Kepler’s laws and universal gravitation in Newton’s Principia

An outline is presented of the line of reasoning which Newton used in his Principia to obtain Kepler’s three laws of planetary motion from his own laws of motion and of universal gravitation. His combination of deductive and retroductive reasoning is related to his general philosophical outlook on the nature of science. The actual structure of the argument differs significantly from that often found in physics texts. A straightforward presentation is developed which allows the modern reader to see the type of derivation Newton employed to deduce Kepler’s three laws. The discussion preserves the essentially geometric character of Newton’s constructions in the Principia. It can even be presented to students in a noncalculus‐based introductory physics course as a case study showing how one of the great achievements of modern science was produced.