Analysis of the Motion of an Extrasolar Planet in a Binary System
Abstract
More than 10% of extrasolar 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 threebody 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 semimajor 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 secondorder 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.
 Publication:

The Astronomical Journal
 Pub Date:
 November 2013
 DOI:
 10.1088/00046256/146/5/108
 arXiv:
 arXiv:1212.3843
 Bibcode:
 2013AJ....146..108P
 Keywords:

 celestial mechanics;
 planets and satellites: dynamical evolution and stability;
 planets and satellites: individual: 16 Cyb HD19994;
 Astrophysics  Earth and Planetary Astrophysics
 EPrint:
 12 pages, 6 figures, 4 tables