# How orbiting bodies arrange themselves in orbital resonance?

1. Nov 23, 2012

### 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

2. Nov 25, 2012

### Drakkith

Staff Emeritus
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.

3. Nov 26, 2012

### 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?

4. Nov 26, 2012

### Drakkith

Staff Emeritus
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.

5. Nov 26, 2012

### 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.

6. Nov 26, 2012

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...

7. Nov 26, 2012

### Neghentropia

thanks.
I'll give a look in the library. I may be lucky

Edit: I am lucky! :)
I'll try to get hold of a copy tomorrow

cheers!