# nLab Bertrand's theorem

Bertrand’s theorem in classical mechanics: the only central forces for which all orbits are closed are $f(r) = a r$ and $f(r) = - b r^{-2}$ where $a,b\gt 0$. In both cases the orbits are ellipses, centered at origin in the first case and with the focus in the center in the second case.

Created on February 1, 2013 at 21:20:19. See the history of this page for a list of all contributions to it.