Planetary orbital resonances The Kirkwood gaps in the asteroid belt are associated with orbital resonances with Jupiter yet planets seem to prefer resonant locations. Why don't asteroids accumulate near the &quot;Kirkwood locations&quot; rather than avoid them??
This is actually a very subtle question, much more so than the answers to the similar questions provided in the comments give it credit for.  When I was in graduate school at Ohio State I routinely asked this question to visiting dynamicists and invariably got different answers.

The very basic answer is that if you have two sufficiently strong resonances sufficiently close together, then the resonance will be unstable.  Otherwise, the resonance will be stable.  But what determines "sufficiently strong" and "sufficiently close" is where things get very complicated quickly.  A basic criterion is the Chirikov criterion.  (The Scholarpedia article is somewhat more detailed.)  However, the Chirikov criterion is not universally valid.

If you have overlapping resonances, then an object gets bounced back and forth between these two resonances chaotically.  These different resonances perturb the orbit in different ways, and eventually they will perturb the orbit into an unstable orbit, thus leading to depletion of the resonance.  If a resonance is "distant" from other resonances, then the resonance tends to keep objects locked in place, leading to an excess of objects in the resonance.

Most of the resonances in the asteroid belt are fairly close together, which leads to them being unstable.  The Kirkwood Gaps are the most prominent manifestation of these instabilities.  For example, the Alinda family of asteroids are in a 1:3 resonance with Jupiter, and are very close to a 4:1 resonance with the Earth.  This leads to instability, and hence very few asteroids in this family.  However, in the outer Solar System, the resonances are generally far apart, and so are mostly stable.  The plutinos are one example of such a stable resonance, being in a 3:2 resonance with Neptune.