The Inverse Cube Force Law

TL;DR

This paper explores Newton's lesser-known discovery that an inverse cube force law can rescale a particle's angular velocity without changing its radial motion, revealing unique properties of this force.

Contribution

It highlights Newton's original work on the inverse cube law and discusses its distinctive features, which are less studied compared to the inverse square law.

Findings

Inverse cube force law can rescale angular velocity without affecting radial motion

Newton's investigation predates modern recognition of this force's properties

The paper discusses unique features of the inverse cube force law

Abstract

Newton's Principia is famous for its investigations of the inverse square force law for gravity. But in this book Newton also did something that remained little-known until fairly recently. He figured out what kind of central force exerted upon a particle can rescale its angular velocity by a constant factor without affecting its radial motion. This turns out to be a force obeying an inverse cube law! Here we discuss this and some other interesting features of the inverse cube force law.