Name: Partner(s): Day/Time: Version: 105

# Phases of the Moon

O swear not by the moon, the inconstant moon,
that monthly changes in her circled orb,
lest that thy love prove likewise variable

-- Romeo and Juliet, Act 2 scene 2

## Overview

• Understand the relationship between the Moon, Earth, and Sun, that causes the Moon's phases.
• Understand when the different Moon phases are visible.
• Link the observed phases with the Moon's rise and set times.

## Introduction

How does the relation between the Moon, Earth, and Sun cause the phases that we see? What is the relation between the Moon's phases, its monthly orbit, and its rise and set times? The central point to understanding the phases of the Moon is that exactly half of the Moon is illuminated at all times, which is the half facing the Sun. The phases result from our viewing angle of the lit side, which depends on the Moon's position in its orbit around the Earth, relative to the Sun. For example, if the Moon is on the opposite side of the Earth from the Sun, we can see the entire lit side, and it is a full moon (Figure 1). If the Moon and Sun are aligned in the same direction, then the lit side is the far side of the Moon, and we see nothing. This is a new Moon. It takes 29.5 days for the Moon to go through a full cycle of its phases.

Figure 1: Top-down view of the Moon's orbit, showing the Moon in various positions, along with the phase that we see from Earth. The lit side always faces the Sun, and from the Earth's viewpoint, we see different fractions of the lit side. As the Earth turns, we experience noon when the observer is facing the Sun, and midnight when the observer is standing diametrically opposite the Sun. Note that East is always toward the leading side of the Earth's rotation. For example, the person in the Figure is experiencing sunset, with the Sun on the west horizon.

Figure 1 shows that as the Moon moves from new to full, we see an increasing fraction of the lit portion, so the Moon's phase is said to be waxing. The opposite happens as it moves from full to new, when it is waning. When the Moon's position is exactly between full and new, it looks like a half-moon. However, as is apparent in Figure 1, we can see one quarter of its surface, so it is formally called the first quarter for a waxing Moon, and last quarter or third quarter for waning. In between the new and quarter phases, the Moon is a crescent. Between the quarter and full, the Moon is in a gibbous phase.

The Moon's rise and set times are linked to the phases. For example, the new moon is aligned toward the Sun, so it will rise and set with the Sun. The full moon is opposite the Sun, so it will rise at sunset, and set at sunrise. This allows basically continuous light on the Earth during this phase; for example, the "Harvest Moon" provides light to continue harvesting the crops near the autumnal equinox. In Figure 1, the person is standing at sunset, with the Sun on the west horizon. If the Moon is in the full phase, it will just be rising in the east. If the the Moon is in the first quarter phase, it is at its highest point (crossing the meridian) at this time of day. For the first quarter to appear on the east horizon, the person must be standing at noon, with the Sun overhead; and for the first quarter to appear on the west horizon, the person must be standing at midnight. So we see that the first quarter moon rises at noon, is highest at sunset, and sets at midnight.

Looking at Figure 1, you might expect that at every new moon, the Moon will actually block out the Sun. This does happen sometimes, resulting in a solar eclipse, but not at every new moon. The Moon’s orbit is tilted about 5º to the ecliptic, so usually the Moon passes above or below the Sun in the sky. Similarly at full Moon, the Moon usually passes above or below Earth’s shadow, avoiding a lunar eclipse. There are usually several eclipses per year, including both solar and lunar eclipses. However, the Moon's shadow on the earth is only a few miles wide, so it's difficult to be in exactly the right place, at the right time, to observe a solar eclipse.

In very dark skies, you might also be able to observe the gegenschein, the point directly opposite the Sun in the sky. Interplanetary dust on the ecliptic will reflect sunlight, and create a very faint glow in the sky at the point exactly opposite the Sun. Although very rare in real life, the planetarium makes use of this effect in order to show the point directly opposite the Sun.

Figure 2: The gegenschein. More information on the gegenschein is at http://apod.nasa.gov/apod/ap080507.html. Click the image for the original taken by Copyright Yuri Beletsky.

# Phases of the Moon Worksheet

## Part 1: Planetarium Observations

The show starts with the Moon in last quarter. Watch carefully and observe both the Sun and Moon, paying special attention to which one rises first. Note the approximate time that the Moon rises, relative to sunrise, noon, sunset, and midnight.

1. When the show pauses, fill in the missing data for the last quarter phase in Table 1. The date is shown at the Sun's position on the ecliptic. Estimate moonset based on when it rises.
2. Label this position in Figure 2, below.

The planetarium operator will move the Moon to the next phase; this shows how the moon's position and phase change throughout the month. Review the sentence below so you know what to look for. Watch the Moon as it moves to this new position and circle the correct answers from each set of words in brackets.

1. The Moon travels [eastward, westward] along the [ecliptic, equator]. When it started moving, the lit fraction got [larger, smaller] which means it was [waxing, waning]. It moved [closer to, farther from] the Sun. It passed through the [new, full] phase and when it stopped, the lit fraction was getting [larger, smaller], so it is [waxing, waning].
2. Fill out the second row in Table 1 and label this position in Figure 2.

The planetarium operator will move the Moon to the next phase.

1. Watch the Moon as it moves to this new position, and complete the third row in Table 1. Label this phase in Figure 2.
 Phase Waxing, waning, full or new Lit on: (E, W, full, new) Rises around/between: sunrise, noon, sunset, midnight Sets around/between: sunrise, noon, sunset, midnight Date Days since 3rd qtr 3rd Quarter waning 0

Figure 2: Label the Figure with the positions of the phases in Table 1.

## Concluding Questions

For simplicity, assume that sunrise is always at 6 AM, sunset is always at 6 PM, and that the Moon also sets 12 hours after it rises (this is true on average, just as on average there are 12 hours of daylight in a day.)

1. In the diagram below, draw a person on the Earth experiencing a time near 9 AM. Include the person's horizon, analogous to Figure 1. Which lunar phase sets near this hour? Which lunar phase is seen highest in the sky, transiting the meridian, near this hour? Be sure to specify waxing or waning. Explain your answer. Figure 1 in the Introduction may be helpful, and you can add more to the diagram, if needed.

1. A witness at a trial says she saw a half moon around 8 PM. What phase is this? She later says that she could see by the light of the moon at 3 AM. Is she lying? Explain.

2. In the Introduction, we saw that only a few people are able to see a solar eclipse at a given time, because the Moon's shadow on the Earth is so small. Would more or fewer people be able to see a lunar eclipse? Explain.

3. A friend of yours comments that when he was driving home 5 evenings ago just after sunset, he saw a beautiful crescent moon near the horizon in front of him.
1. Explain which crescent it was. [waxing, waning]

2. Explain the general direction he driving. [N, S, E, W]

4. You want a dark, moonless night for star gazing, and you prefer to observe between sunset and midnight. Explain which phases of the moon correspond to this condition. You should consider mainly the moon rise and set times.

Updated: 08/27/14 by SAM & MSO