Perturbations of Keplerian Orbits in Stationary Spherically Symmetric Spacetimes

Abstract

We study spherically symmetric perturbations determined by alternative theories of gravity to the gravitational field of a central mass in General Relativity. In particular, we focus on perturbations in the form of power laws and calculate their effect on the secular variations of the orbital elements of a Keplerian orbit. We show that, to lowest approximation order, only the argument of pericentre and mean anomaly undergo secular variations; furthermore, we calculate the variation of the orbital period. We give analytic expressions for these variations which can be used to constrain the impact of alternative theories of gravity.

9 pages, RevTeX, revised to match the version accepted for publication in International Journal of Modern Physics D; some references were corrected

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• Anomalous precession of planets on a Weyl conformastatic solution
• Higher-order geodesic deviations and orbital precession in a Kerr-Newman space-time
• Perihelion advance and trajectory of charged test particles in Reissner-Nordstrom field via the higher-order geodesic deviations
• The relativistic precession of the orbits
• Constraining A String Gauge Field by Galaxy Rotation Curves and Perihelion Precession of Planets