The gravity force is inversely proportional to the square of the distance between the two bodies. Why is the exponent in this formula exactly equal to 2, rather than (say) 1.99997054 or 2.00061833? How was the parameter 2.00000000 determined? Via empirical evidence (data science) or from theoretical principles? Or is it not exactly equal to 2? And if not, does it change over time? Or is it slightly different in different parts of our universe?
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It is from theoretical priciples. Newton's law for gravitational attraction. It is derived from Gauss Law.
General relativity fixed this value slightly upper value from 2.00000 . Mercury perihelon shift was correctly estimated by General Relativity. It was one of first tests of GR. This shift is because of this value. The actual value may change because of Sun gravitational field and GR should be used for actual calculations.
Here are two answers to my question, posted on Google+