De Sitter’s theory of Galilean satellites

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 application 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 among which one sufficiently dominates the others.