More Precisely 1.2 - Celestial Coordinates

Posted by Andri Fadillah Martin on Wednesday, February 8, 2012

Celestial Coordinates


The simplest method of locating stars in the sky is to specify their constellation and then rank the stars in it in order of brightness. The brightest star is denoted by the Greek letter α (alpha), the second brightest by β (beta), and so on (see Figure 1.6). Thus, the two brightest stars in the constellation Orion—Betelgeuse and Rigel—are also known as α Orionis and  β  Orionis, respectively. (More recent, precise observations show that Rigel is actually brighter than Betelgeuse, but the names are now permanent.) Similarly, Sirius, the brightest star in the sky (see Appendix 3), which lies in the constellation Canis Major (the Great Dog), is denoted α Canis Majoris (or α CMa for short); the (present) Pole Star, in Ursa Minor (the Little Bear), is also known as  α  Ursae Minoris (or  α  UMi), and so on. Because there are many more stars in any given constellation than there are letters in the Greek alphabet, this method is of limited utility. However, for naked-eye astronomy, where only bright stars are involved, it is quite satisfactory.

For more precise measurements, astronomers find it helpful to lay down a system of celestial coordinates on the sky. If we think of the stars as being attached to the celestial sphere centered on Earth, then the familiar system of latitude and longitude on Earth’s surface extends naturally to cover the sky. The celestial analogs of latitude and longitude on Earth’s surface are called declination and right ascension, respectively. The accompanying figure illustrates the meanings ofright ascension and declination on the celestial sphere and compares them with longitude and latitude on Earth.

 Declination (dec) is measured in degrees (°) north or south of the celestial equator, just as latitude is measured in degrees north or south of Earth’s equator. (See More Precisely 1-1 for a discussion of angular measure.) Thus, the celestial equator is at a declination of 0°, the north celestial pole is at +90°, and the south celestial pole is at -90° (the minus sign here just means "south of the celestial equator").

 Right ascension (RA) is measured in units called hours, minutes, and seconds, and it increases in the eastward direction. The angular units used to measure right ascension are constructed to parallel the units of time, in order to assist astronomical observation. The two sets of units are connected by the rotation of Earth (or of the celestial sphere). In 24 hours, Earth rotates once on its axis, or through 360°. Thus, in a time period of one hour, Earth rotates through 360°/24 = 15°, or 1h. In one minute of time, Earth rotates through an angle of 1m = 15°/60 = 0.25°, or 15 arc minutes (15´). In one second of time, Earth rotates through an angle of 1s = 15´/60 = 15 arc seconds (15´´). As with longitude, the choice of zero right ascension (the celestial equivalent of the Greenwich Meridian) is quite arbitrary—it is conventionally taken to be the position of the Sun in the sky at the instant of the vernal equinox.

Right ascension and declination specify locations on the sky in much the same way as longitude and latitude allow us to locate a point on Earth’s surface. For example, to find Washington on Earth, look 77° west of the Greenwich Meridian (the line on Earth’s surface with a longitude of zero) and 39° north of the equator. Similarly, to locate the star Betelgeuse on the celestial sphere, look 5h52m0s east of the vernal equinox (the line on the sky with a right ascension of zero) and 7°24' north of the celestial equator. The star Rigel, also mentioned earlier, lies at 5h13m36s (RA), -8°13´ (dec). Thus, we have a quantitative alternative to the use of constellations in specifying the positions of stars in the sky. Just as latitude and longitude are tied to Earth, right ascension and declination are fixed on the celestial sphere. Although the stars appear to move across the sky because of Earth’s rotation, their celestial coordinates remain constant over the course of a night.

Actually, because right ascension is tied to the position of the vernal equinox, the celestial coordinates of any given star slowly drift due to Earth’s precession (see Section 1.4). Since one cycle of precession takes 26,000 years to complete, this represents a shift of a little over 0.1´´ on a night-to-night basis—a small angle, but one that must be taken into account in high-precision astronomical measurements. Rather than deal with slowly changing coordinates for every object in the sky, astronomers conventionally correct their observations to the location of the vernal equinox at some standard epoch (such as 1 January 1950 or 1 January 2000).

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