SYMPLECTIC INTEGRATORS FOR SOLAR-SYSTEM DYNAMICS

Many problems in solar system dynamics are described by Hamiltonians of the form H = H(Kep) + epsilonH(pert), epsilon much less than 1, where H(Kep) is the usual Hamiltonian for the Kepler two-body problem and epsilonH(pert) represents (for example) much weaker perturbations from the planets. We review symplectic integrators for Hamiltonians of this kind, focusing on methods that exploit the integrability of H(Kep). We show that the long-term errors in these integrators can be reduced by a factor of order epsilon by suitable starting procedures, for example, by starting with a very small stepsize and gradually increasing the stepsize to its final value. The resulting integrators are easily the best available for a wide range of solar system problems.