  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 <
10^{-36} 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.
