Note on the perihelion/periastron advance due to cosmological constant

Abstract

We will comment on the perihelion/periastron advance of celestial bodies due to the cosmological constant $\Lambda$. It is well known that the cosmological constant $\Lambda$ causes the perihelion/periastron shift; however, there seems to still exist a discrepancy among the various derived precession formulae. We will point out that the expression $\Delta {\omega }_{\Lambda }=(\pi c^2\Lambda a^3/(GM))\sqrt{1-e^2}$ is the general formula for any orbital eccentricity $e$ and the expression $\Delta {\omega }_{\Lambda }=(\pi c^2\Lambda a^3/(GM))(1-e^2{)}^3$ comes from the nearly circular ($e\ll 1$) approximation.

arXiv comment8 pages, 1 figure, accepted for publication in International Journal of Theoretical Physics

References in corpus (29)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• f(R) Theories Of Gravity
• f(R) theories
• Quantum Gravity at a Lifshitz Point
• The galileon as a local modification of gravity
• Extended Theories of Gravity and their Cosmological and Astrophysical Applications
• Spectral Dimension of the Universe in Quantum Gravity at a Lifshitz Point
• Solar system constraints on f(T) gravity
• The Contribution of the Cosmological Constant to the Relativistic Bending of Light Revisited
• Solar system effects in Schwarzschild--de Sitter spacetime
• Standard Clocks, Orbital Precession and the Cosmological Constant
• Compact calculation of the Perihelion Precession of Mercury in General Relativity, the Cosmological Constant and Jacobi's Inversion problem
• Solar and stellar system tests of the cosmological constant
• Rigorous Approach to the Gravitational Lensing
• The bending of light and the cosmological constant
• Two-body problem with the cosmological constant and observational constraints
• Effect of the cosmological constant on the bending of light and the cosmological lens equation
• The Relevance of the Cosmological Constant for Lensing
• Gravitational deflection of light in the Schwarzschild -de Sitter space time
• On lensing by a cosmological constant
• Does Cosmological Term Influence Gravitational Lensing?
• Can Solar System observations tell us something about the cosmological constant?
• Solar System motions and the cosmological constant: a new approach
• Classical tests of general relativity in the Newtonian limit of Schwarzschild-de Sitter spacetime
• Remark on orbital precession due to central-force perturbations
• The Cosmological Constant and the Gravitational Light Bending
• Expansion-induced contribution to the precession of binary orbits
• Anthropic constraints on the cosmological constant from Sun's motion through the Milky Way

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