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 fa ster than conventional N-body algorithms. This makes them the integrator of choice for many problems in Solar system astronomy. However, in their orig inal formulation, they become inaccurate whenever two bodies approach one a nother closely. This occurs because the potential energy term for the pair undergoing the encounter becomes comparable to the terms representing the u nperturbed motion in the Hamiltonian. The problem can be overcome using a h ybrid method, in which the close encounter term is integrated using a conve ntional integrator, whilst the remaining terms are solved symplectically. I n addition, using a simple separable potential technique, the hybrid scheme can be made symplectic even though it incorporates a non-symplectic compon ent.