Comment on the article “A note on Newton's shell-point equivalency theorem” [Am. J. Phys. 90, 394 (2022)]

Abstract

When central forces follow a power law, Cameron Reed [Am. J. Phys. 90(5), 394–396 (2022)] showed that the resulting force on a test particle located outside an object with spherical symmetry is the same as if the source were located at the center of the sphere, if and only if the potential is either Newtonian, F ∝ r−2, or Hookean, F ∝ r. This Note shares another simple proof of this result and comments on the result in the light of the so-called transmutation law of central forces.