How orbiting bodies arrange themselves in orbital resonance?

[Neghentropia]

Hi guys,
my first post here :)

lately I've been trying to understand how orbiting bodies (i.e. galileian moon of Jupiter) have arranged themselves in resonance

the 1:1 resonance is pretty straightforward to understand. but more complex relations like the one I cited above, how do they take place?



cheers

 

[Drakkith]

I would guess that they are either formed in such resonances, or are driven there by gravitational perturbations and once in the resonance they are stable.

 

[Neghentropia]

hi Drakkith, thanks for the reply

could you explain better how these gravitational perturbations take place?
I'm really curious to understand the mechanics behind the phenomenon
also, I'd like to introduce in the discussion the subject of clearing the neighbourhood which, as far as I understood, is strongly linked with resonance

in particulr, how does the gravitational field of a planet (Jupiter) both arranges in resonance its moons and clears, for example, the asteroids belt from layers upon layers os asteroids?
how does this duplex push-pull effect of gravity take place?

 

[Drakkith]

I couldn't possible go into the details, as I don't know them, however I can say that certain orbits just happen to be stable orbits, resonances being some of them. Those bodies that aren't in stable orbits, well, don't stay in orbit! Resonances have a sort of self-correcting feature, where the orbiting bodies in resonance tug on each other in just the right ways to keep them at the right speed at the right distance. If one object starts to pull slightly ahead of the other, perhaps due to interactions with other objects, it's pulled back when they get close to each other, and vice-versa. There's no real "reason" behind this other than it's simply a result of gravity pulling on objects in certain ways.

That's about the best I could explain it. I'm sure I've butchered it enough for now, so I'll let someone else who's far more familiar with orbital mechanics take it from here.

See this article for more: http://en.wikipedia.org/wiki/Orbital_resonance

 

[Neghentropia]

mhh...

the picture is getting clearer.
and I mean that I'm given to understand the reason of complex resonances is not well understood (n-body problem)

on the other, I hand't considered that orbiting bodies can exchange angular momentum, which explain why a planet can eject an asteroid (or another planet...) from its orbit.

 

[Deadstar]

I would advise getting a hold of Solar System Dynamics by Murray and Dermott since there's a lot on resonance and the disturbing function in the book. Since it focuses on the solar system, it covers Jupiters moons, Saturns rings, etc...

 

[Neghentropia]

thanks.
I'll give a look in the library. I may be luckyEdit: I am lucky! :)
I'll try to get hold of a copy tomorrow

cheers!