  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.
