Newton, Kepler, Inverse-square

Didn't Newton use the inverse-square law to prove that sun attracts planets with force proportional to inverse-square of their distance to the sun? i.e., didn't Newton use inverse-square law to prove inverse-square law? Or did Newton derive inverse-square law from Kepler’s laws? If not, who first came up with inverse-square law, and how did s/he arrive at that?
- Mehran (age 64)

Newton did indeed derive the inverse-square law from Kepler's Third Law relating the orbital periods to the size of the orbits. When he found that this law derived from comparing different planets going around the Sun also worked for comparing the Moon going around the Earth to things falling near the surface of the Earth, he went ahead with his modest generalization to universality.

Mike W.

(published on 10/17/2014)