Constraints On Satellite Formation From Io's Low Inclination

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The Laplace resonances between the satellites Io, Europa, and Ganymede has had a profound effect on the evolution of the jovian system. In its current configuration, the resonances enable some of the spin energy of Jupiter to be tapped to power the volcanos on Io. But when, and equally importantly, at what distance from Jupiter did this resonance first originate? Were the satellites pushed together by tidal forces or by an earlier phase of inward migration? Have the satellites ever been deeper in resonance than they are today? Some of these questions can be addressed by considering clues contained in the current orbital configurations. In particular, the anomalously-low inclination of Io (0.04 degrees) rules out several otherwise plausible scenarios.
The tidal forces that strongly affect orbital semimajor axes and eccentricities only weakly influence inclinations. In addition, slow enough (adiabatic) crossings of the strongest first- and second-order resonances can only increase inclinations. Lowering inclinations, by contrast, is extremely difficult. It is possible with a particular class of weaker third-order resonances, although the conditions under which these resonances occur are somewhat limited. Other scenarios, such as simultaneous interactions with multiple resonances can, at least in principle, also lower inclinations.
So inclinations, once induced, are not easily erased. Making the assumption that the inclination of Io never rose above 0.04 degrees is quite diagnostic and allows us to rule out several scenarios including evolution from deep within the resonance to today's conditions. The inclinations of Europa and Ganymede provide further constraints. In this talk, I will report the progress to date of our ongoing investigation.

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