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since the distance between the earth and moon is
and the amount of days it takes the moon to orbit earth is
, we will have
But, the moon's orbit is elliptical, not circular. So, above result is close. It should be a larger than that because of the elliptical orbit as opposed to circular.
One way you could look at it is that the
of the moon is
.
There are
in a day, therefore
.
(