An effective-gravity perspective on the Sun-Jupiter-comet three-body system

TL;DR

This paper introduces an approximate method to calculate tiny relativistic effective-gravity corrections in the Sun-Jupiter-comet three-body system, enhancing the understanding of relativistic effects on cometary motions.

Contribution

It develops a novel calculational scheme for effective-gravity corrections, bridging Newtonian and relativistic analyses of three-body systems involving comets.

Findings

First calculation of effective-gravity correction in this context

Completes previous Newtonian analyses with relativistic considerations

Provides a step towards understanding relativistic effects on cometary orbits

Abstract

Within the solar system, approximate realizations of the three-body problem occur when a comet approaches a planet while being affected mainly by such a planet and the Sun, and this configuration was investigated by Tisserand within the framework of Newtonian gravity. The exact relativistic treatment of the problem is not an easy task, but the present paper develops an approximate calculational scheme which computes for the first time the tiny effective-gravity correction to the equation of the surface for all points of which it is equally advantageous to regard the heliocentric motion as being perturbed by the attraction of Jupiter, or the jovicentric motion as being perturbed by the attraction of the Sun. This analysis completes the previous theoretical investigations of effective-gravity corrections to the Newtonian analysis of three-body systems, and represents an intermediate step towards relativistic effects on cometary motions.