Orbit and
Phases of the Moon

## Introduction

"Phase" refers to the fact that the moon shows differing amounts of lighted hemispheres as viewed from the earth during its orbit around the earth.

"Cycle" refers to the repetition of these phases, as well as cycles of eclipses. We will investigate these here.

Understanding the observed phases of the moon, requires understanding how light and shadowing works in relation to the sun's light and the orbit of the moon and earth around the sun.

A superstition: It is sometimes believed that when the moon is bright and full, people act crazy. In fact, there is no statistical scientific evidence to support this. It is a myth.

Also: note that there are no monsters devouring the sun, as you might have been told if you were listening to a professor in 2000 BC.

One thing about studying moon phases: it begins to address specifically how what we see observe in astronomy has a very clear scientific explanation.

## Motion of the Moon

First note that if you watch the moon night after night, you will see two key features which are fundamental clues to understanding its motion:

1. It moves eastward against the background stars.

2. It shows same face toward Earth in all phases.

Given these facts, can you infer if the moon rotates around its own axis? (figure 3-2)

Other Key Points:

• The moon orbits quite fast: it moves about 0.5 degrees per hour in the sky. In 24 hours it moves 13 degrees.

• The moon's observed motion eastward results from its physical motion of the moon along its orbit around the Earth.

• The distance from the Earth to the moon is about 60 times the Earth's radius, about 384,000 km.

• The moon orbits counterclockwise around the Earth. Orbit is slightly elliptical and distance from Earth varies 6 %. Period of the orbit is about 27.3 days. This is called the SIDERIAL PERIOD or SIDEREAL MONTH. This is measured with respect to the background stars: the moon takes 1 sidereal period to cycle around once.

• In its eastward motion, the moon stays near the ecliptic. (recall, this is the plane of the sun's motion on the sky). It is tipped by 5 degrees 9' (5 degrees 9 arc seconds) to the plane of the Earth's orbit around the sun and this tilted to ecliptic by same amount.

• This means that the moon also appears to trace the Zodiac along the sky since its deviation from the ecliptic plane on the sky as it orbits is so small.

## Lunar Phases, Phase Cylce

Moon does not produce its own light, and so the light that we see from it is that which is merely reflected from the sun.

As the moon moves around the sky sun illuminates different amounts of its surface. The phase of the moon is thus entirely determined by looking at the Earth's location relative to the sun. The best way to see the phases is to study figure (see also (figure 3-3) of text).

The Moon appears to go through a complete set of phases as viewed from the Earth because of its motion around the Earth, as illustrated below:

 Phases of the Moon

In this figure, the various positions of the moon on its orbit are shown (the motion of the moon on its orbit is assumed to be counter-clockwise). The outer set of figures shows the corresponding phase as viewed from Earth, and the common names for the phases. One can see the progression of phases: New, Waxing Crescent, First quarter, waxing gibbous, full, waning gibbous, 3rd quarter, waning crescent.

Note: the use of the word "quarter" here does not refer to how much of the moon is visible, but the phase in the cycle.

Cycle of lunar phases takes 29.5 days this is the SYNODIC PERIOD.

Why is this longer than the SIDERIAL PERIOD which was 27.3 days? very simple: this is because the moon returns to the same place on the sky once every siderial period, but the sun is also moving on the sky. When the moon returns to the same spot on the sky the sun has moved 27 degrees. Thus the moon now has to take some extra time to catch up. (figure 3-4). The moon takes about 2 days to catch up.

(A good way to understand moonrise and moonset from the book is to look at the picture on page 34 of the text) Imagine standing with the human figure on the globe Now the key point is that the horizon above which the moon is visible, is the plane perpendicular to your body. The time of the day is given by "sunrise, sunset, noon, midnight." Those times of day appear to us as the Earth rotates so that the US passes through them. While the Earth rotates, the position of the moon in its orbit doesnt change much, so we can talk about moonrise and moonset. As you imagine the Earth turning and the various times of day passing you can see how the moonrise and moonset differs for different moon phases.)

## Summary of Moon Motion and Phases

The moon appears to move completely around the celestial sphere once in about 27.3 days as observed from the Earth (a sidereal month) and reflects the corresponding orbital period of 27.3 days

The moon takes 29.5 days to return to the same point on the celestial sphere as referenced to the Sun because of the motion of the Earth around the Sun (synodic month)

Lunar phases as observed from the Earth are correlated with the synodic month.

Since the Moon must move Eastward among the constellations enough to go completely around the sky (360 degrees) in 27.3 days, it must move Eastward by 13.2 degrees each day (in contrast, remember that the Sun only appears to move Eastward by about 1 degree per day). Thus, with respect to the background constellations the Moon will be about 13.2 degrees further East each day. Since the celestial sphere appears to turn 1 degree about every 4 minutes, the Moon crosses our celestial meridian about 13.2 x 4 = 52.8 minutes later each day.

## Perigee and Apogee

The largest separation between the Earth and Moon on its orbit is called apogee and the smallest separation is called perigee.

## Rotational Period and Tidal Locking

The Moon has a spin period of 27.3 days that (except for small fluctuations) exactly coincides with its (sidereal) period for revolution about the Earth. This is equivalent to saying that we see the same face of the moon all the time, as was mentioned above.

This is no coincidence; it is a consequence of tidal coupling between the Earth and Moon. This tidal locking of the periods for revolution and rotation, the Moon always keeps the same face turned toward the Earth