De Sitter's Theory of Galilean Satellites and the Related Quasi-periodic Orbits

TL;DR

This paper mathematically extends De Sitter's theory on the Galilean satellites, demonstrating the existence of stable and quasi-periodic librating orbits in the Jupiter system using KAM theorems and Hamiltonian techniques.

Contribution

It proves the existence of stable periodic and quasi-periodic orbits in the Galilean satellite system, extending De Sitter's classical theory with rigorous mathematical results.

Findings

Existence of De Sitter's family of stable periodic orbits.

Presence of a positive measure set of quasi-periodic librating orbits.

Extension of the theory to include a fourth satellite, Callisto.

Abstract

In this article, we investigate the mathematical part of De Sitter's theory on the Galilean satellites, and further extend this theory by showing the existence of some quasi-periodic librating orbits by applications of KAM theorems. After showing the existence of De Sitter's family of linearly stable periodic orbits in the Jupiter-Io-Europa-Ganymede model by averaging and reduction techniques in the Hamiltonian framework, we further discuss the possible extension of this theory to include a fourth satellite Callisto, and establish the existence of a set of positive measure of quasi-periodic librating orbits in both models for almost all choices of masses.