The nature of the Laplace resonance between the Galilean moons

Abstract The Laplace resonance is a mean-motion resonance that involves the three inner Galilean moons of Jupiter. However, its true nature is in part unclear; in particular, different views can be found in the literature on whether the Laplace resonance is a pure three-body resonance or a mere superposition of two-body resonances. To settle this question, we conduct a thorough analysis of the many resonances involved, starting from the two-body 2:1 commensurabilities of the couples Io–Europa and Europa–Ganymede, and ending with the three-body 4:2:1 commensurability between the three moons. By artificially varying the parameters of the system and monitoring its fundamental frequencies, we cartography all resonances involved and their interactions. From the analysis of the individual 2:1 commensurabilities, we find that despite the oscillation of the resonant angles they are not genuine resonances, as the trajectory of the system in the phase space is not enclosed by separatrices. On the contrary, as suggested by previous works, we show that the only current true mean-motion resonance is the pure three-body resonance between all three satellites. Moreover, we find that the current values of the moons’ orbital elements make the Laplace resonance sufficiently separated from the individual two-body 2:1 resonances, preventing chaotic effects from appearing.