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 Hookian gravitation. We sketch a proof of Bertrand’s Theorem that is accessible to undergraduate students who are familiar with basic notions of advanced calculus and differential equations. This is joint work with John Musgrove and Tyler Schimleck, two former undergraduate mathematics students at OSU.