Re: Solar system building

Brian Davis wrote:

But it might change the orbit only subtly, and more importantly in
this case it changes *both* orbits - details like the migration of the
pericentron of the orbit start to play a major role. So if the mass
ratio is not outrageously one-sided, you can get stabilizing resonances
appearing in places where you weren't expecting them.

What stable relationships are you referring to? Coorbitals, shepherding moons, something else? Shepherding actually involves a case where two "large" moons are affecting the orbits of lots of negligible moonlets without themselves being perturbed essentially at all ...

Yes, but again by this reasoning, there should be little or nothing
at the 3:2 resonance with Jupiter... exactly where the Hilda group
sits.

Yeah, that's true. To put it more carefully, very few of these low-ratio resonances are stable, and for those that are, it's due to special orientations between the two objects -- often involving the smaller object having fairly eccentric or inclined orbits (thus not being usable in this case since we want the smaller planet to have a pretty circular orbit).

The Hildas are stable because of a weird dance they do with Jupiter involving always managing to stay far from it despite being in a 3:2 resonance, alternately having aphelia that move between/near the Sun-Jupiter L3, L4, and L5. The Neptune-Pluto resonance is a similar relationship where they never get much near each other.

So while not rigorously stated, my core point still stands: If the body is consistently closer to Jupiter on certain passes in its resonant orbit, the orbit will be destabilized. The resonances that _are_ stable are so precisely because never get close. I don't know the details of the Gliese 876 bodies in their 2:1 resonance, but I strongly suspect it's a similar thing.

It's certainly true that it's easy to be too flippant about the details of stability and resonance, or stability and anything when it comes to orbital mechanics. But the flip side of that is that it's impossible to be rigorous without essentially writing a book about it, something probably none of us are willing to do for this thread :-). Even the definition of stability itself is problematic for systems like this -- arrangements we call stable are often really metastable, and naive definitions of stability (like the one I gave with restoring forces) wouldn't even result in the Trojan points qualifying as stable! So point taken ...

--
Erik Max Francis && max@xxxxxxxxxxx && http://www.alcyone.com/max/
San Jose, CA, USA && 37 20 N 121 53 W && AIM erikmaxfrancis
The mind is not a vessel to be filled but a fire to be kindled.
-- Plutarch
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