Two-body problem with the cosmological constant and observational constraints

We discuss the influence of the cosmological constant on the gravitational equations of motion of bodies with arbitrary masses and eventually solve the two-body problem. Observational constraints are derived from measurements of the periastron advance in stellar systems, in particular, binary pulsars and the solar system. Up to now, Earth and Mars data give the best constraint, $\Lambda \lesssim {10}^{-36}{\mathrm{km}}^{-2}$; bounds from binary pulsars are potentially competitive with limits from interplanetary measurements. If properly accounting for the gravito-magnetic effect, this upper limit on $\Lambda$ could greatly improve in the near future thanks to new data from planned or already operating space missions.