# Lunar Motion and Phases

The Moon's monthly cycle is due to its orbital motion about the Earth. By tracking the Moon and its phases, we can begin to see the sky in three dimensions.

Background Reading: Stars & Planets, p. 302 to 305 (The Moon).

The Moon is a ball of rock lit by the Sun. As it orbits the Earth, different parts of its surface are illuminated, and we see the Moon go through a cycle of phases from new to full and back to new again. To understand the Moon's phases, you need to understand the play of light and shadow on its surface.

### LIGHT AND SHADOW

A ball illuminated only by a distant source of light will show phases much like the Moon's. Imagine a white ball hanging in space some distance in front of you. We will call the side of the ball which faces you the `visible' surface, even though part of this side may be in shadow, depending on the direction of the light. The table below describes the appearance of the ball as we move the light source around:

 Position of light source Appearance of ball Phase Far behind you Entire visible surface illuminated full Behind and to the left Right edge in shadow gibbous Far off to the left Right half in shadow quarter In front and to the left Most of right side in shadow crescent Far behind the ball Entire visible surface dark new In front and to the right Most of left side in shadow crescent Far off to the right Left half in shadow quarter Behind and to the right Left edge in shadow gibbous
The third column above gives the names of the various shapes or phases of the Moon; `full', `new', and `crescent' are pretty self-explanatory, and `gibbous' merely means not quite full. On the other hand, `quarter' probably seems counter-intuitive, since half, and not a quarter, of the visible surface is illuminated. The explanation is that a quarter moon is either one-quarter or three-quarters of the way through its orbit.

In reality, of course, the Moon is moving about the Earth, while our `source of light', namely the Sun, stays fixed. The odd name astronomers give to a Moon which appears half illuminated reflects this basic fact. But as far as the appearance of the Moon at any given instant is concerned, all that really matters are the relative positions of the Earth (our point of view), the Moon, and the Sun.

With a little experience, you can `read' the appearance of the Moon and figure out the Sun's position. For example, if you see a crescent Moon in the East, with its bright side facing down and somewhat to the left, you can deduce that the Sun is below the horizon and somewhat North of the Moon's position. In doing this, you are also learning to see the Sun and Moon as objects in space, rather than light sources attached to the inside of some imaginary celestial sphere.

#### Earthlight

When you see a crescent Moon in the sky, you may notice that the part in shadow is not completely dark. With binoculars or a telescope, you may even be able to see some details within the shadowed region. This is a beautiful sight, sometimes called `the old Moon in the new Moon's arms'. Of course, the shadowed side of the Moon would be completely dark if the Sun was the only source of light - so what other source of light does the Moon have? The answer, obvious to anyone standing on the Moon, is the Earth.

The best times to see earthlight are just before and just after a new Moon. At these times the Earth appears nearly full as seen from the Moon and therefore provides the greatest amount of light; also, only a slim crescent of the Moon is sunlit so there's less glare to interfere with our view. If you look closely, however, you may be able to see earthlight at other points in the Moon's cycle. The amount of light reflected by the Earth changes from day to day; clouds reflect more light than open ocean, so earthlight tends to be stronger when storms cover most of the Pacific.

### LUNAR MOTION

As the Moon orbits the Earth, its position with respect to the Sun changes from night to night. You can get a good sense of the Moon's motion by looking for it at the same time every evening for a few weeks. You should do this in early February, 2003; the Moon is new on 02/01/03 and full on 02/16/03, so a series of observations during the first two weeks of February will give you a good chance to see the Moon move across the sky. (If February is too cloudy, we'll try again in March.) Observe from a place where you have a fairly clear view to the West (and, if possible, to the East, though this is not as important as the western view). Begin looking around 18:15 (6:15 pm), which is just about sunset in February. If the weather is good, you should be able to spot a slender crescent Moon low in the West by Feb. 2nd or 3rd. Once you've found the Moon, note the time in your observing log, sketch the Moon's appearance, and describe its position in the sky. Come back next day and look at the same time; you'll find the Moon considerably higher in the sky and easier to see. Keep on making observations every night you can, and record them in your log. A half-dozen observations spread over the first two weeks of February will be enough to show you the Moon's motion; don't worry if you miss a few nights due to bad weather or other commitments.

The changing times that the Moon rises and sets are due to its motion about the Earth. Because the Moon moves across the sky in a direction opposite the apparent rotation of the celestial sphere, the average time from one moonrise to the next is almost 25 hours (and likewise for the time from one moonset to the next). For example, on Feb. 1st the Moon will rise and set at almost the same times as the Sun, while on Feb. 16th it will rise about sunset and set about sunrise. The Moon will continue to rise and set later and later through the rest of February; if you want to observe moonrise in late February, for example, you'll have to stay up late, or get up before dawn, or both.

### MOTION AND PHASES

As you track the Moon across the sky, you'll notice that its phase changes from one evening to the next. In early February the Moon appears as a crescent; by the end of the first week it will appear at first quarter, and by the end of the second week it will appear nearly full. If you continue observing the Moon for the rest of the month you will see the phase continues to change from full to last quarter and then back to a crescent; the next new Moon is on Mar. 2nd. This cycle of phases occurs every 29.5 days, which is the time it takes the Moon to make one trip across the sky and come back to the same position with respect to the Sun. We normally count cycles from one new Moon to the next; during the first half of the cycle, the Moon is waxing (getting more full), while during the second half, the Moon is waning (getting less full).

By now it will probably be obvious that the Moon's phase is determined by the angle of the sunlight striking its surface. To reinforce this point, however, you should do a simple experiment. On a clear day in early February, locate the Moon in the daytime sky - this should be pretty easy after Feb. 5th or so if you look late in the afternoon. Hold a small ball up in sunlight next to the Moon, and compare its phase with the phase of the Moon. For best results, use a ball made from some fairly dull, opaque material; if the ball has a shiny surface, you'll get a bright spot which will make it harder to see phases. Repeat this experiment a few times over the next week or so. Do the Moon and the ball always have the same phase?

### SIDEREAL MOTION

To follow the Moon's motion in more detail, you can track its position with respect to the stars. This is pretty easy to do once you've learned to recognize a few constellations. On the evening of Feb. 4 the Moon will be between Aquarius and Pisces, but on the 11th it will be found in Taurus, and on the 18th it will be between Leo and Virgo. (If this sounds like an excerpt from an astrology column, it's because the Moon's path across the sky never strays very far from the ecliptic, the Sun's apparent annual path, which is also the traditional zodiac.)

The Moon takes just 27.3 days to make one complete cycle with respect to the stars. For example, on Mar. 11th, which is exactly 28 days after Feb. 11th, the Moon will have come back through Taurus and continued into Gemini. This 27.3 day sidereal period is the time the Moon actually takes to complete one orbit about the Earth (the term `sidereal' just means `measured with respect to the stars'). Why does the Moon take longer - 29.5 days, to be precise - to make a complete cycle of phases? Remember that the Moon's phase is determined by the relative positions of the Earth, the Moon, and the Sun. Not only does the Moon orbit the Earth; in addition, the Earth and Moon together orbit the Sun! As a result, it takes the Moon slightly more than one orbital period to return to the same position with respect to the Sun. For example, we have a new Moon on 02/01/03, 0:51; at that time, the Moon and the Sun are both in Capricorn. Exactly 27.3 days later, on 02/28/03, 8:03, the Moon will have returned to the same place in Capricorn, but the Sun will now appear in Aquarius as a result of the Earth's orbital motion. The Moon will not catch up with the Sun again until 03/02/03, 16:37, at which time it will again be new.

Although your eye can easily see the Moon's movement with respect to the stars, we can do a much better job using a telescope. To really track the Moon's motion, it helps if you can see a lot of stars fairly close to the Moon, and a telescope reveals stars which would otherwise be overcome by the Moon's brilliant light. They also magnify things so you can measure the Moon's position more accurately. Accurate measurements of the Moon's position with respect to the stars will be useful for at least two interesting exercises. First, we can use such measurements to help estimate the Moon's distance from Earth; this will illustrate one of the key astronomical techniques of distance measurement. Second, we may be able use a series of measurements of the Moon's position to show that the Moon's motion across the sky is not uniform; this is useful in determining the Moon's orbit and testing Kepler's laws.

To make an accurate measurement of the Moon's position, you need a detailed map of the stars behind the Moon; we will provide such a map each night we observe the Moon. Observe the stars around the Moon's position and match them up with the stars on the chart. Once you have done so, draw a circle on the chart showing the Moon's position.

#### Occultations

An occultation occurs when the Moon comes between us and a star or planet. There are no occultations of planets during 2003, but we will have a chance to observe several occultations of stars. Observing an occultation is a direct way to watch the Moon moving with respect to the stars; instead of comparing the Moon's position from one night to the next, you can see the Moon drift in front of a star and cut off its light in an instant. (The rapid cutoff of stellar light also provides evidence that stars are very far away.)

### WEB RESOURCES

• Lunar Phases: high res. (2.8 Mbyte mpeg); low res. (0.8 Mbyte mpeg).

Animation showing lunar phases from 01/14/03, 14:00 to 05/13/03, 8:00 (01/15/03, 0:00 UT to 05/13/03, 18:00 UT). Note that the Moon's size changes as its distance varies; in addition, the Moon `nods' slightly.

• Solar System Simulator

A very nice website where you can generate an image of a Solar System object as seen from elsewhere in the Solar System.

• Lunar Perigee and Apogee Calculator

JavaScript program to calculate dates of new and full Moon, as well as dates of lunar perigee (closest to Earth) and apogee (furthest from Earth). Created by John Walker.

• Astronomy On-Line: How to study the movement of the Moon

Describes a simple tool to measure the angular separation between the Moon and the Sun; provides another way to see that the Moon's orbital motion is not quite uniform. (Fig. 2 of this web-page has a rather silly error; can you spot it?)

### REVIEW QUESTIONS

• Here are four images of the Moon. What is the phase of each image, and where is the Sun with respect to the Moon?

• Suppose the Moon was flat like a coin, with one side always facing us. What would the Moon's phases be like?

• If you face North and observe the Moon at the same time each night, which way will the Moon seem to move about you - clockwise or counter-clockwise?

### REPORT: LUNAR MOTION AND PHASES

Make the observations described in the sections on LUNAR MOTION and MOTION AND PHASES, and write a report on your work. This report should include, in order,

1. a general introduction to the observations,
2. a description of the observing site and equipment you used,
3. a summary of your observations, and
4. the conclusions you have reached.

In more detail, here are several things you should be sure to do in your lab report:

• Describe the Moon's position in the sky each time you observe it, and summarize its motion over the course of your observations.

• Describe the Moon's phase and appearance each time you observe it. How does its phase change over the course of your observations?

• Do you notice earthlight at any time during these observations? Note: binoculars may help you see the dark side more clearly.

• How does the appearance of the Moon compare to the appearance of the ball you hold up next to it? Include a few sketches in your lab report.

Joshua E. Barnes (barnes@ifa.hawaii.edu)