Deviation of trajectories in nonrelativistic and relativistic cases and Shirokov effect

Abstract

We compare the deviations of circular orbits in the nonrelativistic and relativistic cases. General solutions of the deviation equations are obtained. We find the potentials for the nonrelativistic case and the metric components in general relativity for which trajectories close to circular ones are closed curves. Explicit expressions for the pericenter shift of an orbit close to a circular one in a static spherically symmetric spacetime are obtained. Estimates of the cosmological constant effect on the orbit pericenter shift are given. Finally, we find the spherically symmetric metric in which the Shirokov effect is absent.