Full asymptotic expansion of the relativistic orbit of a rest particle under the exact Schwarzschild metric

The perturbation method of Lindstedt and Poincare has been used for the derivation of the asymptotic expression of the relativistic orbit of a test particle influenced by the exact Schwarzschild metric, from which the perihelion advance of a test particle is expressed as a rapidly convergent power series. Numerical results show the convergence characteristics of the modified Newtonian orbital expression. (C) 1998 Elsevier Science B.V.