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Lunar Phase Simulator – Background 2

Moon Geometry

The fraction of the moon that appears illuminated changes since the moon is orbiting the earth. The time it takes the moon to complete one orbit around the earth (with respect to the sun) is also the amount of time it takes to complete one cycle of phases. This period, known as the synodic month, is about 29.5 days.

Thus it takes the moon almost exactly a month to complete one orbit and go through a cycle of phases. You can conclude that if the moon is a waning gibbous on the 15th, then the moon will be waning gibbous (or close to it) on the 15th of the next month. Furthermore, in one week the moon completes about a quarter of its orbit. So if the moon is at first quarter today, then in one week it should be near full.

The diagram below shows the relationship between the position of the moon in its orbit and its appearance from earth. Here we are looking down from far above the earth's North Pole. From this direction, the moon orbits the earth in a counter-clockwise direction.

the geometry of moon phases
The diagram shows a simplified view of the moon's orbit around the earth, seen from above the earth's North Pole, with the sun far off screen to the left. The numbered images at right show the appearance of the moon when it is at the corresponding positions on its orbit.

This diagram is very useful for understanding and memorizing the relationship between the moon's orbital geometry and its phases. But keep in mind that there is no particular reason why we need to draw the sun's light coming in from the left — this is an arbitrary choice, and in fact some diagrams do it differently. The only important thing is the angle between the sun, earth, and moon. When the moon is between the earth and sun it will always be new, regardless of the diagram's orientation. Turn the monitor upside down and the diagram is still true.

The geometry of the earth-moon system also allows us to make various conclusions based on the moon's phase. There is a concrete connection between (A) the moon's phase, (B) the time, and (C) the moon's location in the sky. In fact, given any two of those details, it is always possible to determine the third. Consider the following situation:

Suppose Sherlock Holmes is investigating a crime that took place at 3 AM, away from street lamps and any other artificial light sources. A witness claims he recognized the perpetrator in the light cast by a first quarter moon. Should the detective believe him?

Before we can answer this question we need to look into the details of telling time and describing the locations of objects in the sky.

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