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 \(a < a_\mathrm{Hill}\) are Hill-stable, while all values \(a > a_\mathrm{unstable}\) are unstable in the Hill sense. The first limit is given by the Hill-stability criterion and is a function of the eccentricity. The second limit 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.
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Acknowledgments
This work was supported by research grants from Secretaría de Ciencia y Tecnología/Universidad Nacional de Córdoba (Secyt/UNC), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), and Fondo para la Investigación Científica y Tecnológica (FONCyT). in full. The authors wish to thank Instituto de Astronomía Teórica y Experimental (IATE) and the UNC for extensive use of their computing facilities and to Pablo Benitez-Llambay for his assistance in developing the graphical routines. Finally, we would also like to express our gratitude to an anonymous referee for stimulating discussions that helped improve this paper.
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Ramos, X.S., Correa-Otto, J.A. & Beaugé, C. The resonance overlap and Hill stability criteria revisited. Celest Mech Dyn Astr 123, 453–479 (2015). https://doi.org/10.1007/s10569-015-9646-z
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DOI: https://doi.org/10.1007/s10569-015-9646-z