The Role of Tidal Forces in the Long-term Evolution of the Galilean System

The Galilean satellites of Jupiter are called Io, Europa, Ganymede and Callisto. The first three moons are found in the so-called Laplace resonance, which means that their orbits are locked in a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2:1$$\end{document} resonant chain. Dissipative tidal effects play a fundamental role, especially when considered on long timescales. The main objective of this work is the study of the persistence of the resonance along the evolution of the system when considering the tidal interaction between Jupiter and Io. To constrain the computational cost of the task, we enhance this dissipative effect by means of a multiplying factor. We develop a simplified model to study the propagation of the tidal effects from Io to the other moons, resulting in the outward migration of the satellites. We provide an analytical description of the phenomenon, as well as the behaviour of the semi-major axis of Io as a function of the figure of merit. We also consider the interaction of the inner trio with Callisto, using a more elaborated Hamiltonian model allowing us to study the long-term evolution of the system along few gigayears. We conclude by studying the possibility of the trapping into resonance of Callisto depending on its initial conditions.