A new moon is, by definition, the moment at which the sunlit side of the moon is entirely hidden from us. This can only be the case when the sun is directly behind the moon, and therefore the moon is closest to the sun from our perspective. The moon would be rising with the sun. When the moon rises at sunset, it is by definition on the opposite side of the earth as the sun, and the entire sunlit side is visible; a full moon.
The moon takes 29.5 days to orbit the earth, so every 29.5 days there’s a new moon, and every 29.5 days there’s a full moon, and new moon and full moon occur about 14 or 15 days apart.
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