Closed orbits and the harmonic Manev potential

Abstract

We study conditions for the existence of closed orbits in three distinct potentials. Firstly, we confirm well known conditions for the Manev problem. In a second step, inspired by the result of Bertrand's theorem, we construct a harmonic Manev potential with a harmonic oscillator term instead of the Newtonian one. As in the original Manev potential we find similar conditions for closed orbits that are correlated with restrict values of angular momenta. We analyse also a harmonic corrected Newtonian potential.

Manev potential; Bertrand's theorem; closed orbits