Question

Question #1117f

Answer 1

To my knowledge, the inverse square force idea had been discussed in relation to gravity by many in Newton's time. It was Newton who was able to link this idea to many of the known aspects of planetary motion, and brought it to general acceptance.

Explanation:

I am unaware of a derivation of any sort that Newton used to reach his conclusion about the inverse-square nature of gravity.

However, if one assumes it to be true (and Newton obtained the best available data on the moon's orbit to verify his assumption) then Newton demonstrated that the work of Kepler years earlier (elliptical orbits, and the famous third law of Kepler for instance) could all be shown to be mathematical consequences of this law.

The same would not be true if the denominator was `r` `r^3` or any other exponent.

So, in summary, I believe the equation is essentially empirical. It is created in the form it has because it gives the most accurate predictions possible.

(I would invite others to add to my answer and improve upon it!)