Gaps in the asteroid belt which are cleared out by gravitational interactions with Jupiter. They were first observed by Kirkwood in 1886. The most prominent correspond to 2:1, 3:1, 5:3, and 7:2 resonances (i.e., orbital radii a at which asteroids orbit twice for each Jupiter orbit, three times for each Jupiter orbit, five times for each three Jupiter orbits, etc.), as summarized in the following table.

The origin of the Kirkwood gaps in the asteroid belt lies in chaos. The standard three-body problem is restricted (), circular, and planar and is a three-degree of freedom autonomous system with constant Hamiltonian (related to the Jacobi constant). The motion is therefore integrable and there is no chaos. There is a 4-D phase space, so trajectories lie on a 3-D energy surface.

Asteroid Belt