Kirkwood Gaps and Lagrange Points

Asteroid orbit distributions show evidence for Kirkwood gaps, which are certain average orbital radii within the asteroid belt for which there are few asteroids. These gaps are associated with orbital radii leading to orbital periods that are ratios of integer multiples of Jupiter's orbital period. They result from resonance interactions with Jupiter that tend to eject asteroids from such orbits. The following figure illustrates.

The arrows in this figure mark semimajor axes for asteroid orbits that give an orbital period in resonance with Jupiter. For example, the point marked 5:2 means that an asteroid having this semimajor axis makes exactly 5 revolutions for every 2 revolutions of Jupiter on its orbit. Notice the near absence of asteroids for many of these resonances. For example, there are almost no asteroids having orbital periods of half that of Jupiter (the point labeled 2:1). This animation illustrates asteroid resonances with Jupiter.

Gaps Are in Semimajor Axes

It should be noted that the gaps illustrated in the above plot are in the lengths of the semimajor axes (which determine the orbital period, by Kepler's laws). This does not mean that there are gaps in asteroid density as one goes out in radius in the asteroid belt. This is because many asteroids have elliptical orbits and the length of their semimajor axis is a measure only of their average distance from the Sun, not their distance at any particular time.