On the stability of 3D exoplanetary systems

To date, more than 600 multiple planet systems havebeen discovered. Due to the limitations of the detec-tion methods, our knowledge of the extrasolar sys-tems is usually far from complete. In particular, forplanetary systems discovered with the radial velocitytechnique, the inclinations of the orbital planes (andthus their mutual inclination and the planetary masses)are unknown. Our work aims to constrain the ob-servations of several non-resonant two-planet extraso-lar systems. Through analytical analysis based on afirst-order secular Hamiltonian expansion and numer-ical explorations performed with a chaos detector, weidentify ranges of values for the mutual inclinationswhich ensure the long-term stability of the detectedsystems. Particular attention is also given to deter-mine the possibility for the planetary systems to be ina Lidov-Kozai resonant state.