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Or in other words, are there differences in average Lyapunov timescale between orbits interior to Jupiter and orbits exterior to Jupiter? I'm trying to answer a question at http://www.quora.com/Why-does-Pluto-have-so-many-satellites/answer/Alex-K-Chen but I'm not totally sure if the last part of my answer is right. I'll quote the last part of it:

If the 2nd theory is true, then it's harder to answer this. One thing for sure though: Jupiter is much farther away, so its tug on the system is a much smaller factor than it is for the inner planets (where it can be a major source of instability over the solar system's lifetime)

In fact - I suspect that another factor is that from Pluto's perspective, Jupiter is practically in the center of the solar system anyways, so you're unlikely to see periods of time where Jupiter is in such a position where its constant gravitational tugs (over several Jupiter orbits) can accumulate and tug a satellite into an unstable orbit (which is what can happen with planets that orbit the Sun at distances interior to Jupiter [1]). Anyways I don't fully know the physics on this (yet) so some of my details could be wrong - what I do know is that it could happen to both asteroid belt objects and to Mercury's orbit - http://en.wikipedia.org/wiki/Stability_of_the_Solar_System#Mercury.E2.80.93Jupiter_1:1_resonance - perhaps because there are positions where Jupiter's pull on interior bodies is in a direction opposite to that of the Sun's pull (we never hear about the Sun creating any orbital instabilities). And Mercury is much closer to Jupiter than Pluto is.

Of course, Pluto is vulnerable to Neptune's influence, but Pluto and Neptune have a 3:2 orbital resonance so it's relatively safe from collisions with Neptune (although the resonance may not be constant over the solar system's lifetime)

Anyways, we might finally know more once New Horizons reaches Pluto in a few years

[1] http://www.alpheratz.net/murison/papers/Lyapunov/LFM.pdf says that there is something special about asteroids with orbits interior to Jupiter - I'll try to find more information on this.

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The primary factor that makes asteroids unstable is resonance overlaps with Jupiter, which is why there are many gaps in the distribution of asteroid periods. Far from resonances, it shouldn't make much difference whether the object in question is interior or exterior to Jupiter. Sussman & Wisdom (1988) showed that the Lyapounov time for Pluto is ~20 Myr. Lasker (1988) found the typical Lyapounov time for the inner planets to be ~5 Myr, but considering their much shorter orbital period, I would argue this shows them to be more stable. Also, while they are all technically chaotic, they are also bounded by stability regions, like Pluto's 3:2 resonance keeping it from close encounters with Neptune. This is best expressed by Murray and Dermott (1999): "the solar system is stable and it is likely that the motions of the planets represent another case of bounded chaos."

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Pluto's orbit was shown to be chaotic some years ago (not necessarily unstable). Does it mean Neptune's orbit is also chaotic? –  Peter Mortensen Jul 21 '11 at 14:28

wrt the Pluto moon question, I think that Jupiter has little or nothing to do with it. The important point is that the Sun is so far away, so the typical orbital velocities are small, and it is easier for objects to get captured into Pluto's Hill sphere. So far, it seems like many trans-Neptune objects are binaries.

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The question does mention that from Pluto's POV Jupiter is practically in the center too. –  Andrew Jul 21 '11 at 13:51

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