A semi-analytical model of the Galilean satellites’ dynamics

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 of 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.