A truly elementary proof of Bertrand's theorem

TL;DR

This paper presents a straightforward and elementary proof of Bertrand's theorem by analyzing the radial orbit equation, avoiding complex calculations or integrals.

Contribution

It offers a simple, accessible proof of Bertrand's theorem using basic analysis of the radial orbit equation, without advanced mathematical tools.

Findings

Proof confirms only inverse-square and harmonic oscillator potentials produce closed orbits

Method simplifies understanding of Bertrand's theorem

Avoids complex equations or integrals in the proof

Abstract

An elementary proof of Bertrand's theorem is given by examining the radial orbit equation, without needing to solve complicated equations or integrals.