A note on Newton's shell-point equivalency theorem

Abstract

An isotropic sphere or shell of matter can be regarded as acting as a point mass at its center so far as its gravitational force on an external test mass is concerned. This is well-known, but what is often not appreciated is that this behavior also holds for a central potential of the harmonic form V( r) ∼  r2. This paper proves this assertion and shows that only the gravitational and harmonic potentials possess this property.