A new perspective on Newton’s law of universal gravitation

In this note, we present a new and mathematical way for discovering the functional form of Newton’s law of universal gravitation. The new way is based on clear physical hypotheses, only uses simple calculus, and does not resort to Kepler’s laws of planetary motion. It exhibits new insights into the classical law. Its simpler variant is valid for Ohm’s law, Hooke’s law, and several other classical physical laws.