Elliptical Orbit ⇒ 1/r2 Force

Abstract

Newton's proof of the connection between elliptical orbits and inverse-square forces ranks among the “top ten” calculations in the history of science. This time-honored calculation is a highlight in an upper-level mechanics course. It would be worthwhile if students in introductory physics could prove the relation elliptical orbit ⇒ 1/r2 force without having to rely on upper-level mathematics. We introduce a simple procedure—Newton's Recipe—that allows students to readily and accurately deduce the algebraic form of force laws from a geometric analysis of orbit shapes.