Lambda Perturbations of Keplerian Orbits

To estimate influence of the “dark energy” on the Keplerian orbits, we solve the general relativistic equations of motion of a test particle in the field of a point-like mass embedded in the cosmological background formed by the Lambda-term with realistic cosmological Robertson-Walker asymptotics at infinity. It is found that under certain relations between three crucial parameters of the problem–the initial radius of the orbit, Schwarzschild and de Sitter radii–the specific secular perturbation caused by the Lambda-term becomes significant, i.e. can reach the rate of the standard Hubble flow. This fact is interesting both by itself and may have important consequences for the long-term dynamics of planets and stellar binary systems.