On the local and global properties of the gravitational spheres of influence

TL;DR

This paper refines the concept of a gravitational sphere of influence using classical celestial mechanics, clarifies distinctions among related spheres, and explores their properties and regimes in planetary systems.

Contribution

It provides a broader, more precise definition of the sphere of activity and distinguishes it from similar concepts like the Hill and Chebotarev spheres, with semi-analytical analysis of dynamical regimes.

Findings

Clarified differences among various gravitational spheres of influence.

Developed semi-analytical models of dynamical regimes.

Proposed a broader application to exo-planetary systems.

Abstract

We revisit the concept of sphere of gravitational activity, to which we give both a geometrical and physical meaning. This study aims to refine this concept in a much broader context that could, for instance, be applied to exo-planetary problems (in a Galactic stellar disc-Star-Planets system) to define a first order "border" of a planetary system. The methods used in this paper rely on classical Celestial Mechanics and develop the equations of motion in the framework of the 3-body problem (e.g. Star-Planet-Satellite System). We start with the basic definition of planet's sphere of activity as the region of space in which it is feasible to assume a planet as the central body and the Sun as the perturbing body when computing perturbations of the satellite's motion. We then investigate the geometrical properties and physical meaning of the ratios of Solar accelerations (central and perturbing) and planetary accelerations (central and perturbing), and the boundaries they define. We clearly distinguish throughout the paper between the sphere of activity, the Chebotarev sphere (a particular case of the sphere of activity), Laplace sphere, and the Hill sphere. The last two are often wrongfully thought to be one and the same. Furthermore, taking a closer look and comparing the ratio of the star's accelerations (central/perturbing) to that of the planetary acceleration (central/perturbing) as a function of the planeto-centric distance, we have identified different dynamical regimes which are presented in the semi-analytical analysis.