Abstract
To a close approximation all massive bodies in the solar system possess axial symmetry. General conditions for the existence and stability of circular orbits in the neighborhood of bodies with such symmetry are established. Application is made to: (i) circular orbits about an oblate planet, (ii) circular orbits in the plane of a thin ring or disk, (iii) circular orbits about a planet plus ring or disk, and (iv) circular orbits in the classical two-fixed-force-centers problem. Depending on the mass distribution, it is found that multiple orbits may exist with the same radius but at different positions along the symmetry axis. Such orbits will be alternately stable-unstable. In general, the axial positions of the orbits will shift as the orbital radius changes.
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