A Comprehensive Proof of Bertrand's Theorem

A cornerstone result in Newtonian mechanics is Bertrand's Theorem concerning the behavior of the solutions of the classical two-body problem. It states that among all possible gravitational laws there are only two exhibiting the property that all bounded orbits are closed. One of these is Newtonian gravitation, the other being Hookean gravitation. We present a comprehensive proof of Bertrand's Theorem that is accessible to undergraduate students who are familiar with basic notions from advanced calculus and differential equations.

Automated summary

Bertrand's Theorem in Newtonian mechanics states that there are only two gravitational laws, Newtonian gravitation and Hookean gravitation, that have the property of all bounded orbits being closed. We provide a comprehensive proof of the theorem that can be understood by undergraduate students with knowledge of advanced calculus and differential equations.