Chaos in the Solar System—Introduction

Abstract

In our search for chaos in the universe, the logical place to start is the solar system. There were indications early on that chaos might play an important role in the orbits of the planets. As we saw in an earlier chapter, Poincaré encountered chaos near the beginning of the century while looking into the long-term stability of the solar system. At the time the solution of the two-body problem was well-known; it was relatively easy and had an analytical solution. When Poincaré added a third body, however, he was surprised how monstrously difficult the problem became. He showed that three astronomical bodies under mutual gravitational attraction had no analytic solution. But Poincaré wasn’t one to give up easily. Instead of pursuing the straight forward approach he tried a round-about one: he investigated the orbits qualitatively by plotting them in phase space, then he examined a slice through the trajectories. And in the process he discovered chaos.