Two body problem in presence of cosmological constant

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.

15 pages, 3 figures

References in corpus (17)

• General Relativity and Cosmology: Unsolved Questions and Future Directions
• Solar system effects in Schwarzschild--de Sitter spacetime
• Editorial for the Special Issue 100 Years of Chronogeometrodynamics: The Status of the Einstein's Theory of Gravitation in Its Centennial Year
• Orbital precession due to central-force perturbations
• Solar and stellar system tests of the cosmological constant
• Two-body problem with the cosmological constant and observational constraints
• Evolution of gravitational orbits in the expanding universe
• One Hundred Years of the Cosmological Constant: from 'Superfluous Stunt' to Dark Energy
• Cosmological perturbations on local systems
• Solar System motions and the cosmological constant: a new approach
• Note on the perihelion/periastron advance due to cosmological constant
• Constraining the mass of the Local Group
• Remark on orbital precession due to central-force perturbations
• Perspectives on constraining a cosmological constant-type parameter with pulsar timing in the Galactic Center
• A New Dynamical Mass Measurement for the Virgo Cluster using the Radial Velocity Profile of the Filament Galaxies
• Galaxy clusters in presence of dark energy: a kinetic approach
• Century of $\Lambda$

Cited by in corpus (2)

• Dark Energy as a Critical Period in Binary Motion: Bounds from Multi-scale Binaries
• Orbital precession and other properties of two-body motion in the presence of dark energy