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Lunar Phase Simulator – Background 6

The Witness and the Detective

We should now be able to answer the question posed in the introduction:

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?

Remember that given any two of the following, it is always possible to determine the third: (A) the moon's phase, (B) the time, and (C) the moon's location in the sky. In this case we know the time and phase: 3 AM and first quarter. So we would like to know the moon's position in the sky.

First, since the moon is in first quarter we know that the earth-moon-sun geometry looks like that in part (a) in the figure below. Part (b) shows where an observer would be if the local time is 3 AM. Part (c) shows the combination of these facts and includes the observer's horizon plane. Based on the last diagram, you should be able to answer the detective's question.

Part (c) shows that the first quarter moon is definitely not visible at 3 AM (in fact, it sets at midnight). Without the light from the moon or artificial light sources it was too dark for the witness to identify anyone. So, with a sound understanding of the geometry of the earth-moon system our detective knows that the witness can't be telling the truth.

diagram illustrating detective example
(a) The position of the earth and moon when the moon is in first quarter. (b) An observer at the location where the time is 3 AM. (c) These details plus the horizon plane, showing that the moon is not visible to the witness.