A hybrid symplectic integrator that permits close encounters between massive bodies

Mixed-variable symplectic integrators exhibit no long-term accumulation of energy error, beyond that owing to round-off, and they are substantially faster than conventional N-body algorithms. This makes them the integrator of choice for many problems in Solar system astronomy. However, in their original formulation, they become inaccurate whenever two bodies approach one another closely. This occurs because the potential energy term for the pair undergoing the encounter becomes comparable to the terms representing the unperturbed motion in the Hamiltonian. The problem can be overcome using a hybrid method, in which the close encounter term is integrated using a conventional integrator, whilst the remaining terms are solved symplectically. In addition, using a simple separable potential technique, the hybrid scheme can be made symplectic even though it incorporates a non-symplectic component.