How Does Geometry Explain the Phases of the Moon?

What causes the Moon to change phases throughout the month? Why is it sometimes visible only during the day and other times only at night? What’s the relationship between these times and the Moon’s phases? The answer in all cases is geometry.

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As you’ve probably noticed, the Moon doesn’t always look the same. In fact, the Moon goes through a “moonthly” cycle lasting about 29.5 days (yes, that’s where the word “month” comes from). This cycle takes the Moon through its full range of phases and eventually leaves it back in the phase it started in.

As you’ve probably also noticed, the Moon is occasionally visible during the day. In fact, if you’re paying attention, you may have noticed that it’s visible during the day a lot. But it’s also sometimes only visible during the night. And if you are really paying attention, you may have noticed that there’s a relationship between when the Moon is visible during the day or night and its phase.

What’s behind this relationship? What determines what time of day the Moon is visible? And what causes the Moon to change phases in the first place? The answer is math—and, in particular, geometry.

How does it work? Let's find out.


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