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.