Seminarium Teorii Względności i Grawitacji

In this lecture we present an alternative method of calculus of trajectories and motions of test particles in the vicinity of central massive body. Instead of using successive post-Newtonian approximations, we shall perform successive approximations starting from a special exact solution valid in General Relativity: a circular orbit. Linearizing the geodesic deviation equations, we reduce the problem to a series of coupled harmonic oscillators with non-linear right-hand side. Applications to gravitational waves will be shortly discussed.