It is well known that the orbits of Ganymede, Europa and Io are in a 4:2:1 resonance. Most online sources (including but not limited to Wikipedia) say that such an orbital resonance, along with the 3:2 resonance, is "stable and self-correcting", but fail to explain why this is so.

The textbook Fundamental Astronomy says that this phenomenon is due to "tidal forces" but does not elaborate further. I presume it refers to the tidal deceleration which causes the orbits of the moons to evolve outwards, which, other sources say, caused the moons to eventually enter into resonance, but this also does not explain why the resonance is stable.

I am aware of a similar question here but I'm more interested in stability rather than instability in this case.

In short, why is the orbital resonance of the Galilean moons stable, and how is it different from other cases of orbital resonance that are unstable? I don't mind (and would prefer) if the answer is mathematical in nature.

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    $\begingroup$ lpl.arizona.edu/~renu/malhotra_preprints/rio97.pdf $\endgroup$ – John Rennie Dec 24 '13 at 10:53
  • $\begingroup$ @JohnRennie Thanks a lot for the article! It looks like exactly what I was looking for. Strange I couldn't find it in my searches. I'll digest the math when I find the time to do so. $\endgroup$ – mark2222 Dec 25 '13 at 12:30

Use perturbation theory. Increase and decrease some moon speed a little and see that the forces from the other moons tend to counteract the perturbations.


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