It's very natural in a three-dimensional space that the force tapers off by r^2 as the area it has to cover increases by that. But Newton didn't take that for

It's very natural in a three-dimensional space that the force tapers off by r^2 as the area it has to cover increases by that. But Newton didn't take that for granted, he examined other laws and proved that there were no stable elliptical orbits under them.