The Relativistic Factor in the Orbital Dynamics of Point Masses

TL;DR

This paper reviews how general relativity influences the orbital dynamics of planetary systems, especially in the Solar System, and proposes a correction method for point-mass models to account for relativistic effects.

Contribution

It introduces a suitable relativistic correction for Solar System orbital studies and compares different algorithms to incorporate relativistic effects in numerical simulations.

Findings

Relativistic effects by the Sun significantly alter inner Solar System dynamics.

The Kozai mechanism is modified by relativistic effects.

Planetary relativistic effects are minimal but detectable.

Abstract

There is a growing population of relativistically relevant minor bodies in the Solar System and a growing population of massive extrasolar planets with orbits very close to the central star where relativistic effects should have some signature. Our purpose is to review how general relativity affects the orbital dynamics of the planetary systems and to define a suitable relativistic correction for Solar System orbital studies when only point masses are considered. Using relativistic formulae for the N body problem suited for a planetary system given in the literature we present a series of numerical orbital integrations designed to test the relevance of the effects due to the general theory of relativity in the case of our Solar System. Comparison between different algorithms for accounting for the relativistic corrections are performed. Relativistic effects generated by the Sun or by the central star are the most relevant ones and produce evident modifications in the secular dynamics of the inner Solar System. The Kozai mechanism, for example, is modified due to the relativistic effects on the argument of the perihelion. Relativistic effects generated by planets instead are of very low relevance but detectable in numerical simulations.