Phases of the Moon
From crescent to full moon: a geometry of light and shadow
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Summary
The Moon's shape in the sky changes a little every night: new moon, crescent, first quarter, full moon, last quarter... This change comes not from the shape of the Moon itself but from its position between us and the Sun. Show the model from above and from Earth side by side, and you will see the connection.
In depth
The Moon does not make its own light; the half facing the Sun is always lit and the other half is dark. As the Moon circles the Earth, this lit half slides across the Moon's surface: at new moon the side facing us is dark and the far side fully lit. What we call a "phase" is how much the half facing Earth overlaps with the half facing the Sun. The Moon completes its orbit around the Earth relative to the stars in 27.3 days (the sidereal month); but 29.5 days pass from one full moon to the next (the synodic month). The difference comes from the Earth moving along its own orbit around the Sun in the meantime: the Moon has to travel a little further to return to the same phase.


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