61.12 The mathematical simplicity of the inverse square force

Abstract

The purpose of this note is to show how two first integrals of the equation of motion of a particle moving under the action of an inverse square central force can be obtained very simply using vector techniques. In fact it is shown that, amongst all central forces, only the physically important inverse square force can be treated using the technique given here, thus demonstrating one facet of the mathematical simplicity of that force.