We investigate the stability of prograde versus retrograde planets in circular binary systems using numerical simulations. We show that retrograde planets are stable up to distances closer to the perturber than prograde planets. We develop an analyti
cal model to compute the prograde and retrograde mean motion resonances locations and separatrices. We show that instability is due to single resonance forcing, or caused by nearby resonances overlap. We validate our results regarding the role of single resonances and resonances overlap on orbit stability, by computing surfaces of section of the CR3BP. We conclude that the observed enhanced stability of retrograde planets with respect to prograde planets is due to essential differences between the phase-space topology of retrograde versus prograde resonances (at p/q mean motion ratio, prograde resonance is of order p - q while retrograde resonance is of order p + q).
The HD,196885 system is composed of a binary star and a planet orbiting the primary. The orbit of the binary is fully constrained by astrometry, but for the planet the inclination with respect to the plane of the sky and the longitude of the node are
unknown. Here we perform a full analysis of the HD,196885 system by exploring the two free parameters of the planet and choosing different sets of angular variables. We find that the most likely configurations for the planet is either nearly coplanar orbits (prograde and retrograde), or highly inclined orbits near the Lidov-Kozai equilibrium points, i = 44^{circ} or i = 137^{circ} . Among coplanar orbits, the retrograde ones appear to be less chaotic, while for the orbits near the Lidov-Kozai equilibria, those around omega= 270^{circ} are more reliable, where omega_k is the argument of pericenter of the planets orbit with respect to the binarys orbit. From the observers point of view (plane of the sky) stable areas are restricted to (I1, Omega_1) sim (65^{circ}, 80^{circ}), (65^{circ},260^{circ}), (115^{circ},80^{circ}), and (115^{circ},260^{circ}), where I1 is the inclination of the planet and Omega_1 is the longitude of ascending node.
