Throughout the lunar cycle when the moon is the highest, does the time become progressively earlier or later

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Throughout the lunar cycle when the moon is the highest, does the time become progressively earlier or later?
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When the moon is in the general direction of the Sun, it is called new moon. At this point, it has its dark side towards us, and bright side away from us. The moon is not static, and hence moves eastward each day in its monthly orbit around us. In earth-days, it takes 30 days for the moon to complete a 360° path.  Therefore, the moon moves 12° each day.

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