Newton’s superb theorem: An elementary geometric proof

Abstract

Newton’s “superb theorem” for the gravitational 1/r2 force states that a spherically symmetric mass distribution attracts a body outside as if the entire mass were concentrated at the center. This theorem is crucial for Newton’s comparison of the Moon’s orbit with terrestrial gravity, which is evidence for the 1/r2 law. In this paper, we give an elementary geometric proof, which is simpler than Newton’s geometric proof and more elementary than proofs using calculus.