A semi-analytical model of the Galilean satellites' dynamics

TL;DR

This paper presents a semi-analytical Hamiltonian model of the Galilean satellites' dynamics, incorporating perturbations, inclinations, solar effects, and tidal dissipation to better understand their resonant and secular motions.

Contribution

It introduces a comprehensive semi-analytical model that includes previously neglected effects like inclinations and solar perturbations, along with tidal dissipation, to improve the understanding of satellite dynamics.

Findings

The model accurately captures the resonant and secular motions.

Inclusion of tidal dissipation shows its impact on orbital evolution.

Perturbations and inclination effects are significant for precise modeling.

Abstract

The Galilean satellites' dynamics has been studied extensively during the last century. In the past it was common to use analytical expansions in order to get simple models to integrate, but with the new generation computers it became prevalent the numerical integration of very sophisticated and almost complete equations of motion. In this article we aim to describe the resonant and secular motion of the Galilean satellites through a Hamiltonian, depending on the slow angles only, obtained with an analytical expansion of the perturbing functions and an averaging operation. In order to have a model as near as possible to the actual dynamics, we added perturbations and we considered terms that in similar studies of the past were neglected, such as the terms involving the inclinations and the Sun's perturbation. Moreover, we added the tidal dissipation into the equations, in order to investigate how well the model captures the evolution of the system.