A Quick Method to Identify Secular Resonances in Multi-planet Systems with a Binary Companion

Gravitational perturbations in multi-planet systems caused by an accompanying star are the subject of this investigation. Our dynamical model is based on the binary star HD 41004 AB where a giant planet orbits HD 41004 A. We modify the orbital parameters of this system and analyze the motion of a hypothetical test planet surrounding HD 41004 A on an interior orbit to the detected giant planet. Our numerical computations indicate perturbations due to mean motion and secular resonances (SRs). The locations of these resonances are usually connected to high eccentricity and highly inclined motion depending strongly on the binary-planet architecture. As the positions of mean motion resonances can easily be determined, the main purpose of this study is to present a new semi-analytical method to determine the location of an SR without huge computational effort.