Orbital Resonances

[Elen Sila]

I wasn't sure if this belongs in "Classical Physics" or "Astronomy And Cosmology".

 

Anyway, according to Wikipedia, "In most cases, [orbital resonance] results in an unstable interaction, in which the bodies exchange momentum and shift orbits until the resonance no longer exists. Under some circumstances, a resonant system can be stable and self correcting, so that the bodies remain in resonance."

 

I've been wanting to write a science fiction story for a while that takes place on a planet with two moons, and I wanted the moons' orbits to remain roughly stable over many millennia, but am unsure whether to attempt to fit them into a resonance, or whether this would detriment the stability of the system. I've been using approximations of what I want their respective orbital periods to be, and these happen to be fairly close to a particular integer ratio. I'm unsure as to whether I should actually have them be resonant with each other, though.

 

How can I determine whether a given resonance between two moons of known mass, around a planet with a known mass, will be stable or unstable? What sorts of things will I need to consider? I'm imagining orbital inclination is probably important, as well as the planet's proximity to its sun. What are some factors that can contribute to a strong resonance?

 

(The reason why I need to compute the system's stability accurately is because I need to design a calendar for the story.)

(And yes, I will probably be developing a computer simulation of the system at some point; but I'd like to minimize trial and error as much as possible in setting it up.)

Edited August 30, 2011 by Elen Sila

[csmyth3025]

The Wikipedia article you cite is (for me) the only understandable description I've found. If your looking for stable resonances I would direct your attention to the following passage in that article:

 

A Laplace resonance occurs when three or more orbiting bodies have a simple integer ratio between their orbital periods. For example, Jupiter's moons Ganymede, Europa and Io are in a 1:2:4 orbital resonance. The extrasolar planets Gliese 876e, Gliese 876b and Gliese 876c are also in a 1:2:4 orbital resonance (with periods of 124.3, 61.1 and 30.0 days)

(ref. http://en.wikipedia....es_of_resonance )

 

Preceding this passage there are several other stable orbital resonances mentioned.

 

Chris

[Elen Sila]

So any 2:3 or 1:2:4 resonance will be self-correcting? The only requirement is the orbital ratio, nothing else?

[csmyth3025]

So any 2:3 or 1:2:4 resonance will be self-correcting? The only requirement is the orbital ratio, nothing else?

Sorry, but I really don't know any more than you do about such things. There are others here who are quite knowledgeable, though. Hopefully this thread will catch their eye and they will be able to answer your questions.

 

Chris