Nonlinear Celestial Mechanics Orbits Revisited: An Effective Relativistic Lagrangean Approach

Abstract

In this article we have revisited the orbital calculations for a celestial mechanical system using the relativistic Lagrangean formalism. The differential equations obtained through this procedure, involving a perturbative expansion of the relativistic Lagrangean constituted on an effective gravitational potential based on the classical gravitational potential, presented good solutions for planetary orbits at our solar system. The validity of the trajectories obtained was carefully observed for Mercury, interacting only with the sun, a typical two body problem. Its natural precession, predicted by general relativity, can be recovered with the perturbed Lagrangean, and Mercury trajectory seems to be chaotic in the sense of KAM theorem when we analyzed the Poincare Map in planet phase space.