We consider the Kepler two-body problem in presence of the cosmological constant $Lambda$. Contrary to the classical case, where finite solutions exist for any angular momentum of the system $L$, in presence of $Lambda$ finite solutions exist only in the interval $0<L< L_{lim}(Lambda)$. The qualitative picture of the two-body motion is described, and critical parameters of the problem are found. Application are made to the relative motion of the Local Group and Virgo cluster.
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