Stability of prograde and retrograde planets in circular binary systems

Abstract

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 analytical 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 circular restricted three-body problem. 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, the prograde resonance is of order p-q while the retrograde resonance is of order p+q) [correction added after online publication 2012 June 19: "of the order of" changed to "of order"]. © 2012 The Authors Monthly Notices of the Royal Astronomical Society © 2012 RAS.