On newton's proof that inverse-square orbits must be conics

Summary

Physicists and historians of science have always held that Isaac Newton should receive credit for the first proof that inverse-square orbits must be conics. This conviction derives from a brief argument, regarded as essentially correct, given by Newton in the Principia. Recently, however, it has been contended that this outline or sketch contains irreparable logical flaws. Here, the logical structure of this outline of Newton's, as well as the details that this outline omits, are carefully examined. We find that whilst his argument does indeed contain a flaw, it is a minor omission rather than a serious logical error. Having rectified this omission, we show how Newton's outline expands into a convincing proof that inverse-square orbits must be conics.