Why does the moon appear to change its shape everyday? Relate the moon changes in its shape to how to calculate the days by looking at the moon.

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In reality, the moon doesn't change shape at all.  It is orbiting the Earth at the same time as it is also rotating, and the Earth itself is rotating and revolving around the Sun.  This is why stars move in the sky and why the sun and moon rise and set in different locations each day.

The only thing that changes then is not the shape of the moon, but the appearance of the reflected side - the part that looks bright - to those of us on Earth.  We simply see a different angle of the reflected side each minute, hour, day, week and month.  This gives the appearance of a "new" moon or a "full" moon, when in fact the moon's shape is just the same as it was before.

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