2m-SlL1K73RH3MQ4ilNzMSH2Fb3FJp5IozSCLmZLVX7VAjcm20HYEOqqovzva5mZ2khzvDX4nvkb2KGjbUY49iEm2xvCF7e4/s1600/07+Equation+5.GIF" /></a><span style="background-color: white;"> </span><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times;">= 1.414… times greater) than the speed of a circular orbit at any given radius.<a href="http://astronomylearn.blogspot.com/2012/02/27-newtons-laws.html#Anchor-11481" name="Anchor-At-35882">* </a>At less than the escape speed, the old adage "what goes up must come down" (or at least stay in orbit) still applies. At more than the escape speed, however, a spacecraft will leave Earth for good. Planets, stars, galaxies—all gravitating bodies—have escape speeds. No matter how massive the body, gravity decreases with distance. As a result, the escape speed diminishes with increasing separation. The farther we go from Earth (or any gravitating body), the easier it becomes to escape.</span></div></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=6140913615602906636" name="Anchor-The-52219"></a>The speed of a satellite in a circular orbit just above Earth's atmosphere is 7.9 km/s (roughly 18,000 mph). The satellite would have to travel at 11.2 km/s (about 25,000 mph) to escape from Earth altogether. If an object exceeds the escape speed, its motion is said to be <a href="http://astronomylearn.blogspot.com/p/glossary.html#unbound"><b>unbound</b></a>, and the orbit is no longer an ellipse. In fact, the path of the spacecraft relative to Earth is a related geometric figure called a <i>hyperbola.</i> If we simply change the word <i>ellipse</i> to <i>hyperbola,</i> the modified version of Kepler's first law still applies, as does Kepler's second law. (Kepler's third law does not extend to unbound orbits because it doesn't make sense to talk about a period in those cases.)</span></div><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div><div style="background-color: white;"><span style="font-family: 'Times New Roman', Georgia, Times;">Newton's laws explain the paths of objects moving at any point in space near any gravitating body. These laws provide a firm physical and mathematical foundation for Copernicus's heliocentric model of the solar system and for Kepler's laws of planetary motions. But they do much more than that. Newtonian gravitation governs not only the planets, moons, and satellites in their elliptical orbits but also the stars and galaxies in their motion throughout our universe—as well as apples falling to the ground.</span></div><div style="background-color: white;"><div class="separator" style="clear: both; text-align: center;"><br />
</div><span style="font-family: 'Times New Roman', Georgia, Times;"><a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=6140913615602906636" name="Anchor-11481"></a><a href="http://astronomylearn.blogspot.com/2012/02/27-newtons-laws.html#Anchor-At-35882">*</a> <i>In terms of the formula presented in More Precisely 2-3, the escape speed is given by v<sub>escape</sub> =</i></span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhQ335jDO2SAE8o2lYpoaG206xoCikOI3fX1iVp6ececbdtp_YVem-B4l4W-aOFnPkOhH1u3LUwEu7h9pnClJ230KqrtvS8_8lg3lGcyMjjL2kBkyw5pXbWJ0Txz08JyVICwVdKxn0l0nI/s1600/EQFN.1.gif" imageanchor="1" style="background-color: white; margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhQ335jDO2SAE8o2lYpoaG206xoCikOI3fX1iVp6ececbdtp_YVem-B4l4W-aOFnPkOhH1u3LUwEu7h9pnClJ230KqrtvS8_8lg3lGcyMjjL2kBkyw5pXbWJ0Txz08JyVICwVdKxn0l0nI/s1600/EQFN.1.gif" /></a></div>Andri F Martinhttp://www.blogger.com/profile/11669920311565328714noreply@blogger.com0tag:blogger.com,1999:blog-4374048443162882832.post-25288359334037009202012-02-14T06:55:00.000+07:002012-02-14T06:56:42.208+07:002.6 The Dimensions of the Solar System<h1 style="text-align: center;">The Dimensions of the Solar System</h1><div style="background-color: white; text-align: justify;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjc_WBzxWewXG7k1TO9vYM8_b3TIS-aiDaHgLcHtwsLZqF-Z7NhewRhAqBJy_5O324WJD_9pIw2NgTPPtoso1LyUgMqWCKc0t7CEAdYnH5NjHYp7z3Qra_AfRr0q06ryoVgTSSKoTKXMlc/s1600/LGICON_6.GIF" imageanchor="1" style="background-color: transparent; margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjc_WBzxWewXG7k1TO9vYM8_b3TIS-aiDaHgLcHtwsLZqF-Z7NhewRhAqBJy_5O324WJD_9pIw2NgTPPtoso1LyUgMqWCKc0t7CEAdYnH5NjHYp7z3Qra_AfRr0q06ryoVgTSSKoTKXMlc/s1600/LGICON_6.GIF" /></a><span style="font-family: 'Times New Roman', Georgia, Times;">Kepler's laws allow us to construct a scale model of the solar system, with the correct shapes and <i>relative</i> sizes of all the planetary orbits, but they do not tell us the <i>actual</i> size of any orbit. We can express the distance to each planet only in terms of the distance from Earth to the Sun. Why is this? Because Kepler's triangulation measurements all used a portion of Earth's orbit as a baseline, distances could be expressed only relative to the size of that orbit, which was itself undetermined. Thus our model of the solar system would be like a road map of the United States showing the<i>relative</i> positions of cities and towns but lacking the all-important scale marker indicating distances in kilometers or miles. For example, we would know that Kansas City is about three times more distant from New York than it is from Chicago, but we would not know the actual mileage between any two points on the map.</span><br />
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<tr><td></td><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEimy7jVJYPDkxCvazd6YeFkuxO-jDCoYXxEGmIEEFHV4_rsmeoYn9M33bVjWuWTIA1Kdq2QaTsx9W1_fj3TVCxx_Q1mrT-fB2cJ1AmRbNbbo3cnulQuvddpXUZUBhBGOSOgC_wAOseXrDY/s1600/AACHCKD0.JPG" imageanchor="1" style="font-family: 'Times New Roman'; margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEimy7jVJYPDkxCvazd6YeFkuxO-jDCoYXxEGmIEEFHV4_rsmeoYn9M33bVjWuWTIA1Kdq2QaTsx9W1_fj3TVCxx_Q1mrT-fB2cJ1AmRbNbbo3cnulQuvddpXUZUBhBGOSOgC_wAOseXrDY/s1600/AACHCKD0.JPG" /></a></td></tr>
<tr><td><img height="6" src="file:///G:/CHAISSON/COMART/SPACER.GIF" width="6" /></td><td bgcolor="#fffad7"><div style="text-align: justify;"><span style="color: #e32e3a; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>Figure 2.15</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b> Solar Transit</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"> </span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;">The transit of Mercury across the face of the Sun. Such transits happen only about once per decade, because Mercury's orbit does not quite coincide with the plane of the ecliptic. Transits of Venus are even rarer, occurring only about twice per century. <i>(AURA)</i></span></div></td></tr>
</tbody></table><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">If we could somehow determine the value of the astronomical unit—in kilometers, say—we would be able to add the vital scale marker to our map of the solar system and compute the exact distances between the Sun and each of the planets. We might propose using triangulation to measure the distance from Earth to the Sun directly. However, we would find it impossible to measure the Sun's parallax using Earth's diameter as a baseline. The Sun is too bright, too big, and too fuzzy for us to distinguish any apparent displacement relative to a field of distant stars. To measure the Sun's distance from Earth, we must resort to some other method.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div><div style="background-color: white;"><div style="text-align: justify;"><a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=2528835933403700920" name="Anchor-Before-21368"></a><span style="font-family: 'Times New Roman', Georgia, Times;">Before the middle of the twentieth century, the most accurate measurements of the astronomical unit were made using triangulation on the planets Mercury and Venus during their rare <i>transits</i> of the Sun—that is, during the brief periods when those planets passed directly between the Sun and Earth (as shown for the case of Mercury in Figure 2.15). Because the time at which a transit occurs can be determined with great precision, astronomers can use this information to make accurate measurements of a planet's position in the sky. They can then use simple geometry to compute the distance to the planet by combining observations made from different locations on Earth, as discussed earlier in Chapter 1.<a href="http://astronomylearn.blogspot.com/2012/02/15-measurement-of-distance.html">(Sec. 1.5)</a> For example, the parallax of Venus at closest approach to Earth, as seen from two diametrically opposite points on Earth (separated by about 13,000 km), is about 1 arc minute (1/60º)—at the limit of naked-eye capabilities but easily measurable telescopically. Using the second formula presented in <a href="http://astronomylearn.blogspot.com/2012/02/more-precisely-14-measuring-distances.html"><i>More Precisely 1-4</i></a><i>, </i>we find that this parallax represents a distance of 13,000 km x 57.3º/(1/60º), or approximately 45,000,000 km.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Knowing the distance to Venus, we can compute the magnitude of the astronomical unit. Figure 2.16 is an idealized diagram of the Sun–Earth–Venus orbital geometry. The planetary orbits are drawn as circles here, but in reality they are slight ellipses. This is a subtle difference, and we can correct for it using detailed knowledge of orbital motions. Assuming for the sake of simplicity that the orbits are perfect circles, we see from the figure that the distance from Earth to Venus at closest approach is approximately 0.3 A.U. Knowing that 0.3 A.U. is 45,000,000 km makes determining 1 A.U. straightforward—the answer is 45,000,000/0.3, or 150,000,000 km.</span></div></div><div class="separator" style="clear: both; text-align: center;"><br />
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<tr><td></td><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFWJHLKs2YfF2hJSOWTOY8r7-yB6Zbna-VKAoiyMw_nBZZOXRxNHHoQDZzJZ-bWUp19Bp4ncyRbyLlHbgZNj7Tyx6V8OL7JUUIQ29UbZV59ygPTmvn-hUtU4mOqYk54GUNtAGtUn63gdQ/s1600/AACHCKE0.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFWJHLKs2YfF2hJSOWTOY8r7-yB6Zbna-VKAoiyMw_nBZZOXRxNHHoQDZzJZ-bWUp19Bp4ncyRbyLlHbgZNj7Tyx6V8OL7JUUIQ29UbZV59ygPTmvn-hUtU4mOqYk54GUNtAGtUn63gdQ/s1600/AACHCKE0.JPG" /></a></td></tr>
<tr><td><img height="6" src="file:///G:/CHAISSON/COMART/SPACER.GIF" width="6" /></td><td bgcolor="#fffad7"><div style="text-align: justify;"><span style="color: #e32e3a; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>Figure 2.16</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b> Astronomical Unit</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"> </span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;">Simplified geometry of the orbits of Earth and Venus as they move around the Sun. The wavy lines represent the paths along which radar signals might be transmitted toward Venus and received back at Earth at the particular moment (chosen for simplicity) when Venus is at its minimum distance from Earth. Because the radius of Earth's orbit is 1 A.U. and that of Venus is about 0.7 A.U., we know that this distance is 0.3 A.U. Thus, radar measurements allow us to determine the astronomical unit in kilometers.</span></div></td></tr>
</tbody></table><div style="text-align: justify;"><a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=2528835933403700920" name="Anchor-The-54742"></a><span style="font-family: 'Times New Roman', Georgia, Times;">The modern method for deriving the absolute scale (that is, the scale expressed in kilometers, rather than just relative to Earth's orbit) of the solar system uses radar rather than triangulation. The word <a href="http://astronomylearn.blogspot.com/p/glossary.html#radar"><b>radar</b></a> is an acronym for <b>r</b>adio <b>d</b>etection and <b>r</b>anging. In this technique, radio waves are transmitted toward an astronomical body, such as a planet. (We cannot use radar ranging to measure the distance to the Sun directly because radio signals are absorbed at the solar surface and not reflected to Earth.) The returning echo indicates the body's direction and range, or distance, in absolute terms—that is, in kilometers rather than in astronomical units. </span><a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=2528835933403700920" name="Anchor-Multiplying-46716"></a><span style="font-family: 'Times New Roman', Georgia, Times;">Multiplying the 300-second round-trip travel time of the radar signal (the time elapsed between transmission of the signal and reception of the echo) by the speed of light (300,000 km/s, which is also the speed of radio waves), we obtain twice the distance to the target planet.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Venus, whose orbit periodically brings it closest to Earth, is the most common target for radar ranging. The round-trip travel time (for example, at closest approach, as indicated by the wavy lines on Figure 2.16) can be measured with high precision—in fact, well enough to determine the planet's distance to an accuracy of about 1 km. In this way, the astronomical unit is now known to be 149,597,870 km. We will use the rounded-off value of 1.5 x 10<sup>8</sup> km in this text.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Having determined the value of the astronomical unit, we can reexpress the sizes of the other planetary orbits in terms of more familiar units, such as miles or kilometers. The entire scale of the solar system can then be calibrated to high precision.</span></div></div>Andri F Martinhttp://www.blogger.com/profile/11669920311565328714noreply@blogger.com0tag:blogger.com,1999:blog-4374048443162882832.post-37409343957973485722012-02-13T20:10:00.000+07:002012-02-13T20:10:25.056+07:00Discovery 2.2 - The Scientific Method<h1 style="text-align: center;">The Scientific Method</h1><span style="background-color: #f8f8ee; font-family: 'Times New Roman', Georgia, Times; text-align: justify;">The earliest known models of the universe were based largely on imagination and mythology, and made little attempt to explain the workings of the heavens in terms of known earthly experience. However, history shows that some early scientists did come to realize the importance of careful observation and testing to the formulation of their theories. The success of their approach changed, slowly but surely, the way science was done and opened the door to a fuller understanding of nature.</span><br />
<div style="text-align: justify;"><span style="background-color: #f8f8ee;"></span></div><div style="text-align: justify;"><span style="background-color: #f8f8ee; font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div><div style="background-color: #f8f8ee;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">As knowledge from all sources was sought and embraced for its own sake, the influence of logic and reasoned argument grew and the power of myth diminished. People began to inquire more critically about themselves and the universe. They realized that thinking about nature was no longer sufficient; looking at it was also necessary. Experiments and observations became a central part of the process of inquiry. To be effective, a <i>theory</i>—the framework of ideas and assumptions used to explain some set of observations and make predictions about the real world—must be continually tested. If experiments and observations favor it, a theory can be further developed and refined, but if they do not, it must be rejected, no matter how appealing it originally seemed.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: #f8f8ee;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">The process is illustrated (very) schematically in the accompanying figure. This new approach to investigation, combining thinking and doing—that is, theory and experiment—is often known as the <i>scientific method.</i> It separates science from pseudoscience, fact from fiction.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
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<tr><td><img height="6" src="file:///G:/CHAISSON/COMART/SPACER.GIF" width="10" /></td><td><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOJdsoMDGPTOMb2gRzfDIzuitvoz501ladlyqxeca2b7mj_FwQanHeVqk-UWI_hZHdUw3bLKm21XWWloUNvr_SM5DU7F0JgwaWumWqBDFPADv6QGhnPQQ0eLAd4ZI-ESU2n5IvrS6TfDs/s1600/AACHCKM0.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOJdsoMDGPTOMb2gRzfDIzuitvoz501ladlyqxeca2b7mj_FwQanHeVqk-UWI_hZHdUw3bLKm21XWWloUNvr_SM5DU7F0JgwaWumWqBDFPADv6QGhnPQQ0eLAd4ZI-ESU2n5IvrS6TfDs/s1600/AACHCKM0.JPG" /></a></div></td></tr>
</tbody></table><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Notice that there is no "end point" to the process depicted in the figure. A theory can be invalidated by a single wrong prediction, but no amount of observation or experimentation can ever prove it correct. Theories simply become more and more widely accepted as their predictions are repeatedly confirmed.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div><div style="background-color: #f8f8ee;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">The notion that theories must be tested and may be proven wrong sometimes leads people to dismiss their importance. We have all heard the expression, "Of course, it’s only a theory," used to undermine an idea that someone finds unacceptable. Don’t be fooled by this abuse of the concept! Gravity (Section 2.7) is only a theory, but calculations based on it have guided human spacecraft throughout the solar system. Electromagnetism (Chapter 3) and quantum mechanics (Chapter 4) are theories too, yet they form the foundation for most of twentieth (and twenty-first) century technology.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: #f8f8ee;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">In astronomy we are rarely afforded the luxury of performing experiments to test our theories, so observation becomes vitally important. The birth of modern science is usually associated with the Renaissance (and indeed, scientific inquiry can legitimately be said to have blossomed since the time of the Copernican revolution). However, one of the first documented uses of the scientific method in an astronomical context was performed by Aristotle (384–322 B.C.) nearly 25 centuries ago.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: #f8f8ee;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Aristotle noticed that, during a lunar eclipse, when Earth is positioned between the Sun and the Moon, it casts a curved shadow onto the Moon’s surface. The accompanying figure shows a series of photographs taken during a recent lunar eclipse. Earth’s shadow is indeed slightly curved. This is what Aristotle must have seen and recorded so long ago.</span></div></div><br />
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<tr><td><i>(G. Schneider)</i></td></tr>
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</span><br />
<div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Because the observed shadow seemed always to be an arc of the same circle, Aristotle concluded that Earth, the cause of the shadow, must be a sphere. On the basis of this<i>hypothesis</i>—this possible explanation of the observed facts—he then went on to predict that any and all future lunar eclipses would show that Earth’s shadow was curved, regardless of the orientation of our planet. That prediction has been tested every time a lunar eclipse has occurred. It has yet to be proved wrong. Aristotle was not the first person to argue that Earth is round, but he was apparently the first to offer evidence of it using the lunar-eclipse method.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: #f8f8ee;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">The reasoning procedure Aristotle used forms the basis of all scientific inquiry today. Observation, theory, and testing are the cornerstones of the scientific method, a technique whose power will be demonstrated again and again throughout our text. Scientists throughout the world today use an approach that relies heavily on testing ideas. They gather data, form a working hypothesis that explains the data, then proceed to test the implications of the hypothesis using experiment and observation. Eventually, one or more "well-tested" hypotheses may be elevated to the stature of physical laws and come to form the basis of a theory of even broader applicability. The new predictions of the theory will in turn be tested, as scientific knowledge continues to grow.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: #f8f8ee;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Experiment and observation are integral parts of the process of scientific inquiry. Untestable theories, or theories unsupported by experimental evidence, rarely gain any measure of acceptance in scientific circles. Used properly over a period of time, this rational, methodical approach enables us to arrive at conclusions that are mostly free of the personal bias and human values of any one scientist. The scientific method is designed to yield an objective view of the universe we inhabit.</span></div></div>Andri F Martinhttp://www.blogger.com/profile/11669920311565328714noreply@blogger.com0tag:blogger.com,1999:blog-4374048443162882832.post-58908233817546274662012-02-13T19:50:00.000+07:002012-02-13T20:04:33.132+07:002.5 The Laws of Planetary Motion<h1 style="text-align: center;">The Laws of Planetary Motion</h1><div style="background-color: white;"><span style="font-family: 'Times New Roman', Georgia, Times;"></span></div><table align="right" border="0" cellpadding="0" cellspacing="2" style="width: 134px;"><tbody>
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<tr><td><img height="6" src="file:///G:/CHAISSON/COMART/SPACER.GIF" width="10" /></td><td bgcolor="#fffad7"><div style="text-align: justify;"><span style="color: #e32e3a; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>Figure 2.11</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b> Johannes Kepler</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;"> (1571–1630). <i>(E. Lessing / Art Resource, NY)</i></span></div></td></tr>
</tbody></table><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">At about the same time as Galileo was becoming famous—or notorious—for his pioneering telescopic observations and outspoken promotion of the Copernican system, Johannes Kepler (Figure 2.11), a German mathematician and astronomer, was developing the laws of planetary motion that now bear his name. Galileo was in many ways the first "modern" observer. He used emerging technology, in the form of the telescope, to achieve new insights into the universe. </span><a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=5890823381754627466" name="Anchor-In-5944"></a><span style="font-family: 'Times New Roman', Georgia, Times;">In contrast, Kepler was a pure theorist. His groundbreaking work that so clarified our knowledge of planetary motion was based almost entirely on the observations of others, principally an extensive collection of data compiled by Tycho Brahe (1546–1601), Kepler's employer and arguably one of the greatest observational astronomers that has ever lived.</span></div><h4 style="background-color: white;"><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;">BRAHE'S COMPLEX DATA</span></h4><div style="background-color: white;"><div class="separator" style="clear: both; text-align: justify;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhyIIQmfEvEcSnN3CVbR2KZeDq56rV0CWlw3kCv-niHq8DSP2AlR8tezxJRzOhvQc7fJVvPUS5f9xjMnFO7YCmVo6N0CS5ir15tGO6kE7d9ZmgAODnQK7pmF0Tt3z_-8Sij99rArgJlv_M/s1600/LGICON_2.GIF" imageanchor="1" style="background-color: white; margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhyIIQmfEvEcSnN3CVbR2KZeDq56rV0CWlw3kCv-niHq8DSP2AlR8tezxJRzOhvQc7fJVvPUS5f9xjMnFO7YCmVo6N0CS5ir15tGO6kE7d9ZmgAODnQK7pmF0Tt3z_-8Sij99rArgJlv_M/s1600/LGICON_2.GIF" /></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi7BP-072_rJf_a6j879EXh5dxwRChAL8MSSshDxJzWKgCV2cYUdqSRcY23tVUo_GWcFSiHWLjAbp4wfdbu01NHbxUOL9_hspd1du6Q01LTVY6Hhfqhj5EeVEF5rC3DQJpcjtEjA-EjKwI/s1600/LGICON_4.GIF" imageanchor="1" style="background-color: white; margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi7BP-072_rJf_a6j879EXh5dxwRChAL8MSSshDxJzWKgCV2cYUdqSRcY23tVUo_GWcFSiHWLjAbp4wfdbu01NHbxUOL9_hspd1du6Q01LTVY6Hhfqhj5EeVEF5rC3DQJpcjtEjA-EjKwI/s1600/LGICON_4.GIF" /></a><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;">Tycho, as he is often called, was both an eccentric aristocrat and a skillful observer. Born in Denmark, he was educated at some of the best universities in Europe, where he studied astrology, alchemy, and medicine. Most of his observations, which predated the invention of the telescope by several decades, were made at his own observatory, named <i>Uraniborg,</i> in Denmark (Figure 2.12). There, using instruments of his own design, Tycho maintained meticulous and accurate records of the stars, planets, and other noteworthy celestial events (including a comet and a supernova, the appearance of which helped convince Tycho that the Aristotelean view of the universe could not be correct).</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
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<tr><td><img height="6" src="file:///G:/CHAISSON/COMART/SPACER.GIF" width="10" /></td><td bgcolor="#fffad7"><div style="text-align: justify;"><span style="color: #e32e3a; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>Figure 2.12</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b> Tycho Brahe</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;"> in his observatory <i>Uraniborg</i>, on the island of Hveen in Denmark. Brahe's observations of the positions of stars and planets on the sky were the most accurate and complete set of naked-eye measurements ever made. <i>(The Royal Ontario Museum, © ROM)</i></span></div></td></tr>
</tbody></table><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">In 1597, having fallen out of favor with the Danish court, Tycho moved to Prague as Imperial Mathematician of the Holy Roman Empire. Prague happens to be fairly close to Graz, in Austria, where Kepler lived and worked.<a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=5890823381754627466" name="Anchor-45238"></a> Kepler joined Tycho in Prague in 1600 and was put to work trying to find a theory that could explain Brahe's planetary data. When Tycho died a year later, Kepler inherited not only Brahe's position but also his most priceless possession: the accumulated observations of the planets, spanning several decades. <a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=5890823381754627466" name="Anchor-17405"></a>Tycho's observations, though made with the naked eye, were nevertheless of very high quality. In most cases, his measured positions of stars and planets were accurate to within about 1'. Kepler set to work seeking a unifying principle to explain in detail the motions of the planets, without the need for epicycles. The effort was to occupy much of the remaining 29 years of his life.</span><br />
<span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Kepler had already accepted the heliocentric picture of the solar system. His goal was to find a simple and elegant description of the solar system, within the Copernican framework, that fit Tycho's complex mass of detailed observations. In the end, he found it necessary to abandon Copernicus's original simple idea of circular planetary orbits. However, even greater simplicity emerged as a result. After long years of studying Brahe's planetary data and many false starts and blind alleys, Kepler developed the laws of planetary motion that now bear his name.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><div style="text-align: justify;"><a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=5890823381754627466" name="Anchor-Kepler-20001"></a><span style="font-family: 'Times New Roman', Georgia, Times;">Kepler determined the shape of each planet's orbit by triangulation—not from different points on Earth, but from different points on Earth's orbit, using observations made at many different times of the year. <a href="http://astronomylearn.blogspot.com/2012/02/15-measurement-of-distance.html">(Sec. 1.5)</a> By using a portion of Earth's orbit as a baseline, Kepler was able to measure the relative sizes of the other planetary orbits. Noting where the planets were on successive nights, he found the speeds at which the planets move. We do not know how many geometric shapes Kepler tried for the orbits before he hit upon the correct one. His difficult task was made even more complex because he had to determine Earth's own orbit, too. Nevertheless, he eventually succeeded in summarizing the motions of all the known planets, including Earth, in just three laws, the <a href="http://astronomylearn.blogspot.com/p/glossary.html#laws of planetary motion"><b>laws of planetary motion</b></a>.</span></div></div><h4 style="background-color: white;"><span style="font-family: 'Times New Roman', Georgia, Times;"><table align="right" border="0" cellpadding="0" cellspacing="2" style="width: 134px;"><tbody>
<tr><td></td><td><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj4D9iGEkW8j42bTD7GPLLE_sEtKnwz74ZFnYHR6A_fIfs5lfQGqV63tn1k4a0nVZvi_UGO_GKMx9iFE-GnTYCTUu3r7NdqnBEz6rC94Ph_GZS2JDsWk28MB9_dUjVfX75tB_4OFGCAqwI/s1600/AACHCKB0.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj4D9iGEkW8j42bTD7GPLLE_sEtKnwz74ZFnYHR6A_fIfs5lfQGqV63tn1k4a0nVZvi_UGO_GKMx9iFE-GnTYCTUu3r7NdqnBEz6rC94Ph_GZS2JDsWk28MB9_dUjVfX75tB_4OFGCAqwI/s1600/AACHCKB0.JPG" /></a></div></td></tr>
<tr><td><img height="6" src="file:///G:/CHAISSON/COMART/SPACER.GIF" width="10" /></td><td bgcolor="#fffad7"><div style="text-align: justify;"><span style="color: #e32e3a; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>Figure 2.13</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b> Ellipse</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;"> An ellipse can be drawn with the aid of a string, a pencil, and two thumbtacks. The wider the separation of the foci, the more elongated, or eccentric, is the ellipse. In the special case where the two foci are at the same place, the drawn curve is a circle.</span></div></td></tr>
</tbody></table></span><a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=5890823381754627466" name="Anchor-49211"></a><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;">KEPLER'S SIMPLE LAWS</span></h4><div style="background-color: white;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMus-VgdsUWlWlS1YspJhgcuMhgoPjXpsJV32E2K0raiDUZWsjwyPqS70qD4vkwVFeTj_6f07XNkjZEOIljMKcxjpmHyXHzfOHxbee8BuVa-ErL6jD2cG9BVSmbdJ3DwcQgR8s27I1mX4/s1600/LGICON_5.GIF" imageanchor="1" style="background-color: white; margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMus-VgdsUWlWlS1YspJhgcuMhgoPjXpsJV32E2K0raiDUZWsjwyPqS70qD4vkwVFeTj_6f07XNkjZEOIljMKcxjpmHyXHzfOHxbee8BuVa-ErL6jD2cG9BVSmbdJ3DwcQgR8s27I1mX4/s1600/LGICON_5.GIF" /></a><span style="font-family: 'Times New Roman', Georgia, Times;"><i>Kepler's first law</i> has to do with the shapes of the planetary orbits:</span></div><blockquote style="background-color: white;"><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;">I. The orbital paths of the planets are elliptical (not circular), with the Sun at one focus.</span></blockquote><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=5890823381754627466" name="Anchor-An-38256"></a>An <a href="http://astronomylearn.blogspot.com/p/glossary.html#ellipse"><b>ellipse</b></a> is simply a flattened circle. Figure 2.13 illustrates a means of constructing an ellipse using a piece of string and two thumbtacks. Each point at which the string is pinned is called a <a href="http://astronomylearn.blogspot.com/p/glossary.html#focus"><b>focus</b></a> (plural: <i>foci</i>) of the ellipse. <a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=5890823381754627466" name="Anchor-The-4742"></a>The long axis of the ellipse, containing the two foci, is known as the <i>major axis.</i> Half the length of this long axis is referred to as the <a href="http://astronomylearn.blogspot.com/p/glossary.html#semi-major axis"><b>semi-major axis</b></a>; it is a measure of the ellipse's size. The <a href="http://astronomylearn.blogspot.com/p/glossary.html#eccentricity"><b>eccentricity</b></a> of the ellipse is the ratio of the distance between the foci to the length of the major axis. Note that, while the Sun resides at one focus, the other focus is empty and has no particular physical significance.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">The length of the semi-major axis and the eccentricity are all we need to describe the size and shape of a planet's orbital path (see <a href="http://astronomylearn.blogspot.com/2012/02/more-precisely-21-some-properties-of.html"><i>More Precisely 2-1</i></a>). A circle is a special kind of ellipse in which the two foci happen to coincide, so the eccentricity is zero. The semi-major axis of a circle is simply its radius. In fact, no planet's elliptical orbit is nearly as elongated as the one shown in Figure 2.13. With two exceptions (the paths of Mercury and Pluto), planetary orbits in our solar system have such small eccentricities that our eyes would have trouble distinguishing them from true circles. Only because the orbits are so nearly circular were the Ptolemaic and Copernican models able to come as close as they did to describing reality.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Kepler's substitution of elliptical for circular orbits was no small advance. It amounted to abandoning an aesthetic bias—the Aristotelian belief in the perfection of the circle—that had governed astronomy since Greek antiquity. Even Galileo Galilei, not known for his conservatism in scholarly matters, clung to the idea of circular motion and never accepted that the planets move on elliptical paths.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><span style="font-family: 'Times New Roman', Georgia, Times;"><i></i></span></div><table align="right" border="0" cellpadding="0" cellspacing="2" style="width: 137px;"><tbody>
<tr><td></td><td><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgm0NTMH51P98fHNL9hya3PywgCiOhOXAv2KGd_Ew0gzCbi39J4oKrYC8ka0F8W0-w2ijTgR-j6b0dzxOIdDdn05FmeR2J8OspwsEOxaMBs2abauviAw3NvaxPQxgJxnI4ju_bvTO2gx5Q/s1600/AACHCKC0.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgm0NTMH51P98fHNL9hya3PywgCiOhOXAv2KGd_Ew0gzCbi39J4oKrYC8ka0F8W0-w2ijTgR-j6b0dzxOIdDdn05FmeR2J8OspwsEOxaMBs2abauviAw3NvaxPQxgJxnI4ju_bvTO2gx5Q/s1600/AACHCKC0.JPG" /></a></div></td></tr>
<tr><td><img height="6" src="file:///G:/CHAISSON/COMART/SPACER.GIF" width="10" /></td><td bgcolor="#fffad7"><div style="text-align: justify;"><span style="color: #e32e3a; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>Figure 2.14</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b> Kepler's Second Law</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;"> Equal areas are swept out in equal intervals of time. The three shaded areas (A, B, and C) are equal. Note that an object would travel the length of each of the three red arrows in the same amount of time. Therefore, planets move faster when closer to the Sun.</span></div></td></tr>
</tbody></table><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><i>Kepler's second law,</i> illustrated in Figure 2.14, addresses the speed at which a planet traverses different parts of its orbit:</span></div><blockquote style="background-color: white;"><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;">II. An imaginary line connecting the Sun to any planet sweeps out equal areas of the ellipse in equal intervals of time.</span></blockquote><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">While orbiting the Sun, a planet traces the arcs labeled A, B, and C in Figure 2.14 in equal times. Notice, however, that the distance traveled by the planet along arc C is greater than the distance traveled along arc A or arc B. Because the time is the same and the distance is different, the speed must vary.<a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=5890823381754627466" name="Anchor-When-28949"></a>When a planet is close to the Sun, as in sector C, it moves much faster than when farther away, as in sector A.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">By taking into account the relative speeds and positions of the planets in their elliptical orbits about the Sun, Kepler's first two laws explained the variations in planetary brightness and some observed peculiar nonuniform motions that could not be accommodated within the assumption of circular motion, even with the inclusion of epicycles. Gone at last were the circles within circles that rolled across the sky. Kepler's modification of the Copernican theory to allow the possibility of elliptical orbits both greatly simplified the model of the solar system and at the same time provided much greater predictive accuracy than had previously been possible. Note, too, that these laws are not restricted to planets. They apply to <i>any</i> orbiting object. Spy satellites, for example, move very rapidly as they swoop close to Earth's surface not because they are propelled with powerful on-board rockets but because their highly eccentric orbits are governed by Kepler's laws.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=5890823381754627466" name="Anchor-Kepler-56770"></a>Kepler published his first two laws in 1609, stating that he had proved them only for the orbit of Mars. <a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=5890823381754627466" name="Anchor-Ten-36059"></a>Ten years later, he extended them to all the then-known planets (Mercury, Venus, Earth, Mars, Jupiter, and Saturn) and added a third law relating the size of a planet's orbit to its sidereal orbital <a href="http://astronomylearn.blogspot.com/p/glossary.html#period"><b>period</b></a>—the time needed for the planet to complete one circuit around the Sun. <i>Kepler's third law</i> states that:</span></div></div><blockquote style="background-color: white;"><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;">III. The square of a planet's orbital period is proportional to the cube of its semi-major axis.</span></blockquote><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=5890823381754627466" name="Anchor-This-42452"></a>This law becomes particularly simple when we choose the (Earth sidereal) year as our unit of time and the <i>astronomical unit</i> as our unit of length. <a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=5890823381754627466" name="Anchor-One-50347"></a>One <a href="http://astronomylearn.blogspot.com/p/glossary.html#astronomical unit (A.U.)"><b>astronomical unit</b></a> (A.U.) is the semi-major axis of Earth's orbit around the Sun—essentially the average distance between Earth and the Sun. Like the light-year, the astronomical unit is custom-made for the vast distances encountered in astronomy. Using these units for time and distance, we can write Kepler's third law for any planet as</span></div></div><blockquote style="background-color: white;"><span style="font-family: 'Times New Roman', Georgia, Times;"><i><a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=5890823381754627466" name="Anchor-P2-41402"></a>P</i><sup>2</sup> (in Earth years) = <i>a</i><sup>3</sup> (in astronomical units),</span></blockquote><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">where <i>P</i> is the planet's sidereal orbital period, and <i>a</i> is the length of its semi-major axis. The law implies that a planet's "year" <i>P</i> increases more rapidly than does the size of its orbit <i>a</i>. For example, Earth, with an orbital semi-major axis of 1 A.U., has an orbital period of one Earth year. The planet Venus, orbiting at a distance of roughly 0.7 A.U., takes only 0.6 Earth years—about 225 days—to complete one circuit. By contrast, Saturn, almost 10 A.U. from the Sun, takes considerably more than 10 Earth years—in fact, nearly 30 years—to orbit the Sun just once.</span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh6rozgajMVHIV4yRHvumk1p8GSmev0Al9AV_fa-VtUJUsS4HQyNQKEM3lTlbxzC43JRv0p5yjuesOC18XR75arD2vzbxeWFJ0az_uqkJHqVR9fqfWRCErgPG6iL3vJ1FrXpxU271Q87pc/s1600/table2_1.GIF" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh6rozgajMVHIV4yRHvumk1p8GSmev0Al9AV_fa-VtUJUsS4HQyNQKEM3lTlbxzC43JRv0p5yjuesOC18XR75arD2vzbxeWFJ0az_uqkJHqVR9fqfWRCErgPG6iL3vJ1FrXpxU271Q87pc/s1600/table2_1.GIF" /></a></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Table 2.1</span><span style="font-family: 'Times New Roman', Georgia, Times;"> presents basic data describing the orbits of the nine planets now known. Renaissance astronomers knew these properties for the innermost six planets and used them to construct the currently accepted heliocentric model of the solar system. The second column presents each planet's orbital semi-major axis, measured in astronomical units; the third column gives the orbital period, in Earth years. The fourth column lists the planets' orbital eccentricities. For purposes of verifying Kepler's third law, the fifth column lists the ratio <i>P</i><sup>2</sup>/<i>a</i><sup>3</sup>. As we have just seen, the third law implies that this number should always equal one in the units used in the table.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">The main points to be grasped from Table 2.1 are these: (1) With the exception of Mercury and Pluto, the planets' orbits are nearly circular (that is, their eccentricities are close to zero); and (2) the farther a planet is from the Sun, the greater is its orbital period, in agreement with Kepler's third law to within the accuracy of the numbers in the table. (The small but significant deviations of <i>P</i><sup>2</sup>/<i>a</i><sup>3</sup>from one in the cases of Uranus and Neptune are caused by the gravitational attraction between those two planets; see Chapter 13.) <a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=5890823381754627466" name="Anchor-Most-11631"></a>Most important, note that Kepler's laws are obeyed by <i>all</i> the known planets, <i>not just by the six on which he based his conclusions.</i></span></div><span style="font-family: 'Times New Roman', Georgia, Times;"><i><br />
</i></span></div><div style="background-color: white;"><span style="font-family: 'Times New Roman', Georgia, Times;">The laws developed by Kepler were far more than mere fits to existing data. They also made definite, testable predictions about the future locations of the planets. Those predictions have been borne out to high accuracy every time they have been tested by observation—the hallmark of any scientific theory.</span></div>Andri F Martinhttp://www.blogger.com/profile/11669920311565328714noreply@blogger.com0tag:blogger.com,1999:blog-4374048443162882832.post-12689106453301741902012-02-13T16:25:00.000+07:002012-02-13T16:25:49.733+07:00More Precisely 2.1 - Some Properties of Planetary Orbit<h1 style="text-align: center;">Some Properties of Planetary Orbit</h1><div style="text-align: justify;"><span style="background-color: #f8f8ee; font-family: 'Times New Roman', Georgia, Times;">Two numbers—semi-major axis and eccentricity—are all that are needed to describe the size and shape of a planet’s orbital path. From them we can derive many other useful quantities. Two of the most important are the planet’s </span><i style="background-color: #f8f8ee; font-family: 'Times New Roman', Georgia, Times;">perihelion</i><span style="background-color: #f8f8ee; font-family: 'Times New Roman', Georgia, Times;"> (its point of closest approach to the Sun) and its </span><i style="background-color: #f8f8ee; font-family: 'Times New Roman', Georgia, Times;">aphelion</i><span style="background-color: #f8f8ee; font-family: 'Times New Roman', Georgia, Times;"> (greatest distance from the Sun). From the definitions presented in the text, it follows that if the planet’s orbit has semi-major axis </span><i style="background-color: #f8f8ee; font-family: 'Times New Roman', Georgia, Times;">a</i><span style="background-color: #f8f8ee; font-family: 'Times New Roman', Georgia, Times;"> and eccentricity </span><i style="background-color: #f8f8ee; font-family: 'Times New Roman', Georgia, Times;">e,</i><span style="background-color: #f8f8ee; font-family: 'Times New Roman', Georgia, Times;"> its perihelion is at a distance </span><i style="background-color: #f8f8ee; font-family: 'Times New Roman', Georgia, Times;">a</i><span style="background-color: #f8f8ee; font-family: 'Times New Roman', Georgia, Times;">(1– </span><i style="background-color: #f8f8ee; font-family: 'Times New Roman', Georgia, Times;">e</i><span style="background-color: #f8f8ee; font-family: 'Times New Roman', Georgia, Times;">) from the Sun, while its aphelion is at </span><i style="background-color: #f8f8ee; font-family: 'Times New Roman', Georgia, Times;">a</i><span style="background-color: #f8f8ee; font-family: 'Times New Roman', Georgia, Times;"> (1+ </span><i style="background-color: #f8f8ee; font-family: 'Times New Roman', Georgia, Times;">e</i><span style="background-color: #f8f8ee; font-family: 'Times New Roman', Georgia, Times;">). These points and distances are illustrated in the accompanying figure.</span></div><div style="text-align: justify;"><span style="background-color: #f8f8ee;"></span></div><br />
<div class="separator" style="clear: both; text-align: center;"><br />
</div><center style="background-color: #f8f8ee;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEguwcDlFDkIDFI4tqFbLsIsNcQ9dtxr1yn-L2DXkjgdx2UeiBRlop9ch2UTTGltuaWU0Cwnd3oHIg48K_CdjA8RFOhppET0PLU0d1l5Kgl3vVivK3DRwJd85O1hQ24tAWHE-5ofymV-yYs/s1600/AACHCKO0.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEguwcDlFDkIDFI4tqFbLsIsNcQ9dtxr1yn-L2DXkjgdx2UeiBRlop9ch2UTTGltuaWU0Cwnd3oHIg48K_CdjA8RFOhppET0PLU0d1l5Kgl3vVivK3DRwJd85O1hQ24tAWHE-5ofymV-yYs/s1600/AACHCKO0.JPG" /></a> </center><br />
<div style="background-color: #f8f8ee;"><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><br />
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<div style="text-align: justify;"><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;">EXAMPLE:</span><span style="font-family: 'Times New Roman', Georgia, Times;"> A (hypothetical) planet with a semi-major axis of 400 million km and an eccentricity of 0.5 (the eccentricity of the ellipse shown in the diagram) would range between 400 x (1 - 0.5) = 200 million km and 400 x 3 (1 + 0.5) 5 600 million km from the Sun over the course of one complete orbit. With <i>e</i> = 0.9, the range would be 40–760 million km, and so on.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: #f8f8ee;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">No planet has an orbital eccentricity as large as 0.5—the planet with the most eccentric orbit is Pluto, with <i>e</i> = 0.249 (see Table 2.1). However, many meteoroids, and all comets (see Chapter 14) have eccentricities considerably greater than this. In fact, most comets visible from Earth have eccentricities very close to <i>e</i> = 1. Their highly elongated orbits approach within a few astronomical units of the Sun at perihelion, yet these tiny frozen worlds spend most of their time far beyond the orbit of Pluto.</span></div></div>Andri F Martinhttp://www.blogger.com/profile/11669920311565328714noreply@blogger.com0tag:blogger.com,1999:blog-4374048443162882832.post-5222343406373130612012-02-13T13:46:00.000+07:002012-02-13T20:12:19.098+07:002.4 The Birth of Modern Astronomy<h1>The Birth of Modern Astronomy</h1><br />
<div style="background-color: white;"><span style="font-family: 'Times New Roman', Georgia, Times;"></span></div><table align="right" border="0" cellpadding="0" cellspacing="2" style="width: 137px;"><tbody>
<tr><td></td><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgKVbnmBq8xsgH1P6eVfLc1SUaUpCcYFfjIwKOAsd2srAYGLk2jRqsAN3UqNv7TcASfL_gQrqklBhpjtWafVbWGpU8bn3JbszVW7lIhKNf9VTLKfYCFn_jCQAlgHecndhOcboRyWVJ2VX4/s1600/AACHCJX0.JPG" imageanchor="1" style="font-family: 'Times New Roman'; margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgKVbnmBq8xsgH1P6eVfLc1SUaUpCcYFfjIwKOAsd2srAYGLk2jRqsAN3UqNv7TcASfL_gQrqklBhpjtWafVbWGpU8bn3JbszVW7lIhKNf9VTLKfYCFn_jCQAlgHecndhOcboRyWVJ2VX4/s1600/AACHCJX0.JPG" /></a></td></tr>
<tr><td><img height="6" src="file:///G:/CHAISSON/COMART/SPACER.GIF" width="10" /></td><td bgcolor="#fffad7"><div style="text-align: justify;"><span style="color: #e32e3a; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>Figure 2.9</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b> Galileo Galilei</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;"><i><b></b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;">(1564–1642). <i>(Art Resource, NY)</i></span></div></td></tr>
</tbody></table><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">In the century following the death of Copernicus and the publication of his theory of the solar system, two scientists—Galileo Galilei and Johannes Kepler—made indelible imprints on the study of astronomy. Contemporaries, they were aware of each other's work and corresponded from time to time about their theories. Each achieved fame for his discoveries and made great strides in popularizing the Copernican viewpoint, yet in their approaches to astronomy they were as different as night and day.</span></div><h4 style="background-color: white;"><a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=522234340637313061" name="Anchor-5593"></a><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;">GALILEO'S HISTORIC OBSERVATIONS</span></h4><div style="background-color: white;"><div style="text-align: justify;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhyIIQmfEvEcSnN3CVbR2KZeDq56rV0CWlw3kCv-niHq8DSP2AlR8tezxJRzOhvQc7fJVvPUS5f9xjMnFO7YCmVo6N0CS5ir15tGO6kE7d9ZmgAODnQK7pmF0Tt3z_-8Sij99rArgJlv_M/s1600/LGICON_2.GIF" imageanchor="1" style="background-color: white; margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhyIIQmfEvEcSnN3CVbR2KZeDq56rV0CWlw3kCv-niHq8DSP2AlR8tezxJRzOhvQc7fJVvPUS5f9xjMnFO7YCmVo6N0CS5ir15tGO6kE7d9ZmgAODnQK7pmF0Tt3z_-8Sij99rArgJlv_M/s1600/LGICON_2.GIF" /></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi7BP-072_rJf_a6j879EXh5dxwRChAL8MSSshDxJzWKgCV2cYUdqSRcY23tVUo_GWcFSiHWLjAbp4wfdbu01NHbxUOL9_hspd1du6Q01LTVY6Hhfqhj5EeVEF5rC3DQJpcjtEjA-EjKwI/s1600/LGICON_4.GIF" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi7BP-072_rJf_a6j879EXh5dxwRChAL8MSSshDxJzWKgCV2cYUdqSRcY23tVUo_GWcFSiHWLjAbp4wfdbu01NHbxUOL9_hspd1du6Q01LTVY6Hhfqhj5EeVEF5rC3DQJpcjtEjA-EjKwI/s1600/LGICON_4.GIF" /></a><span style="font-family: 'Times New Roman', Georgia, Times;">Galileo Galilei (Figure 2.9) was an Italian mathematician and philosopher. By his willingness to perform experiments to test his ideas—a rather radical approach in those days (see <a href="http://astronomylearn.blogspot.com/2012/02/discovery-22-scientific-method.html"><i>Discovery 2-2</i></a>)—and by embracing the brand-new technology of the telescope, he revolutionized the way in which science was done, so much so that he is now widely regarded as the father of experimental science.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">The telescope was invented in Holland in the early seventeenth century. Hearing of the invention (but without having seen one), Galileo built a telescope for himself in 1609 and aimed it at the sky. What he saw conflicted greatly with the philosophy of Aristotle and provided much new data to support the ideas of Copernicus.<a href="http://astronomylearn.blogspot.com/2012/02/24-birth-of-modern-astronomy.html#Anchor-49575" name="Anchor-47857">*</a></span></div><div style="text-align: justify;"><br />
</div></div><div style="background-color: white;"><div style="text-align: justify;"><a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=522234340637313061" name="Anchor-Using-64689"></a><span style="font-family: 'Times New Roman', Georgia, Times;">Using his telescope, Galileo discovered that the Moon had mountains, valleys, and craters—terrain in many ways reminiscent of that on Earth. Looking at the Sun (something that should <i>never</i> be done directly, and which may eventually have blinded Galileo), he found imperfections—dark blemishes now known as <i>sunspots.</i> These observations ran directly counter to the orthodox wisdom of the day. By noting the changing appearance of these sunspots from day to day, Galileo inferred that the Sun <i>rotates,</i> approximately once per month, around an axis roughly perpendicular to the ecliptic plane.</span></div></div><div style="background-color: white;"></div><table align="right" border="0" cellpadding="0" cellspacing="2" style="width: 75px;"><tbody>
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<tr><td bgcolor="#fffad7"><div style="text-align: justify;"><span style="color: #e32e3a; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>Figure 2.10</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b> Venus Phases</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;"> (a) The phases of Venus, rendered at different points in the planet's orbit. If Venus orbits the Sun and is closer to the Sun than is Earth, as Copernicus maintained, then Venus should display phases, much as our Moon does. As shown here, when directly between Earth and the Sun, Venus's unlit side faces us, and the planet is invisible to us. As Venus moves in its orbit (at a faster speed than Earth moves in its orbit), progressively more of its illuminated face is visible from Earth. Note also the connection between orbital phase and the apparent size of the planet. Venus seems much larger in its crescent phase than when it is full because it is much closer to us during its crescent phase. (The insets at bottom left and right are actual photographs of Venus at two of its crescent phases.) (b) The Ptolemaic model (see also Figure 2.6) is unable to account for these observations. In particular, the full phase of the planet cannot be explained. Seen from Earth, Venus reaches only a "fat crescent" phase, then begins to wane as it nears the Sun.</span></div></td></tr>
</tbody></table><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div><div style="text-align: justify;"><a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=522234340637313061" name="Anchor-Galileo-59545"></a><span style="font-family: 'Times New Roman', Georgia, Times;">Galileo also saw four small points of light, invisible to the naked eye, orbiting the planet Jupiter and realized that they were moons. To Galileo, the fact that another planet had moons provided the strongest support for the Copernican model. Clearly, Earth was not the center of all things. He also found that Venus showed a complete cycle of phases, like those of our Moon (Figure 2.10), a finding that could be explained only by the planet's motion around the Sun. These observations were more strong evidence that Earth is not the center of all things and that at least one planet orbited the Sun.</span></div><div style="background-color: white;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span><br />
<div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">In 1610, Galileo published a book called <i>Sidereus Nuncius (The Starry Messenger)</i>, detailing his observational findings and his controversial conclusions supporting the Copernican theory. In reporting and interpreting the wondrous observations made with his new telescope, Galileo was directly challenging both the scientific orthodoxy and the religious dogma of his day. He was (literally) playing with fire—he must certainly have been aware that only a few years earlier, in 1600, the astronomer Giordano Bruno had been burned at the stake in Rome, in part for his heretical teaching that Earth orbited the Sun. <a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=522234340637313061" name="Anchor-However-45163"></a>However, by all accounts, Galileo delighted in publicly ridiculing and irritating his Aristotelian colleagues. In 1616 his ideas were judged heretical, Copernicus's works were banned by the Roman Catholic Church, and Galileo was instructed to abandon his astronomical pursuits.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">But Galileo would not desist. In 1632 he raised the stakes by publishing <i>Dialogue Concerning the Two Chief World Systems,</i> which compared the Ptolemaic and Copernican models. The book presented a discussion among three people: one of them a dull-witted Aristotelian, whose views time and again were roundly defeated by the arguments of one of his two companions, an articulate proponent of the heliocentric system. To make the book accessible to a wide popular audience, Galileo wrote it in Italian rather than Latin.</span></div></div><div style="background-color: white;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
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<div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">These actions brought Galileo into direct conflict with the authority of the Church. Eventually, the Inquisition forced him, under threat of torture, to retract his claim that Earth orbits the Sun, and he was placed under house arrest in 1633. He remained imprisoned for the rest of his life. Not until 1992 did the Church publicly forgive Galileo's "crimes." But the damage to the orthodox view of the universe was done, and the Copernican genie was out of the bottle once and for all.</span></div></div><h4 style="background-color: white;"><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;">THE ASCENDANCY OF THE COPERNICAN SYSTEM</span></h4><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Although Renaissance scholars were correct, they could not <i>prove</i> that our planetary system is centered on the Sun, or even that Earth moves through space. Direct evidence for this was obtained only in the early eighteenth century, when astronomers discovered the <i>aberration of starlight</i>—a slight (20") shift in the observed direction to a star, caused by Earth's motion perpendicular to the line of sight. Additional proof came in the mid-nineteenth century, with the first unambiguous measurement of stellar parallax. Further verification of the heliocentricity of the solar system came gradually, with innumerable observational tests that culminated with the expeditions of our unmanned space probes of the 1960s, 1970s, and 1980s. The development and eventual acceptance of the heliocentric model were milestones in human thinking. <a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=522234340637313061" name="Anchor-This-14944"></a>This removal of Earth from any position of great cosmic significance is generally known, even today, as the <i>Copernican principle.</i></span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><i><br />
</i></span></div></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">The Copernican revolution is a good example of how the scientific method, though affected at any given time by the subjective whims, human biases, and even sheer luck of researchers, does ultimately lead to a definite degree of objectivity. Over time, many groups of scientists checking, confirming, and refining experimental tests can neutralize the subjective attitudes of individuals. Usually one generation of scientists can bring sufficient objectivity to bear on a problem, though some especially revolutionary concepts are so swamped by tradition, religion, and politics that more time is necessary. In the case of heliocentricity, objective confirmation was not obtained until about three centuries after Copernicus published his work and more than 2000 years after Aristarchus had proposed the concept. Nonetheless, objectivity <i>did in fact</i> eventually prevail, and our knowledge of the universe has expanded immeasurably as a result.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><span style="font-family: 'Times New Roman', Georgia, Times; font-size: x-small;"><a href="http://www.blogger.com/post-edit.g?blogID=4374048443162882832&postID=522234340637313061" name="Anchor-49575"></a><a href="http://astronomylearn.blogspot.com/2012/02/24-birth-of-modern-astronomy.html#Anchor-47857">*</a> <i>In fact, Galileo had already abandoned Aristotle in favor of Copernicus, although he had not published these beliefs at the time he began his telescopic observations.</i></span></div>Andri F Martinhttp://www.blogger.com/profile/11669920311565328714noreply@blogger.com0tag:blogger.com,1999:blog-4374048443162882832.post-53069802552521122072012-02-13T11:59:00.000+07:002012-02-13T11:59:46.450+07:00Discovery 2.1 - The Foundations of the Copernican Revolution<h1 style="text-align: center;">The Foundations of the Copernican Revolution</h1><span style="background-color: #f8f8ee; font-family: 'Times New Roman', Georgia, Times;">The following seven points are essentially Copernicus’s own words. The italicized material is additional explanation.</span><br />
<span style="background-color: #f8f8ee;"></span><br />
<ol style="background-color: #f8f8ee;"><li><span style="font-family: 'Times New Roman', Georgia, Times;">The celestial spheres do not have just one common center. <i>Specifically, Earth is not at the center of everything.</i></span></li>
<li><span style="font-family: 'Times New Roman', Georgia, Times;">The center of Earth is not the center of the universe but is instead only the center of gravity and of the lunar orbit.</span></li>
<li><span style="font-family: 'Times New Roman', Georgia, Times;">All the spheres revolve around the Sun. <i>By spheres, Copernicus meant the planets.</i></span></li>
<li><span style="font-family: 'Times New Roman', Georgia, Times;">The ratio of Earth’s distance from the Sun to the height of the firmament is so much smaller than the ratio of Earth’s radius to the distance to the Sun that the distance to the Sun is imperceptible when compared with the height of the firmament. <i>By firmament, Copernicus meant the distant stars. The point he was making is that the stars are very much farther away than the Sun.</i></span></li>
<li><span style="font-family: 'Times New Roman', Georgia, Times;">The motions appearing in the firmament are not its motions but those of Earth. Earth performs a daily rotation around its fixed poles while the firmament remains immobile as the highest heaven. <i>Because the stars are so far away, any apparent motion we see in them is the result of Earth’s rotation.</i></span></li>
<li><span style="font-family: 'Times New Roman', Georgia, Times;">The motions of the Sun are not its motions but the motion of Earth. <i>Similarly, the Sun’s apparent daily and yearly motion are actually due to the various motions of Earth.</i></span></li>
</ol><div style="background-color: #f8f8ee;"><span style="font-family: 'Times New Roman', Georgia, Times;">What appears to us as retrograde and forward motion of the planets is not their own but that of Earth. <i>The heliocentric picture provides a natural explanation for retrograde planetary motion, again as a consequence of Earth’s motion.</i></span></div>Andri F Martinhttp://www.blogger.com/profile/11669920311565328714noreply@blogger.com0tag:blogger.com,1999:blog-4374048443162882832.post-31481035734200335702012-02-13T11:47:00.000+07:002012-02-13T19:57:24.107+07:002.3 The Heliocentric Model of the Solar System<h1>The Heliocentric Model of the Solar System</h1><div style="background-color: white;"><span style="font-family: 'Times New Roman', Georgia, Times;"></span></div><table align="right" border="0" cellpadding="0" cellspacing="2" style="width: 134px;"><tbody>
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<tr><td><img height="6" src="file:///G:/CHAISSON/COMART/SPACER.GIF" width="10" /></td><td bgcolor="#fffad7"><span style="color: #e32e3a; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>Figure 2.7</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b> Nicholas Copernicus</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;"> (1473–1543). <i>(E. Lessing / Art Resource, NY)</i></span></td></tr>
</tbody></table><div style="text-align: justify;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhyIIQmfEvEcSnN3CVbR2KZeDq56rV0CWlw3kCv-niHq8DSP2AlR8tezxJRzOhvQc7fJVvPUS5f9xjMnFO7YCmVo6N0CS5ir15tGO6kE7d9ZmgAODnQK7pmF0Tt3z_-8Sij99rArgJlv_M/s1600/LGICON_2.GIF" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhyIIQmfEvEcSnN3CVbR2KZeDq56rV0CWlw3kCv-niHq8DSP2AlR8tezxJRzOhvQc7fJVvPUS5f9xjMnFO7YCmVo6N0CS5ir15tGO6kE7d9ZmgAODnQK7pmF0Tt3z_-8Sij99rArgJlv_M/s1600/LGICON_2.GIF" /></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjro4NwCtC2TCdCM0U8llIjQWPaqnmu4Nt2WLO_hJXMRRt6pjUDNl52NfT4zBngnC52mY9Jyz9gm_C7nhxdDYZ3UdXQFZmOhsitag5SnErKeorWf9nncczB8fnqqR0HGCan4k26Y0kL1QE/s1600/LGICON_3.GIF" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjro4NwCtC2TCdCM0U8llIjQWPaqnmu4Nt2WLO_hJXMRRt6pjUDNl52NfT4zBngnC52mY9Jyz9gm_C7nhxdDYZ3UdXQFZmOhsitag5SnErKeorWf9nncczB8fnqqR0HGCan4k26Y0kL1QE/s1600/LGICON_3.GIF" /></a><span style="font-family: 'Times New Roman', Georgia, Times;">The Ptolemaic picture of the universe survived, more or less intact, for almost 13 centuries, until a sixteenth-century Polish cleric, </span><a href="" name="Anchor-Nicholas-40360"></a><span style="font-family: 'Times New Roman', Georgia, Times;">Nicholas Copernicus (Figure 2.7), rediscovered Aristarchus's <a href="http://astronomylearn.blogspot.com/p/glossary.html#heliocentric model"><b>heliocentric</b></a> (Sun-centered) model and showed how, in its harmony and organization, it provided a more natural explanation of the observed facts than did the tangled geocentric cosmology. Copernicus asserted that Earth spins on its axis and, like the other planets, orbits the Sun. Only the Moon, he said, orbits Earth. Not only does this model explain the observed daily and seasonal changes in the heavens, as we saw in Chapter 1, but it also naturally accounts for planetary retrograde motion and brightness variations. <a href="" name="Anchor-The-7447"></a>The critical realization that Earth is not at the center of the universe is now known as the <a href="http://astronomylearn.blogspot.com/p/glossary.html#Copernican revolution"><b>Copernican revolution</b></a>. The seven crucial statements that form its foundation are summarized in <a href="http://astronomylearn.blogspot.com/2012/02/discovery-21-foundations-of-copernican.html"><i>Discovery 2-1</i></a><i>.</i></span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><i><br />
</i></span></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Figure 2.8 shows how the Copernican view explains both the varying brightness of a planet (in this case, Mars) and its observed looping motions. If we suppose that Earth moves faster than Mars, then every so often Earth "overtakes" that planet. Mars will then appear to move backward in the sky, in much the same way as a car we overtake on the highway seems to slip backward relative to us. Notice that in the Copernican picture the planet's looping motions are only apparent. In the Ptolemaic view, they were real.</span></div></div><br />
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<tr><td bgcolor="#fffad7"><div style="text-align: justify;"><span style="color: #e32e3a; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>Figure 2.8</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b> Retrograde Motion</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;"> The Copernican model of the solar system explains both the varying brightnesses of the planets and the phenomenon of retrograde motion. Here, for example, when Earth and Mars are relatively close to one another in their respective orbits (as at position 6), Mars seems brighter. When they are farther apart (as at position 1), Mars seems dimmer. Also, because the line of sight from Earth to Mars changes as the two planets orbit the Sun, Mars appears to loop back and forth in retrograde motion. The line of sight changes because Earth, on the inside track, moves faster in its orbit than does Mars. The white curves are the actual planetary orbits. The apparent motion of Mars, as seen from Earth, is shown as the red curve.</span></div></td></tr>
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<div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Copernicus's major motivation for introducing the heliocentric model was simplicity. Even so, he was still influenced by Greek thinking and clung to the idea of circles to model the planets' motions. To bring his theory into agreement with observations, he was forced to retain the idea of epicyclic motion, although with the deferent centered on the Sun rather than on Earth, and with smaller epicycles than in the Ptolemaic picture. Thus, he retained unnecessary complexity and actually gained little in accuracy over the geocentric model. The heliocentric model did rectify some small discrepancies and inconsistencies in the Ptolemaic system, but for Copernicus, the primary attraction of heliocentricity was its simplicity, its being "more pleasing to the mind." His theory was more something he <i>felt</i> than he could <i>prove.</i> To the present day, scientists still are guided by simplicity, symmetry, and beauty in modeling all aspects of the universe.</span></div><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Despite the support of some observational data, neither his fellow scholars nor the general public easily accepted Copernicus's model. For the learned, heliocentricity went against the grain of much previous thinking and violated many of the religious teachings of the time, largely because it relegated Earth to a noncentral and undistinguished place within the solar system and the universe. And Copernicus's work had little impact on the general populace of his time, at least in part because it was published in Latin (the standard language of academic discourse at the time), which most people could not read. <a href="" name="Anchor-Only-42626"></a>Only long after Copernicus's death, when others—notably Galileo Galilei—popularized his ideas, did the Roman Catholic Church take them seriously enough to bother banning them. Copernicus's writings on the heliocentric universe were placed on the <i>Index of Prohibited Books</i> in 1616, 73 years after they were first published. They remained there until the end of the eighteenth century.</span></div></div>Andri F Martinhttp://www.blogger.com/profile/11669920311565328714noreply@blogger.com0tag:blogger.com,1999:blog-4374048443162882832.post-40869305699937355712012-02-13T11:18:00.000+07:002012-02-13T20:00:17.577+07:002.2 The Geocentric Universe<h1 style="text-align: center;">The Geocentric Universe</h1><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;">The Greeks of antiquity, and undoubtedly civilizations before them, built models of the universe. The study of the workings of the universe on the largest scales is called </span><i style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;">cosmology.</i><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;"> Today, cosmology entails looking at the universe on scales so large that even entire galaxies can be regarded as mere points of light scattered throughout space. To the Greeks, however, the universe was basically the </span><i style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;">solar system</i><span style="background-color: white; font-family: 'Times New Roman', Georgia, Times; text-align: justify;">—namely, the Sun, Earth, Moon, and the planets known at that time. The stars beyond were surely part of the universe, but they were considered to be fixed, unchanging beacons on the celestial sphere. The Greeks did not consider the Sun, the Moon, and the planets to be part of this mammoth celestial dome, however. Those objects had patterns of behavior that set them apart.</span><br />
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</span></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Greek astronomers observed that over the course of a night, the stars slid smoothly across the sky. Over the course of a month, the Moon moved smoothly and steadily along its path on the sky relative to the stars, passing through its familiar cycle of phases. Over the course of a year, the Sun progressed along the ecliptic at an almost constant rate, varying little in brightness from day to day. In short, the behavior of both Sun and Moon seemed fairly simple and orderly. But ancient astronomers were also aware of five other bodies in the sky—the planets Mercury, Venus, Mars, Jupiter, and Saturn—whose behavior was not so easy to grasp. Their motions ultimately led to the downfall of an entire theory of the solar system and to a fundamental change in humankind's view of the universe.</span></div><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div><div style="background-color: white;"><div style="text-align: justify;"><a href="" name="Anchor-Planets-33812"></a><span style="font-family: 'Times New Roman', Georgia, Times;">Planets do not behave in as regular and predictable a fashion as the Sun, Moon, and stars. They vary in brightness, and they don't maintain a fixed position in the sky. Unlike the Sun and Moon, the planets seem to wander around the celestial sphere—indeed, the word planet derives from the Greek word <i>planetes,</i> meaning "wanderer." Planets never stray far from the ecliptic and generally traverse the celestial sphere from west to east, like the Sun. However, they seem to speed up and slow down during their journeys, and at times they even appear to loop back and forth relative to the stars, as shown in Figure 2.4. In other words, there are periods when a planet's eastward motion (relative to the stars) stops, and the planet appears to move westward in the sky for a month or two before reversing direction again and continuing on its eastward journey.</span><a href="" name="Anchor-32698"></a><span style="font-family: 'Times New Roman', Georgia, Times;"> Motion in the eastward sense is usually referred to as <i>direct,</i> or <i>prograde,</i> motion; the backward (westward) loops are known as <a href="http://astronomylearn.blogspot.com/p/glossary.html#retrograde motion"><b>retrograde motion</b></a>.</span></div></div><br />
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<tr><td bgcolor="#fffad7"><div style="text-align: justify;"><span style="color: #e32e3a; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>Figure 2.4</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b> Planetary Motion</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;"> Most of the time, planets move from west to east relative to the background stars. Occasionally—roughly once per year—however, they change direction and temporarily undergo retrograde motion before looping back. The main figure shows an actual retrograde loop in the motion of the planet Mars. The inset above depicts the movements of several planets over the course of several years, as reproduced on the inside dome of a planetarium. The motion of the planets relative to the stars (represented as unmoving points) produces continuous streaks on the planetarium "sky." (<i>Museum of Science, Boston</i>)</span></div></td></tr>
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<div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Like the Moon, the planets produce no light of their own; instead, they shine by reflected sunlight. Ancient astronomers correctly reasoned that the apparent brightness of a planet in the night sky is related to its distance from Earth—planets appear brightest when closest to us. However, the planets Mars, Jupiter, and Saturn are always brightest during the retrograde portions of their orbits. The challenge facing astronomers was to explain the observed motions of the planets and to relate those motions to the variations in planetary brightness.</span></div><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><a href="" name="Anchor-The-46548"></a>The earliest models of the solar system followed the teachings of the Greek philosopher Aristotle (384–322 B.C.) and were <a href="http://astronomylearn.blogspot.com/p/glossary.html#geocentric model"><b>geocentric</b></a>, meaning that Earth lay at the center of the universe and all other bodies moved around it. (Figures 1.7 and 1.10a illustrate the basic geocentric view.) <a href="http://astronomylearn.blogspot.com/2012/02/more-precisely-12-celestial-coordinates.html">(Sec. 1.2)</a> These models employed what Aristotle, and Plato before him, had taught was the perfect form: the circle. The simplest possible description—uniform motion around a circle with Earth at its center—provided a fairly good approximation to the orbits of the Sun and the Moon, but it could not account for the observed variations in planetary brightness or their retrograde motion. A more complex model was needed to describe the planets.</span></div></div><div style="background-color: white;"><span style="font-family: 'Times New Roman', Georgia, Times;"></span></div><table align="right" border="0" cellpadding="0" cellspacing="2" style="width: 137px;"><tbody>
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<tr><td><img height="6" src="file:///G:/CHAISSON/COMART/SPACER.GIF" width="10" /></td><td bgcolor="#fffad7"><div style="text-align: justify;"><span style="color: #e32e3a; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>Figure 2.5</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b> Geocentric Model</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;"> In the geocentric model of the solar system, the observed motions of the planets made it impossible to assume that they moved on simple circular paths around Earth. Instead, each planet was thought to follow a small circular orbit (the epicycle) about an imaginary point that itself traveled in a large, circular orbit (the deferent) about Earth.</span></div></td></tr>
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<div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><a href="" name="Anchor-In-8984"></a>In the first step toward this new model, each planet was taken to move uniformly around a small circle, called an <a href="http://astronomylearn.blogspot.com/p/glossary.html#epicycle"><b>epicycle</b></a>, whose <i>center</i>moved uniformly around Earth on a second and larger circle, known as the <b><a href="http://astronomylearn.blogspot.com/p/glossary.html#deferent">deferent</a> </b>(Figure 2.5). The motion was now composed of two separate circular orbits, creating the possibility that, at some times, the planet's apparent motion could be retrograde. Also, the distance from the planet to Earth would vary, accounting for changes in brightness. By tinkering with the relative sizes of epicycle and deferent, with the planet's speed on the epicycle, and with the epicycle's speed along the deferent, early astronomers were able to bring this "epicyclic" motion into fairly good agreement with the observed paths of the planets in the sky. Moreover, this model had good predictive power, at least to the accuracy of observations at the time.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><a href="" name="Anchor-However-53746"></a>However, as the number and the quality of observations increased, it became clear that the simple epicyclic model was not perfect. Small corrections had to be introduced to bring it into line with new observations. The center of the deferents had to be shifted slightly from Earth's center, and the motion of the epicycles had to be imagined uniform with respect to yet another point in space, not Earth. </span><a href="" name="Anchor-Around-1465"></a><span style="font-family: 'Times New Roman', Georgia, Times;">Around A.D. 140, a Greek astronomer named Ptolemy constructed perhaps the best geocentric model of all time. Illustrated in simplified form in Figure 2.6, it explained remarkably well the observed paths of the five planets then known, as well as the paths of the Sun and the Moon. However, to achieve its explanatory and predictive power, the full </span><a href="" name="Anchor-Ptolemaic-59037"></a><a href="http://astronomylearn.blogspot.com/p/glossary.html#Ptolemaic model"><span style="font-family: 'Times New Roman', Georgia, Times;"><b>Ptolemaic model</b></span></a><span style="font-family: 'Times New Roman', Georgia, Times;"> required a series of no fewer than 80 distinct circles. To account for the paths of the Sun, Moon, and all nine planets (and their moons) that we know today would require a vastly more complex set. Nevertheless, Ptolemy's text on the topic,<i>Syntaxis</i> (better known today by its Arabic name <i>Almagest</i>—"the greatest"), provided the intellectual framework for all discussion of the universe for well over a thousand years.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
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<tr><td><img height="6" src="file:///G:/CHAISSON/COMART/SPACER.GIF" width="10" /></td><td bgcolor="#fffad7"><div style="text-align: justify;"><span style="color: #e32e3a; font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b>Figure 2.6</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular;"><i><b> Ptolemy's Model</b></i></span><span style="font-family: Arial, Helvetica, Geneva, Swiss, SunSans-Regular; font-size: x-small;"> The basic features, drawn roughly to scale, of the geocentric model of the inner solar system that enjoyed widespread popularity prior to the Renaissance. The planets' deferents were considered to move on spheres lying within the celestial sphere that held the stars. The celestial sphere carried all interior spheres around with it, but the planetary (and solar) spheres had additional motions of their own, causing the Sun and planets to move relative to the stars. To avoid confusion, partial paths (dashed) of only two planets, Venus and Jupiter, are drawn here.</span></div></td></tr>
</tbody></table><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Today, our scientific training leads us to seek simplicity, because simplicity in the physical sciences has so often proved to be an indicator of truth. </span><a href="" name="Anchor-We-60152"></a><span style="font-family: 'Times New Roman', Georgia, Times;">We would regard the intricacy of a model as complicated as the Ptolemaic system as a clear sign of a fundamentally flawed theory. With the benefit of hindsight, we now recognize that the major error lay in the assumption of a geocentric universe. This was compounded by the insistence on uniform circular motion, whose basis was largely philosophical, rather than scientific, in nature.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">Actually, history records that some ancient Greek astronomers reasoned differently about the motions of heavenly bodies.<a href="" name="Anchor-Foremost-37657"></a>Foremost among them was Aristarchus of Samos (310–230 B.C.), who proposed that all the planets, including Earth, revolve around the Sun and, furthermore, that Earth rotates on its axis once each day. This, he argued, would create an <i>apparent</i> motion of the sky—a simple idea that is familiar to anyone who has ridden on a merry-go-round and watched the landscape appear to move past in the opposite direction. However, Aristarchus's description of the heavens, though essentially correct, did not gain widespread acceptance during his lifetime. Aristotle's influence was too strong, his followers too numerous, his writings too comprehensive. The geocentric model went largely unchallenged until the sixteenth century A.D.</span></div><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;"><br />
</span></div></div><div style="background-color: white;"><div style="text-align: justify;"><span style="font-family: 'Times New Roman', Georgia, Times;">The Aristotelian school did present some simple and (at the time) compelling arguments in favor of their views. First, of course, Earth doesn't <i>feel</i> as if it's moving. And if it were, wouldn't there be a strong wind as we move at high speed around the Sun? Then again, considering that the vantage point from which we view the stars changes over the course of a year, why don't we see stellar parallax? Nowadays we might be inclined to dismiss the first two points as merely naïve, but the third is a valid argument and the reasoning is essentially sound. We now know that there <i>is</i> stellar parallax as Earth orbits the Sun. However, because the stars are so distant, it amounts to less than 1", even for the closest stars. Early astronomers simply would not have noticed it. We will encounter many other instances in astronomy where correct reasoning has led to the wrong conclusions because it was based on inadequate data.</span></div></div>Andri F Martinhttp://www.blogger.com/profile/11669920311565328714noreply@blogger.com0