How does Newton's law of universal gravitation apply to Earth and the moon?

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Newton's law of universal gravitation states that any two bodies with a mass are attracted towards each other by a force directly proportional to the product of their mass and inversely proportional to the distance between them. For the Earth and the Moon, if the mass of the Earth is Me and the mass of the moon is Mm, the force of attraction between them is given by F = G*Me*Mm/R^2 where R is the distance between them. G is a constant and is equal to 6.67×10^-11 N m^2*kg^-2.

It is this force between the two due to gravity that makes the moon revolve around the Earth. It provides the centripetal force that makes the Moon move in a circular path. The gravitational force is also responsible for effects like the tides that occur on the Earth.

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Any two bodies with a mass are attracted towards each other by a force directly proportional to the product of theit mass and inversely proportional to the distance between them.

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