Modern Integrations of Solar System Dynamics

Until the early 1990s, numerical simulations of Solar System dynamics were done using accurate but slow integrators. The typical timescales were on the order of a million years, apart from exceptions achieved by considering averaged equations or using specifically designed supercomputers. In the last decade, new numerical integration methods for Solar System dynamics have been introduced. The mixed variable symplectic method (Wisdom & Holman 1991) has permitted the study, in the absence of close encounters, of the evolution of planets and small bodies on timescales comparable to the age of the Solar System. The regularized mixed variable scheme (Levison & Duncan 1994) has allowed the compilation of statistics on the evolution of thousands of near-Earth asteroids and comets, from their source regions to their dynamical elimination. The Symba and the Mercury codes (Duncan et al. 1998, Chambers 1999), which treat close encounters between massive bodies in a symplectic way, have permitted the simulations of planetary accretion and of the early phase of the highly chaotic evolution of the Solar System. This paper reviews the most exciting results obtained with these new integrators. Emphasis is given to the conceptual steps that these works represent in our understanding of Solar System dynamics.