Kepler's laws follow which law discovered by sir isaac newton?

Kepler took Brahe's detailed descriptions and measurements of the motion of the planets in the sky over many years, and derived his 3 laws of Planetary Motion based purely on what Brahe saw.

A hundred years AFTER Kepler, Newton proposed his Law of Universal Gravitation.

Using his own Law of Universal Gravitation, along with his laws of motion, Newton showed that IF his "laws" were correct, then planets HAVE TO move exactly according to Kepler's laws.  (He had to invent Calculus in order to demonstrate this.)

This was an awesome, powerful confirmation of Kepler's work and Newton's work.  Boat uvum.

In my Physics courses, I used to be able to take Newton's laws of gravity and motion, fold in some calculus and some geometry, mix until smooth, and derive Kepler's laws of planetary motion.  But that was long ago, in a galaxy far away, and, sadly, ya don't get to use it very often as an Electrical Engineer.  So I imagine it's still true, but I can't prove it now.