Effect of inhomogeneity of the Universe on a gravitationally bound local system: A no-go result for explaining the secular increase in the astronomical unit

Abstract

We will investigate the influence of the inhomogeneity of the universe, especially that of the Lema{î}tre-Tolman-Bondi (LTB) model, on a gravitationally bound local system such as the solar system. We concentrate on the dynamical perturbation to the planetary motion and derive the leading order effect generated from the LTB model. It will be shown that there appear not only a well-known cosmological effect arisen from the homogeneous and isotropic model, such as the Robertson-Walker (RW) model, but also the additional terms due to the radial inhomogeneity of the LTB model. We will also apply the obtained results to the problem of secular increase in the astronomical unit, reported by Krasinsky and Brumberg (2004), and imply that the inhomogeneity of the universe cannot have a significant effect for explaining the observed $d\mathrm{AU}/dt=15\pm 4[m/century]$.

12 pages, no figure, accepted for publication in Journal of Astrophysics and Astronomy

References in corpus (8)

• Influence of global cosmological expansion on local dynamics and kinematics
• The Laser Astrometric Test of Relativity (LATOR) Mission
• On the recently determined anomalous perihelion precession of Saturn
• Tidal Dynamics in Cosmological Spacetimes
• Apparent Acceleration through Large-scale Inhomogeneities --Post-Friedmannian Effects of Inhomogeneities on the Luminosity Distance--
• Time Delay in Robertson-McVittie Spacetime and its Application to Increase of Astronomical Unit
• Influence of Dark Matter on Light Propagation in Solar System
• Relativistic Reference Frames for Astrometry and Navigation in the Solar System

Cited by in corpus (1)

• Gravitational Anomalies in the Solar System?