Urey prize lecture: Chaotic dynamics in the solar system

Abstract

Newton's equations have chaotic solutions as well as regular solutions. There are several physical situations in the solar system where chaotic solutions of Newton's equations play an important role. There are examples of both chaotic rotation and chaotic orbital evolution. Hyperion is currently tumbling chaotically. Many of the other irregularly shaped satellites in the solar system have had chaotic rotations in the past. This episode of chaotic tumbling could have had a significant effect on the orbital histories of these satellites. Chaotic orbital evolution seems to be an essential ingredient in the explanation of the Kirkwood gaps in the distribution of asteroids. The phase space boundary of the chaotic zone at the 3 1 mean-motion commensurability with Jupiter is in excellent agreement with the boundary of the observed population of asteroids. Chaotic trajectories at the 3 1 commensurability have the correct properties to provide a dynamical route for the transport of meteoritic material from the asteroid belt to Earth. There is a large chaotic zone at the 2 1 commensurability, where there is a Kirkwood gap, but the phase space near the Hilda group of asteroids at the 3 2 commensurability is dominated by quasiperiodic behavior. Chaotic trajectories in the 2 1 chaotic zone reach very high eccentricities by a path that temporarily takes them to high inclinations. The long-term evolution of Pluto is suspiciously complicated, but objective criteria have not yet indicated that the motion is chaotic.