Universal Gravitation

The inverse-square law of universal gravitation states that every particle of matter attracts every other particle with a force proportional to the product of their masses and inversely proportional to the square of the distance between them. First derived mathematically by Newton in the Principia from Kepler's laws of planetary motion, it was the first successful unification of celestial and terrestrial physics — the same force that guides an apple to the ground guides the Moon around the Earth. The law remained unchallenged for two centuries until Einstein's general relativity revealed it as the low-curvature limit of a more general geometric theory.

Universal gravitation is not merely a force law. It is the claim that the cosmos is a single mechanical system — that the same equations govern the falling apple and the orbiting planet. This unification was not an empirical discovery but a theoretical imposition: Newton asserted that the heavens obey terrestrial mechanics, and two centuries of observation confirmed it. The history of physics is, in part, the history of extending this strategy — the same equations, ever more general, governing ever more phenomena.