Newton's Principia and inverse-square orbits: The flaw reexamined

AbstractAfter a brief review of the flaw in the treatment of inverse-square orbits in Newton's Principia, there follow a detailed presentation and an analysis of the most interesting approach that has been offered in defense of that treatment. The defending approach is based on a cogent argument constructed from ingredients taken from Propositions XI–XIII cum Corollary 1 of Principia Book One and one additional ingredient; but the claim that it accurately reflects the argument outlined in the Principia is here shown to be spurious. As a by-product of the analysis there emerges a refutation of the Principia-defending claim presented by E. J. Aiton (Archives Internationales d'Histoire des Sciences 38, 271–276 (1988)). Finally, it is pointed out that the conclusion one must draw in Propositions XI–XIII is different from that which has been drawn for the past three centuries—a fact which has, however, no direction-altering impact on the main thrust of this paper