Importance of Conic Section “size” in the Derivation of Propositions X-XVI in Newton’s Principia Book I

Authors: Gopi Krishna Vijaya

The “direct problem” of the inverse-square law is examined, by retracing the derivations of Propositions X-XVI in Newton’s Principia. It is found that transfers of constants of proportionality are inconsistent between the propositions, leading to errors in the derived relations for multiple orbits. Proposition X has to be corrected for the relations of time period to the force law by including the area constants for conic sections. Propositions XI-XIII assume the expression 2h^2/L to be constant, that in turn implicitly assume a modified version of Kepler’s third law, while Propositions XIV-XVI apply this to multiple orbits leading to further “size” inconsistencies with the original form of Kepler’s third law. It has been shown how this relevance of “size” has been missed in the Newtonian literature, leading to a necessity of revising the existence of an exact inverse-square law.

Comments: 14 Pages.

Download: PDF

Submission history

[v1] 2018-01-18 10:49:50

Unique-IP document downloads: 39 times is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus