A Lie integrator program and test for the elliptic restricted three body problem

A new algorithm for the calculation of orbits of massless bodies in the elliptic restricted three body problem is presented and tested. It uses a Lie series development and avoids the integration of the orbit of the primary bodies. The computer version of the algorithm is straightforward and comprehensible. It is shown that large stepsizes still give enough accuracy. Compared with another high accuracy program, the need of CPU-time is about only one third up to one half of the time normally necessary.