# Two body problem in presence of cosmological constant

## TL;DR

This paper explores how the cosmological constant affects the classical two-body problem, revealing that finite solutions only exist within a specific angular momentum range and applying findings to cosmic structures.

## Contribution

It introduces the impact of the cosmological constant on the two-body problem, identifying the limited angular momentum range for finite solutions and analyzing the motion qualitatively.

## Key findings

- Finite solutions exist only for 0 < L < L_lim(Λ).
- Critical parameters of the two-body system are identified.
- Application to Local Group and Virgo cluster motion.

## Abstract

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.