On geodesic deviation in static spherically symmetric situations

Abstract

We review the derivation of the standard geodesic deviation equation in spherically symmetric situations. We reconsider the deviation equation in Newtonian gravity first to uncover in a second step the relativistic effects within the full theory of General Relativity. In both cases, we solve the standard deviation equation for circular reference curves and, in particular, we describe two special kinds of perturbed orbits that are useful for satellite geodesy and gravimetry missions: the so-called pendulum and cartwheel orbits. These appear as solutions of the deviation equation and can be constructed within the framework that is sketched here.