If we classify the asteroids according to their periods, the resulting histogram shows clearly that the distribution is not random, but saw-toothed.
The distribution shows also some spikes. Gaps and spikes correspond to periods that are simple divisors of simple multiples of Jupiter's period. As for instance, it is clear in the figure that there are very few asteroids with semimajor axis 2.5 A.U, period 4 years, which is one-third of the orbital period of Jupiter.
Gaps were thought by Kirkwood to be caused by orbital resonances, i.e., by the gravitational perturbations from Jupiter. In other words, the idea is that if an asteroid happens to orbit three times around the Sun in the time it takes for Jupiter to orbit once, then the asteroid gets tugged out of that orbit.
Maybe this would deorbit any asteroid near a gap and eventually make it collide with some planet or the Sun. The devil is in the details, though; long-term behaviour of asteroid orbits is difficult to predict, and according to this abstract, the motions of some 3:1 resonance asteroids don't look unstable at all.
Spikes in the histogram would similarly happen where the perturbations from Jupiter help stabilize the orbits.
The Kirkwood gaps are located at mean orbital radii of:
- 1.9 AU (2:9 resonance)
- 2.06 AU (1:4 resonance)
- 2.25 AU (2:7 resonance)
- 2.5 AU (1:3 resonance), but see the Alindas group of asteroids
- 2.706 AU (3:8 resonance)
- 2.82 AU (2:5 resonance)
- 3.27 AU (1:2 resonance), but see the Griquas group of asteroids
- 3.7 AU (3:5 resonance)
A way to kludge a crude short-term simulation of asteroid orbit changes near Kirkwood gaps is described here.
