The Phases of the Moon |
(Think about these carefully before you consult the answers below)
QUESTIONS
1) How would the phases change if the Moon were farther from the Earth? Closer? <answer>
2) How would the phases be affected if the Moon's Period around the Earth were the same as the Earth's period around the Sun (one year)? <answer>
3) The Moon's orbit is slightly elliptical, not circular. This has only a minimal effect on the phases. What would the effect be, however, if the Moon's orbit were significantly elliptical (elongated)? <answer>
4) When is the best time to observe particular lunar features with a telescope? <answer>
5) Why are the same features of the Moon always visible at the same phase? <answer>
6) If the Moon were more massive than it is right now, would that have an effect on the phases? <answer>
7) What if the Moon didn't Exist? What would be affected? <answer>
ANSWERS
1) The main affect that the Moon's distance has on the phases is on the exact timing. If the Moon were farther from Earth, it's orbital period would be greater, and hence the timing between phases would be greater. As an example, if the Moon were twice as far from the Earth on average as it is today, the "month" would be 2.83 times as long as it is today, or about 80 days. The time between successive phases would be 2.83 times as great also, or about 20 days.
On the other hand, if the Moon were closer, the time periods would be accordingly shorter. The exact relationship of average distance (A) to orbital period (P) is:
P = A 1.5
Thus, leaving it as it is, P is 1 and A is 1, leaving 1 = 1
If the average distance increases to twice the original, we get P = 2 1.5 = 2.83 (rounded).
2) Presuming that motion of the moon continued in the same direction, the effect would be to stop the phases altogether. The phase would depend on the Moon's orientation relative to the Sun, as it does now, but with the two orbital periods in sync, there would be no change of phase at all. If the Moon were Full, it would always remain full -- every night would have a Full Moon that rose at about sunset and set at about sunrise. The only change would be a slight variation in apparent size due to the variations in the Moon's distance from the Earth, and a slight "wobble" due to the fact that the Moon's orbit is slightly inclined relative to the Earth's orbit around the Sun.
3) If the Moon's orbit were significantly elliptical, the timing of the phases would be affected. Because of Kepler's 2nd Law (or more precisely, Newton's reformulation of Kepler's 2nd Law, now known as the Law of Conservation of Angular Momentum), the speed of the Moon would be greater when it was closer to the Earth than when it is farther away. Thus the time between successive phases would be shorter when the Moon was nearer the Earth and longer when it was farther away. Thus in one example, the time between New Moon and First Quarter might be 4 days, but the time between First Quarter and Full Moon might be 20 days. The exact timing, however, would depend on the precise combination of average distance and eccentricity.
4) The best time to observer lunar features with a telescope is usually when that feature is near the terminator, or the line between daylight and dark on the Moon. This is because shadows are longer and more prominent at this time, and thus features are easier to pick out. At Full Moon the features near the center of the Moon's visible surface cast only very short shadows or none at all, decreasing their contrast with surrounding terrain.
5) The same features are visible each time at the same phase of the Moon because the Moon always keeps one face toward Earth. The Moon is said to be in "synchronous" orbit, meaning the the time it takes to orbit the Earth (the Moon's version of a "year") is exactly the same time it takes to turn once on its axis (a lunar day). The two motions offset each other and the face of the Moon turned toward Earth is always the same. (There are slight variations, called "librations," that allow the Moon to "nod" slightly, exposing a bit more of its surface from time to time. At any one time, only 50 percent of the Moon's surface is turned toward Earth, but an additional 9 percent is exposed to our view from time to time.)
By the way, people used to refer to the side of the Moon turned away from us as the "Dark Side of the Moon." However, this is inaccurate. The Far Side of the Moon gets as much sunshine as the side facing us. When the Moon is New (that is, the side facing us is dark), then the Far Side is illuminated by the Sun. Unfortunately we can't see it.
6) If the Moon were more massive than it is right now, there would be changes in the timing of phases. Strictly speaking, the Moon does not orbit the Earth, but rather orbits a point known as the barycenter, which is the center of mass of the Earth-Moon system. The Earth also orbits around this point. Since the Earth is much more massive than the Moon (81 times), the barycenter is much closer to the center of the Earth than the Moon. In fact, it is located roughly 1440 kilometers under the surface of the Earth, along a line between the Earth and Moon.
If the Moon were more massive than it is now, the barycenter would be located closer to the Moon. If the Earth and Moon were of equal mass, the barycenter would be half-way between the two bodies. Imagine that the Moon were 10 times as massive as it is now. In that case the barycenter would be 20 times closer to the Moon than it is now. . Our world would orbit this otherwise empty bit of space about 60 thousand miles from the center of the Earth, and the Moon would orbit with a radius of about 180 thousand miles. Consequently, the Moon and Earth would sometimes come much closer than they do today. This, in turn, would alter the Moon's apparent motion through the heavens and the timing between phases.
7) I won't answer this specifically, other than to say that many things, from ocean tides to human intellectual progress, would be greatly affected. Take some time and come up with your own answers and theories. For ideas, there is a great little book of the same title, What if the Moon Didn't Exist by Neil Comins (HarperPerennial, 1993)
Back