The resonance overlap and Hill stability criteria revisited

Abstract

We review the orbital stability of the planar circular restricted three-body problemin the case of massless particles initially located between both massive bodies. We presentnew estimates of the resonance overlap criterion and the Hill stability limit and compare theirpredictions with detailed dynamical maps constructed with N-body simulations. We showthat the boundary between (Hill) stable and unstable orbits is not smooth but characterizedby a rich structure generated by the superposition of different mean-motion resonances,which does not allow for a simple global expression for stability. We propose that, for agiven perturbing mass m 1 and initial eccentricity e, there are actually two critical valuesof the semimajor axis. All values a < aHill are Hill-stable, while all values a > aunstableare unstable in the Hill sense. The first limit is given by the Hill-stability criterion and is afunction of the eccentricity. The second limit is virtually insensitive to the initial eccentricityand closely resembles a new resonance overlap condition (for circular orbits) developed interms of the intersection between first- and second-order mean-motion resonances.