High Quality Content by WIKIPEDIA articles! In classical mechanics, Bertrand's theorem states that only two types of potentials produce stable, closed orbits: an inverse-square central force such as the gravitational or electrostatic potential and the radial harmonic oscillator potential. All attractive central forces can produce circular orbits, which are naturally closed orbits. The only requirement is that the central force exactly equals the centripetal force requirement, which determines the required angular velocity for a given circular radius. Non-central forces (i.e., those that depend on the angular variables as well as the radius) are ignored here, since they do not produce circular orbits in general

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