1.4 The Motion of the Moon

Posted by Andri Fadillah Martin on Friday, February 10, 2012

The Motion of the Moon

 The Moon is our nearest neighbor in space. Apart from the Sun, it is the brightest object in the sky. Like the Sun, the Moon appears to move relative to the background stars. Unlike the Sun, however, the Moon really does revolve around Earth. It crosses the sky at a rate of about 12° per day, which means it moves an angular distance equal to its own diameter—30 arc minutes—in about an hour.

LUNAR PHASES

The Moon's appearance undergoes a regular cycle of changes, or phases, taking a little more than 29 days to complete. (The word month is derived from the word moon.) Figure 1.15 illustrates the appearance of the Moon at different times in this monthly cycle. Starting from the new Moon,which is all but invisible in the sky, the Moon appears to wax (or grow) a little each night and is visible as a growing crescent (panel 1 of Figure 1.15). One week after new Moon, half of the lunar disk can be seen (panel 2). This phase is known as a quarter Moon. During the next week, the Moon continues to wax, passing through the gibbous phase (panel 3) until, two weeks after new Moon, the full Moon (panel 4) is visible. During the next two weeks, the Moon wanes (or shrinks), passing in turn through the gibbous, quarter, and crescent phases (panels 5–7), eventually becoming new again.

Figure 1.15 Lunar Phases Because the Moon orbits Earth, the visible fraction of the sunlit face differs from night to night. The complete cycle of lunar phases takes 29.5 days to complete. (UC/Lick Observatory)


The Moon doesn't actually change its size and shape from night to night, of course. Its full circular disk is present at all times. Why then don't we always see a full Moon? The answer to this question lies in the fact that, unlike the Sun and the other stars, the Moon emits no light of its own. Instead, it shines by reflected sunlight. As illustrated in Figure 1.15, half of the Moon's surface is illuminated by the Sun at any instant. However, not all of the Moon's sunlit face can be seen because of the Moon's position with respect to Earth and the Sun. When the Moon is full, we see the entire "daylit" face because the Sun and the Moon are in opposite directions from Earth in the sky. In the case of a new Moon, the Moon and the Sun are in almost the same part of the sky, and the sunlit side of the Moon is oriented away from us. At new Moon, the Sun must be almost behind the Moon, from our perspective.


Figure 1.16 Sidereal Month The difference between a synodic and a sidereal month stems from the motion of Earth relative to the Sun. Because Earth orbits the Sun in 365 days, in the 29.5 days from one new Moon to the next (one synodic month), Earth moves through an angle of approximately 29°. Thus the Moon must revolve more than 360° between new Moons. The sidereal month, which is the time taken for the Moon to revolve through exactly 360°, relative to the stars, is about two days shorter.
As it revolves around Earth, the Moon's position in the sky changes with respect to the stars. In one sidereal month (27.3 days), the Moon completes one revolution and returns to its starting point on the celestial sphere, having traced out a great circle in the sky. The time required for the Moon to complete a full cycle of phases, one synodic month, is a little longer—about 29.5 days. The synodic month is a little longer than the sidereal month for the same reason that a solar day is slightly longer than a sidereal day: Because of Earth's motion around the Sun, the Moon must complete slightly more than one full revolution to return to the same phase in its orbit (Figure 1.16).

ECLIPSES

From time to time—but only at new or full Moon—the Sun and the Moon line up precisely as seen from Earth, and we observe the spectacular phenomenon known as an eclipseWhen the Sun and the Moon are in exactly opposite directions, as seen from Earth, Earth's shadow sweeps across the Moon, temporarily blocking the Sun's light and darkening the Moon in a lunar eclipse, as illustrated in Figure 1.17. From Earth, we see the curved edge of Earth's shadow begin to cut across the face of the full Moon and slowly eat its way into the lunar disk. Usually, the alignment of the Sun, Earth, and Moon is imperfect, so the shadow never completely covers the Moon. Such an occurrence is known as a partial lunar eclipseOccasionally, however, the entire lunar surface is obscured in a total lunar eclipse, such as that shown in the inset of Figure 1.17. Total lunar eclipses last only as long as is needed for the Moon to pass through Earth's shadow—no more than about 100 minutes. During that time, the Moon often acquires an eerie, deep red coloration—the result of a small amount of sunlight reddened by Earth's atmosphere (for the same reason that sunsets appear red—see More Precisely 7-1) and refracted (bent) onto the lunar surface, preventing the shadow from being completely black.


Figure 1.17 Lunar Eclipse A lunar eclipse occurs when the Moon passes through Earth's shadow. At these times we see a darkened, copper-colored Moon, as shown in the inset photograph. The red coloration is caused by sunlight being reddened and deflected by Earth's atmosphere onto the Moon's surface. An observer on the Moon would see Earth surrounded by a bright but narrow ring of orange sunlight. Note that this figure is not drawn to scale, and only Earth's umbra (see text and Figure 1.19) is shown. (Inset: G. Schneider)


When the Moon and the Sun are in exactly the same direction, as seen from Earth, an even more awe-inspiring event occurs. The Moon passes directly in front of the Sun, briefly turning day into night in a solar eclipse. In a total solar eclipse, when the alignment is perfect, planets and some stars become visible in the daytime as the Sun's light is reduced to nearly nothing. We can also see the Sun's ghostly outer atmosphere, or corona (Figure 1.18a).* In a partial solar eclipse, the Moon's path is slightly "off center," and only a portion of the Sun's face is covered. In either case, the sight of the Sun apparently being swallowed up by the black disk of the Moon is disconcerting even today. It must surely have inspired fear in early observers. Small wonder that the ability to predict such events was a highly prized skill.

Figure 1.18 Solar Eclipse (a) During a total solar eclipse the Sun's corona becomes visible as an irregularly shaped halo surrounding the blotted-out disk of the Sun. This was the August 1999 eclipse, as seen from the banks of the Danube River near Sofia, Bulgaria. (b) During an annular eclipse, the Moon fails to completely hide the Sun, so a thin ring of light remains. No corona is seen in this case because even the small amount of the Sun still visible completely overwhelms the corona's faint glow. This was the December 1973 eclipse, as seen from Algiers. (The gray fuzzy areas at top left and right are clouds in Earth's atmosphere.) (Bencho Angelov; G. Schneider)


Unlike a lunar eclipse, which is simultaneously visible from all locations on Earth's night side, a total solar eclipse can be seen from only a small portion of Earth's daytime side. The Moon's shadow on Earth's surface is about 7000 kilometers wide—roughly twice the diameter of the Moon (Figure 1.19). Outside of that shadow, no eclipse is seen. However, within the central region of the shadow, called the umbra, the eclipse is total. Within the shadow but outside the umbra, in the penumbra, the eclipse is partial, with less and less of the Sun obscured the farther one travels from the shadow's center. The connections among the umbra, the penumbra, and the relative locations of Earth, Sun, and Moon are illustrated in Figure 1.20. One of the reasons that total solar eclipses are rare is that although the penumbra is some 7000 kilometers across, the umbra is always very small. Even under the most favorable circumstances, its diameter never exceeds 270 kilometers. Because the shadow sweeps across Earth's surface at over 1700 kilometers per hour, the duration of a total eclipse at any given point can never exceed 7.5 minutes.

Figure 1.19 Lunar Shadow Photograph taken by an Earth-orbiting weather satellite of the Moon's shadow projected onto Earth's surface (off the coast of Baja California) during the total solar eclipse of July 11, 1991. (Inset: NOAA)


The Moon's orbit around Earth is not exactly circular. Thus, the Moon may be far enough from Earth at the moment of an eclipse that its disk fails to cover the disk of the Sun completely, even though their centers coincide. In that case, there is no region of totality—the umbra never reaches Earth at all, and a thin ring of sunlight can still be seen surrounding the Moon. Such an occurrence, called an annular eclipse, is depicted in Figures 1.18(b) and 1.20. Roughly half of all solar eclipses are annular.


Figure 1.20 Solar Eclipse Types The Moon's shadow on Earth during a solar eclipse consists of the umbra, where the eclipse is total, and the penumbra, where the Sun is only partially obscured. If the Moon is too far from Earth at the moment of the eclipse, there is no region of totality; instead, an annular eclipse is seen. (Inset: G. Schneider)


Why isn't there a solar eclipse at every new Moon and a lunar eclipse at every full Moon? The answer is that the Moon's orbit is slightly inclined to the ecliptic (at an angle of 5.2°), so the chance that a new (or full) Moon will occur just as the Moon happens to cross the ecliptic plane (so Earth, Moon, and Sun are perfectly aligned) is quite low. Figure 1.21 illustrates some possible configurations of the three bodies. If the Moon happens to lie above or below the plane of the ecliptic when new (or full), a solar (or lunar) eclipse cannot occur. Such a configuration is termed unfavorable for producing an eclipse. In a favorable configuration, the Moon is new or full just as it crosses the ecliptic plane, and eclipses are seen. Unfavorable configurations are much more common than favorable ones, so eclipses are relatively rare events.


Figure 1.21 Eclipse Geometry (a) An eclipse occurs when Earth, Moon, and Sun are precisely aligned. If the Moon's orbital plane lies in exactly the plane of the ecliptic, this alignment would occur once a month. However, the Moon's orbit is inclined at about 5° to the ecliptic, so not all configurations are favorable for producing an eclipse. (b) For an eclipse to occur, the line of intersection of the two planes must lie along the Earth–Sun line. Thus, eclipses can occur only at specific times of the year. Only the umbra of each shadow is shown, for clarity (see Figure 1.19).


As indicated on Figure 1.21(b), the two points on the Moon's orbit where it crosses the ecliptic plane are known as the nodes of the orbit. The line joining them, which is also the line of intersection of Earth's and the Moon's orbital planes, is known as the line of nodes. When the line of nodes is not directed toward the Sun conditions are unfavorable for eclipses. However, when the line of nodes briefly lies along Earth–Sun line, eclipses are possible. These two periods, known as eclipse seasons, are the only times at which an eclipse can occur. Notice that there is no guarantee that an eclipse will occur. For a solar eclipse, we must have a new Moon during an eclipse season. Similarly, a lunar eclipse can occur only at full Moon during an eclipse season. Figure 1.22 shows the location and duration of all total and annular eclipses of the Sun between 2000 and 2020. Because we know the orbits of Earth and the Moon to great accuracy, we can predict eclipses far into the future.

Figure 1.22 Eclipse Tracks Regions of Earth that will see total or annular solar eclipses between the years 2000 and 2020. Each track represents the path of the Moon's umbra across Earth's surface during an eclipse. The width of the track depends upon latitude on Earth and upon the distance from Earth to the Moon during the eclipse. High-latitude tracks are broader because sunlight strikes Earth's surface at an oblique angle near the poles (and also because of the projection of the map). The closer the Moon is to Earth during a total eclipse, the wider the umbra (see Figure 1.19).


The solar eclipses that we do see highlight a remarkable cosmic coincidence. Although the Sun is many times farther away from Earth than is the Moon, it is also much larger. In fact, the ratio of distances is almost exactly the same as the ratio of sizes, so the Sun and the Moon both have roughly the same angular diameter—about half a degree seen from Earth. Thus, the Moon covers the face of the Sun almost exactly. If the Moon was larger, we would never see annular eclipses, and total eclipses would be much more common. If the Moon was a little smaller, we would see only annular eclipses.

The gravitational tug of the Sun causes the Moon's orbital orientation, and hence the direction of the line of nodes, to change slowly with time. As a result, the time interval between one orbital configuration with the line of nodes pointing at the Sun and the next (with the Moon crossing the ecliptic in the same sense in each case) is not exactly 1 year, but instead is 346.6 days—oneeclipse year. Thus the eclipse seasons gradually progress backward through the calendar, occurring about 19 days earlier each year. This phenomenon is known as the regression of the line of nodes.


In 1991 the eclipse seasons were in January and July; on July 11 a total eclipse actually occurred, visible in Hawaii, Mexico, and parts of Central and South America. Three years later, in 1994, the eclipse seasons were in May and October; on May 10 an annular eclipse was visible across much of the continental United States. By 1999, the eclipse seasons had drifted into February and August, and on August 11 much of Europe and southern Asia was treated to the last total eclipse of the millennium.

The combination of the eclipse year and the Moon's synodic period leads to an interesting long-term cycle in solar (and lunar) eclipses. A simple calculation shows that 19 eclipse years is almost exactly 223 lunar months. Thus, every 6585 solar days (actually 18 years, 11.3 days) the "same" eclipse recurs. This repetition is called the Saros cycle. Well known to ancient astronomers, it undoubtedly was the key to their "mystical" ability to predict eclipses!.

*Actually, although a total solar eclipse is undeniably a spectacular occurrence, the visibility of the corona is probably the most important astronomical aspect of such an event today. It enables us to study this otherwise hard-to-see part of our Sun (see Chapter 16).

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