Numerical Experiments on Planetary Orbits in Double Stars

Abstract

This is a numerical study of orbits in the elliptic restricted three-body problem concerning the dependence of the critical orbits on the eccentricity of the primaries. They are defined as being the separatrix between stable and unstable single periodic orbits. As our results are adapted to the existence of planetary orbits in double stars we concentrated first on the P-orbits (defined to surround both primaries). Due to the complexity of the elliptic problem there is no analytical approach possible. Using the results of some 300 integrated orbits for 10³ to 3.10³ periods of the primaries we established lower and upper bounds for the critical orbits for different values of the eccentricity.