Lambda Perturbations of Keplerian Orbits in the Expanding Universe
To estimate the influence of “dark energy” on Keplerian orbits, we solve the general-relativistic equations of motion of a test particle in the field of a pointlike mass embedded in the cosmological background formed by the cosmological constant 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, the Schwarzschild and de Sitter radii—a specific secular perturbation caused by $$\Lambda$$
 -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.