Analytic orbit propagation of planets in binary star systems

International audienceWe present an analytical framework that accurately describes the motion of co-planar planets in binary star systems on orbital as well as secular timescales. The method builds upon analytic solutions of the differential equations governing the behavior of the system's perturbed Laplace-Runge-Lenz vectors. Multiple time-scale analysis is used to derive the short period evolutions of the system, while octupole secular theory is applied to describe its long term behavior. A post Newtonian correction on the stellar orbit is included for circumbinary planets. Our model is tested against results from numerical integrations of the full equations of motion. An application to circumbinary planetary systems discovered by NASA's Kepler satellite reveals that the formation history of the systems Kepler-34 and Kepler-413 has most likely been different from the one of Kepler-16, Kepler-35, Kepler-38 and Kepler-64, as the former systems are not compatible with the assumption of almost circular initial planetary orbits