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Centripetal force in the form of gravitational force
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The Moon's distance from the Earth is such that the gravitational force of attraction doesn't let it go away and it just balances the centripetal force of rotational motion, so it does not fall on Earth either.
In this manner it rotates around the Earth in an orbit. The same applies to the Earth, with an orbital speed that keeps it at a relatively constant distance from the Sun.

Hope this helps:)
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