Perturbations of Keplerian Orbits in Stationary Spherically Symmetric Spacetimes

TL;DR

This paper analyzes how spherically symmetric perturbations from alternative gravity theories affect Keplerian orbits, providing formulas to test these theories against orbital data.

Contribution

It derives analytic expressions for secular variations in orbital elements caused by alternative gravity perturbations, aiding experimental constraints.

Findings

Only argument of pericentre and mean anomaly have secular variations.

Orbital period variation is calculated.

Formulas can constrain alternative gravity theories.

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.