One of Newton’s biggest contributions was figuring out how to show that gravity was the same force that caused both objects like an apple to fall to the earth at a rate of 9.81 m/s2 AND the moon being accelerated toward the earth but at a different rate of 0.00272 m/s2. If these are both due to the same force of gravity, why are they different numbers then? Why is the acceleration of the moon 1/3600th the acceleration of objects near the surface of the earth? It has to do with the fact that gravity decreases the further you are from an object. The moon is in orbit about 60 times further from the earth’s center than an object on the surface of the earth, which indicates that gravity is proportional to the inverse of the square of the distance (also called the inverse square law). So the force of gravity acts between any two objects and is inversely proportional to the square of the distance between the two centers. The further apart the objects are, the less they force of gravity is between the two of them. If you separate the objects by twice the distance, the gravitational force goes down by a factor of 4.
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