Understanding Lunar Phases: Exploring the Earth-Moon System

23 Name: _________________________________ Partner(s): _____________________________ _____________________________ AST 111: Lab #3 Relative Motions of the Earth-Moon-Sun System: Part 2 (Phases of the Moon) Objectives • To kinesthetically investigate the causes of the phases of the Moon • To construct a lunar phase diagram • To determine when a lunar phase will occur • To determine the times on Earth that a lunar phase will occur • To understand the scale of the Earth-Moon system Materials • Table-top planetarium • Ruler • Softball • Ping-Pong ball • Flashlight References • None Introduction As seen elsewhere, the relative positions and motions of the Earth, Moon, and Sun give rise to our most common everyday units of time, the day and the month. But they also are important for understanding the phases of the Moon, eclipses of the Moon and Sun, the seasons and even climatic changes on the Earth. The purpose of this lab and the next will be to improve our understanding of how these phenomena are determined by these relative motions. As we have seen in a previous lab, the Moon’s orbit can be separated into two types: the sidereal (i.e. with respect to the stars) and the synodic (i.e. with respect to the Sun). The Moon’s sidereal period – about 27 1/3 days long – can be said to be its “real” orbital period, but the synodic period – about 29 ½ days long – is the period people pay attention to, because it shows the cycle of the phases of the Moon. Here we will examine in detail the characteristics of the lunar phases.

24 Activity #1: The Phases of the Moon – Part 1 The Moon is the second-brightest natural object in the sky, following of course the Sun. The Sun gives off light of its own accord, and therefore always appears as a bright disk. In contrast, the Moon merely reflects light. 1 The appearance of the Moon therefore depends not only on the side of the Moon facing the Sun, but also on the amount of the sun-lit side of the Moon facing the Earth. The specific appearance of the Moon is called a phase . We will begin our investigation of lunar phases by walking through the orbit of the Moon about the Earth, in conjunction with a short discussion using a lighted planetarium with models of the Earth and Moon. (a) The instructor will ask three students to act as the Sun, the Earth, and the Moon: (i) The first student will represent the Sun by holding a bright flashlight at one end of the room. The room will be darkened in order to emphasize the effects. (ii) A second student will represent the Earth by holding a small sphere, such as a softball. The model Earth should be held in a place so that a model Moon can freely orbit the model Earth. (iii) A third student will represent the Moon by holding a smaller sphere, such as a Ping-Pong ball. The student will have to hold the model Moon in such a way that the other students in the classroom will be able to see it. Also, the student will have to hold the model Moon slightly higher than the model Earth so that their shadows do not hit each other (we will learn why in a future lab). (b) The model Sun, Earth and Moon should be held first in a manner as shown by Figure 3-1a on the following page. Also refer to Figure 3-1b for a close-up of the Earth and Moon. In all figures, we view the system from above the Earth’s North Pole. Neither figure is to scale. (c) Note which side of the Moon (and Earth) is lit by sunlight and which side is in darkness. Use a pencil or pen to shade the dark sides of the Moon and Earth in Figure 3-1b. 1 Oddly enough, even though the full Moon is capable of casting shadows at night, only six percent of the sunlight hitting the Moon is reflected back to space. The percentage of light reflected is called albedo and depends primarily on the composition of the surface.

25 Figure 3-1a. A Model of the “New” Phase of the Moon (not to scale). Figure 3-1b. A Close- Up of the “New” Phase of the Moon (not to scale). (d) From this orientation, which side (left or right) of the Moon is in sunlight? Which side is in darkness? (e) Similarly for the Earth, which side (left or right) is in sunlight? Which side is in darkness? (f) In order for the Moon to be in your sky for this phase, on which side of the Earth must you be? Will that side be experiencing day or night? Light from the Sun (Flashlight) The Moon The Earth Incoming Sunlight The Moon The Earth

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26 (g) Which side of the Moon is facing the Earth, the light or dark side? (h) Given this particular set of relative positions of the Sun, Earth, and Moon, how much of the lit Moon do you expect to see in this phase? (i) Now we will take a look at the opposite case or phase. Hold the model Sun, Earth and Moon in the manner shown by Figure 3-2a on the following page. Also refer to Figure 3-2b for a close-up of the Earth and Moon. Again, neither figure is to scale. (j) Note which side of the Moon (and Earth) is lit by sunlight and which side is in darkness. Use a pencil or pen to shade the dark sides of the Moon and Earth in Figure 3-2b. (k) From this orientation, which side (left or right) of the Moon is in sunlight? Which side is in darkness? (l) Similarly for the Earth, which side (left or right) is in sunlight? Which side is in darkness? (m) In order for the Moon to be in your sky for this phase, on which side of the Earth must you be? Will that side be experiencing day or night? (n) Which side of the Moon is facing the Earth, the light or dark side? (o) Given this particular set of relative positions of the Sun, Earth, and Moon, how much of the lit Moon do you expect to see in this phase?

27 Figure 3- 2a. A Model of the “Full” Phase of the Moon (not to scale). Figure 3-2b. A Close- Up of the “Full” Phase of the Moon (not to scale). Activity #2: The Phases of the Moon – Part 2 It is relatively easy to visualize the appearance (phase) of the Moon when it is aligned with the Earth and the Sun. It is harder when the Moon is not so aligned. First we will consider the phase of the Moon when it is at a right angle to the Earth and Sun. (a) Now hold the model Sun, Earth and Moon in the manner shown by Figure 3-3a on the following page. Refer to Figure 3-3b for a close-up of the Earth and Moon. Neither figure is to scale. (b) Note which side of the Moon (and Earth) is lit by sunlight and which side is in darkness. Use a pencil or pen to shade the dark sides of the Moon and Earth in Figure 3-3b. Light from the Sun (Flashlight) The Moon The Earth Incoming Sunlight The Moon The Earth

28 Figure 3- 3a. A Model of a “Quarter” Phase of the Moon (not to scale). Figure 3-3b. A Close- Up of a “Quarter” Phase of the Moon (not to scale). (c) On which side of the Earth (left, right, upper, lower) do you need to be for the Moon to be in your sky? (d) How much of the entire side of the Moon is visible from the Earth? (e) How much of the entire Moon is visible from the Earth? Hint: it is not the same answer as question (d) above. Light from the Sun (Flashlight) The Moon Incoming Sunlight The Moon The Earth The Earth

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29 (f) What is the range of time on the side of the Earth that has the Moon in its sky? Is this the same as the range of time that the Moon can be seen from the Earth? If not, why not? Hint: the Earth rotates counterclockwise in these figures. (g) How far has the Moon moved in its orbit (in terms of fractions) about the Earth from New to Quarter? Hint: the Moon orbits the Earth counterclockwise in these figures. Next we will construct a lunar phase diagram. This diagram allows us to determine the characteristics of any lunar phase. Figure 3-4 shows the Earth at the center with sunlight approaching from one direction. The eight smaller circles represent various positions of the Moon in its orbit about the Earth. All motions (the Earth’s rotation and the Moon’s orbit) are counterclockwise and we are looking down on the Earth’s North Pole. (h) Shade in the dark sides of each Moon in Figure 3-4 (i.e. the lunar phase diagram). Also shade in the dark side of the Earth. (i) The Earth has four triangles, representing specific times of the day – noon, 6 pm, midnight, and 6 am. Identify which triangle corresponds to which time on Earth and write the answer in the boxes near each triangle on Figure 3-4. (j) For each numbered Moon, write the name of its phase in Table 3-1. A “crescent” moon shows a sliver of moon, while a “gibbous” 2 moon shows most, but not all, of the lit moon facing us. (k) What do you think the terms “waxing” and “waning” mean for lunar phases? (l) For each phase, determine the time each moon rises, the time each moon passes the meridian and the time each moon sets. Record the results in Table 3-1. (m) For each phase, determine whether the Sun lights the eastern or the western side of the Moon. Record the results in Table 3-1. 2 The term “gibbous” means “humpback”, which may help to remember its shape.

30 Table 3-1. Characteristics of the Lunar Phases 1 New Noon Far Phase of Moon # Moon Rises at… Moon on meridian at… Moon Sets at… Side of Moon lit by Sun Appearance of the Moon from the Earth 2 3 4 5 6 7 8 Waxing Gibbous Third (or last) Quarter Waning Crescent Noon 6 p.m. Midnight West 9 p.m. 6 p.m. Near East Noon 9 a.m.

31 Incoming sunlight Figure 3-4. A Lunar Phases Diagram. 1 2 3 8 7 5 6 4

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32 (n) For each phase, sketch the appearance of the Moon as seen from Earth in Table 3-1. Sketch the amount of Moon lit by sunlight (a few examples have already been drawn). (o) The orbit of the Moon about the Earth is 29.5 days long. About how long does each of these eight phases last? (p) If the Moon’s phases are waxing, does the Sun light the e astern or western side of the Moon? What if the Moon’s phases are waning? (q) Does it make sense to talk about a “dark” side of the Moon? Is that the same as the far side of the Moon? (r) Suppose the Moon rises at 3 p.m. What is its phase? (s) The eastern half of the Moon is lit with sunlight. What is its phase? (t) Which do you expect to be noticed by more people, a first quarter phase or a third (last) quarter phase? Why? (u) Is it possible for other natural objects to show phases? If so, list at least three of them.

LAB #3

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