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From wikipedia: The orbit of the Moon around the Earth is completed in approximately 27.3 days. The Earth and Moon orbit about their common center of mass, which lies about 4,700 kilometres from Earth's center (about three quarters of the Earth's radius). On average, the Moon is at a distance of about 385,000 km from the center of the Earth, which corresponds to about 60 Earth radii. With a mean orbital speed of 1.023 km/s, the Moon moves relative to the stars each hour by an amount roughly equal to its angular diameter, or by about 0.5°. The Moon differs from most satellites of other planets in that its orbit is close to the plane of the ecliptic, and not to the Earth's equatorial plane. The lunar orbit plane is inclined to the ecliptic by 5.1°, whereas the Moon's spin axis is inclined by only 1.5°. http://en.wikipedia.org/wiki/Orbit_of_the_Moon
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i'm going to assume you mean "at what rate does the moon orbit the earth." this is a duplicate as well, so i will be flagging it. please check to make sure your question hasn't already been asked.
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