Solar System dynamics, beyond the two-body-problem approach

When one thinks of the solar system, he has usually in mind the picture based on the solution of the two-body problem approximation presented by Newton, namely the ordered clockwork motion of planets on fixed, non-intersecting orbits around the Sun. However, already by the end of the 18th century this picture was proven to be wrong. As discussed by Laplace and Lagrange (for a modern approach see [3] or [2]), the interaction between the various planets leads to secular changes in their orbits, which nevertheless were believed to be corrections of higher order to the Keplerian elliptical motion.This idea has changed completely the last decades. Now it is well know that the solar system was created from a state of chaotic interactions of planetesimals, primordial bodies the size of a small asteroid, and that since this time many episodes of cataclysmic collisions have shaken all major planets, due to the pronounced chaotic motion of the minor bodies. A new discipline has emerged out of the above new ideas, which is based on the statistical approach to chaotic motion of bodies, in particular those in the asteroid belt. At the same time it has been understood that non-gravitational forces, in particular the Yarkovsky effect, may play an important role on the long-time evolution of the trajectories of kilometer-sized bodies.