The epic journey from Kepler's laws to Newton's law of universal gravitation revisited

TL;DR

This paper reviews Newton's derivation of universal gravitation from Kepler's laws, providing simple proofs based on symmetry and Kepler's law to clarify Newton's reasoning for students.

Contribution

It offers elementary, accessible proofs of Newton's results, emphasizing symmetry and Kepler's law, to enhance understanding of the transition from Kepler's laws to Newton's law.

Findings

Newton's proofs rely on symmetry of spheres and Kepler's law of area.

Elementary proofs clarify Newton's reasoning for students.

The approach highlights the connection between Kepler's laws and universal gravitation.

Abstract

In this article, we review the main results of Volume I of Newton's Principia which relates Kepler's law of planets and universal gravitation. In order to clarify the reasoning of Newton, elementary and simple proofs are given to inspire earnest young students. All proofs are based on either the symmetry of spheres or taking great advantage of Kepler's law of area which also reflects the symmetry of centripedal forces.