Explain the law of universal gravitation

Answer 1

Here is a reasonable place to start:

http://csep10.phys.utk.edu/astr161/lect/history/newtongrav.html

It probably tells you more than you want to know.

Answer 2

I should warn you that Newton's universal "law" of gravity is not perfectly accurate, and has been replaced by the more accurate, and much more complicated, General Theory of Relativity of Einstein. The Einstein theory has met all experimental tests, and correctly predicted black holes, which have been observed indirectly by their effects.