Bertrand's theorem and orbits Prove Bertrand's theorem for closed orbits in detail. 1. Show that for an orbit close to a circular shape, the particle executes the motion of simple harmonic motion. 2. Choose a central potential, different from the harmonic and from Kepler, and explain by means of a graph what kind of orbits would exist according to the chosen potential.

Bertrand's theorem and orbits Prove Bertrand's theorem for closed orbits in detail. 1. Show that for an orbit close to a circular shape, the particle executes the motion of simple harmonic motion. 2. Choose a central potential, different from the harmonic and from Kepler, and explain by means of a graph what kind of orbits would exist according to the chosen potential.