Perturbations of Keplerian orbits in stationary spherically symmetric spacetimes

We study spherically symmetric perturbations determined by alternative theories of gravity to the gravitational field of a central mass in General Relativity (GR). 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 pericenter 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.