Io’s tidal heating is due to its orbital eccentricity which is maintained by the Laplace resonance with Europa and Ganymede. All that is necessary for Io to ‘break free’ of its ‘orbital imprisonment’ and ‘go dormant’ is for that resonance to be disrupted.

]]>The four Jovian satellites are a mini-solar system of sorts, except Jupiter is not a star. So it is certainly possible that 5-body interactions of Io, one with Jupiter and the rest with the other moons can certainly nudge Io outwards. Yet I wonder by how much. If Jupiter had a Neptune mass orbiting around it further out (a double gas giant — maybe possible out there) then this larger body has lots of energy and angular momenta to transfer to its light weight cousins further in.

There are of course resonance conditions. In the perturbation expansion there is a first order perturbative term which is a ratio of frequencies, that can go singular at exact resonant conditions. Interestingly the Earth and Jupiter have a 1:11.8 periodic relationship which is nearly resonant. This is common throughout the solar system. In about 1 billion year the ratio of Earth-Jovian orbital periods will be 1:11.9 — slightly closer to resonance. In another billion years resonance will be reached!

What happens if orbital drift reaches exact resonance? This is a sticky mathematical problem. It is one which Kolmogorov, Arnold and Moser addressed in the 1960’s in their celebrated KAM result. Near resonance the energy surface for dynamics becomes chaotic as the so called KAM surface is disrupted or “ounctured.” The KAM surface is the limit of irrational winding. At resonance the dynamics becomes completely chaotic. However, this chaos is brief and shoves the planets off resonance and some relative order is restored — though what that is is not really predictable. So except for some highly symmetric situations an orbtial system can pass through resonance with only a rather brief period of chaotic motion that is not likely to be disasterous.

There are some highly symmetric models with 3 or 4 bodies where one body can end up expelled from the gravitational system with infinite velocity. Remember this is the domain of pure classical mechanics so we are ignoring relativity.

So back to the case of Io, clearly something like this must happen. The physics is much more complicated for this many bodies and the techniques involve prolongation of Lie symmetries for the orbits. It is really serious mathy stuff — outside of my interests and beyond my patience for calculation..

]]>Maybe I’m wrong, but I can’t see this happening just like that.

]]>And of course when the last two moons (I guess not Io) breaks free from their mutual resonance, _they_ will sort of affect each other more. But as I said, dunno what Io free on its lonesome will do.

]]>The title of the article, and the first paragraph, states that Io could leave Jupiter’s hold.

The fourth and fifth paragraph says Io is moving inwards toward Jupiter (but out of its Laplace orbital resonance).

How can Io move inward and out of Jupiter’s gravity well at the same time? Wouldn’t an inward trek make tidal forces greater? What am I missing here?

(Also, there are two quotes in this article that are exactly the same. Perhaps there is a cut and paste editing error?)

]]>As regards disrupting orbits, apparently, from the article, Io is in orbital resonance, and already in the process of breaking free of that. If its continuing orbit around Jupiter but outside of resonance will disrupt other orbits I don’t know. (Note that apparently also Europa, with its tidal heated ocean, and Ganymede is also already in the process of changing orbits.)

]]>Io is Jupiter’s innermost moon: Metis? Adrastea? Amalthea? Thebe?¹

Io may be the innermost Galilean satellite, but not the innermost Jovian moon. Amalthea’s discovery even predates the 20th Century.

¹ Moons of Jupiter found at Wikipedia.

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