The dynamics of the elliptic Hill problem : Periodic orbits and stability regions

TL;DR

This paper investigates the elliptic Hill problem by computing and classifying numerous periodic orbits and their stability, revealing how planetary eccentricity influences satellite orbit stability and identifying stable regions even at high eccentricities.

Contribution

It extends previous studies by systematically computing and classifying families of periodic orbits in the elliptic Hill model, including stability analysis and resonance classification.

Findings

Many stable periodic orbits exist despite high planetary eccentricity.

Regular orbits are found near stable periodic orbits even at large eccentricities.

Most irregular orbits are escape trajectories.

Abstract

The motion of a satellite around a planet can be studied by the Hill model, which is a modification of the restricted three body problem pertaining to motion of a satellite around a planet. Although the dynamics of the circular Hill model have been extensively studied in the literature, only few results about the dynamics of the elliptic model were known up to now, namely the equations of motion and few unstable families of periodic orbits. In the present study we extend these results by computing a large set of families of periodic orbits and their linear stability and classify them according to their resonance condition. Although most of them are unstable, we were able to find a considerable number of stable ones. By computing appropriate maps of dynamical stability, we study the effect of the planetary eccentricity on the stability of satellite orbits. We see that, even for large values of the planetary eccentricity, regular orbits can be found in the vicinity of stable periodic orbits. The majority of irregular orbits are escape orbits.