The tides of Io

A theory is developed for the origin and evaluation of the orbital resonances between the Galilean satellites Io, Europa and Ganymede as a result of the effects of dissipative tides in Jupiter and its satellites. Following a preliminary consideration of the consequences of tidal interaction for satellite orbits and a comprehensive Hamiltonian theory of the resonance interactions which allows terms up to third order in eccentricity to be included, a dynamic model of the origin and evolution of the resonance locks is presented in which the relative expansion of the orbits by tidal torques from Jupiter together with tidal dissipation in Io lead to the rapid driving out of Io until it is captured into a 2:1 resonance with Europa and the resonance with Ganymede is achieved. Consideration of the effects of other commensurabilities on the orbital evolution of the system reveals that second-order Laplace-like resonances would act to excite free eccentricites, while the resonances associated with the two-body 3:1 commensurability could not have been encountered. Analysis of the hypothesis that the Laplace relation is primordial shows that the bounds on the tidal dissipation of Jupiter still can not be relaxed. Recent determinations of the tidal dissipation in Jupiter are discussed, and it is noted that none is sufficiently small to be consistent with the high heat flux estimates for Io. Finally, the possibility of the observational determination of the tidal dissipation in Jupiter by the measurement of the secular acceleration of Io's main motion is considered.