Title：The Resonance Overlap and Hill Stability Criteria Revisited

　　Speaker：C. Beauge (Astronomical Observatory, Cordoba National University, Argentina；Vice-President of IAU Division A Commission 7 Celestial Mechanics & Dynamical Astronomy)

　　Abstract：We review the orbital stability of the planar circular restricted three-body problem, in the case of massless particles initially located between both massive bodies. We present new estimates of the resonance overlap criterion and the Hill stability limit, and compare their predictions with detailed dynamical maps constructed with N-body simulations. We show that the boundary between (Hill) stable and unstable orbits is not smooth but characterized by 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 a given perturbing mass $m_1$ and initial eccentricity $e$, there are actually two critical values of the semimajor axis. All values $a < a_{\rm Hill}$ are Hill-stable, while all values $a > a_{\rm unstable}$ are unstable in the Hill sense. The first limit is given by the Hill-stability criteria and is a function of the eccentricity. The second limit {\bf is virtually insensitive to the initial eccentricity, and} closely resembles a new resonance overlap condition (for circular orbits) developed in terms of the intersection between first and second-order mean-motion resonances.

　　Time：Sep. 1st (Tuesday), 10:00am

　　Place：Room 302, Astronomy Building

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