How long does it take the moon to completely rotate around the earth

27.32 days

Explanation:

The Moon is one of the largest bodies in the Solar system. Its orbit is almost circular (eccentricity ε = 0.05) and the plane of its orbit is inclined 5º with respect to the plane of the Earth's orbit.

The average distance between the center of the Earth and the Moon is 384,400 km. Its period of rotation around the Earth is 27,322 days. Changing the position of the Moon with respect to the Sun gives rise to the phases of the Moon.

The Moon always presents the same face to the Earth observer, due to the effect of the tidal forces exerted by the Earth on the Moon. Which means, that the period of rotation of the Moon around its axis coincides and the time it takes to complete an orbit around the Earth.

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explanation:

the masses of the objects and the distance between them