2013AJ....146..108P

More than 10% of extra-solar planets (EPs) orbit in a binary or multiple stellar system. We investigated the motion of planets revolving in binary systems in the case of the three-body problem. We carried out an analysis of the motion of an EP revolving in a binary system with the following conditions: (1) a planet in a binary system revolves around one of the components (parent star); (2) the distance between the star's components is greater than that between the parent star and the orbiting planet (ratio of the semi-major axes is a small parameter); and (3) the mass of the planet is smaller than the mass of the stars, but is not negligible. The Hamiltonian of the system without short periodic terms was used. We expanded the Hamiltonian in terms of the Legendre polynomial and truncated after the second-order term, depending on only one angular variable. In this case, the solution of the system was obtained and the qualitative analysis of the motion was produced. We have applied this theory to real EPs and compared to the numerical integration. Analyses of the possible regions of motion are presented. It is shown that stable and unstable motions of EPs are possible. We applied our calculations to two binary systems hosting an EP and calculated the possible values for their unknown orbital elements.