Understanding Strong & Weak Resonance

[tony873004]

I'm reading a few papers on resonant captures, and I come across the terms strong resonance and weak resonance, without actually seeing them defined.

I've got my guesses. I think 3:2 and 2:1 are considered strong, and I believe that it's because objects in 3:2 and 2:1 will complete a resonance cycle rather quickly, where as something like 17:16 will take a long time to complete a single cycle of this resonance. Does anybody have any insight or perhaps a definition?

 

[tony873004]

Let me add a few more terms to my list.

super resonance and Kozai resonance. I know what the Kozai mechanism is, but not the Kozai resonance.

Googling isn't getting me very far. There's articles that use the terms, but they don't define them. I starting to get a sense of what they are through the context in which they're used, but everytime I think I've got it figured out, I read something else that contradicts what I though I figured out.

 

[Soul Surfer]

My guess is that they are not precisely defined.

The gravitational dynamics of multiple gravitiating noncolliding bodies is incredibly complex, far more complex than gas dynamics. This is because close interactions between bodies can have very dramatic and unpredictable results.

I am also quite interested in complex gravitational dynamics. My standard astronomical textbooks do not really touch the subject, and the published papers are usually too specific and assume a thorough knowledge. A few years ago I saw a new book on the subject reviewed and its contents pages but I can't find my reference to itm maybe others can.

It is only by simulation with high performance computer systems that an understanding of the many and varied configurations with longer lives than a transient single interection can be understood. There are several general areas of study. That of many similar gravitatiting objects like stars in a galaxy, That of light particles (no significant self gravitational fields) moving around in a complex gravitiational environment and the long term dynamical interactions of multiple orbiting bodies like the solar system or multiple star systems.

The kozai resonance falls into the second category being a zone of nominally elliptical orbits with quite large changes in their parameters but still a good degree of long term stability. These are related to the low energy ways of getting around the solar syatem that planetary probes are now using. There is quite an interesting but very non technical article on this in this weeks New scientist.

 

[tony873004]

My standard astronomical textbooks do not really touch the subject, and the published papers are usually too specific and assume a thorough knowledge.

That's the problem I'm running into. I can't find any middle ground. I might actually have to go to the library . The New Scientist article sounds interesting. I'll have to pick up a copy.

 

[tony873004]

I e-mailed my question to Dr. Paul Wiegert, the astronomer who wrote one of the papers I'm reading. He was kind enough to reply.

As for strong/weak resonances, there's not really a formal definition.
You can show that some resonances generally are weaker than others eg
that the 2:1 and 3:2 mean motion resonances are stronger than the, say,
37:42 or 89:1045 (as a rule, for a m:n resonance, the smaller is m+n,
the stronger the resonance). But there's no specified dividing line
between weak and strong.