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Analytical treatment of planetary resonances

Batygin, K. and Morbidelli, A. (2013) Analytical treatment of planetary resonances. Astronomy and Astrophysics, 556 . Art. No. A28. ISSN 0004-6361. doi:10.1051/0004-6361/201220907.

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An ever-growing observational aggregate of extrasolar planets has revealed that systems of planets that reside in or near mean-motion resonances are relatively common. While the origin of such systems is attributed to protoplanetary disk-driven migration, a qualitative description of the dynamical evolution of resonant planets remains largely elusive. Aided by the pioneering works of the last century, we formulate an approximate, integrable theory for first-order resonant motion. We utilize the developed theory to construct an intuitive, geometrical representation of resonances within the context of the unrestricted three-body problem. Moreover, we derive a simple analytical criterion for the appearance of secondary resonances between resonant and secular motion. Subsequently, we demonstrate the onset of rapid chaotic motion as a result of overlap among neighboring first-order mean-motion resonances, as well as the appearance of slow chaos as a result of secular modulation of the planetary orbits. Finally, we take advantage of the integrable theory to analytically show that, in the adiabatic regime, divergent encounters with first-order mean-motion resonances always lead to persistent apsidal anti-alignment.

Item Type:Article
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URLURL TypeDescription DOIArticle
Batygin, K.0000-0002-7094-7908
Additional Information:© 2013 ESO. Article published by EDP Sciences. Received 13 December 2012; Accepted 22 May 2013; Published online 19 July 2013. We wish to thank Jake Ketchum and Matt Holman for carefully reviewing the manuscript and providing helpful suggestions. We wish to thank Christian Beauge for a very thorough and insightful referee report that greatly enhanced the quality of this manuscript. K.B. acknowledges the generous support from the ITC Prize Postdoctoral Fellowship at the Institute for Theory and Computation, Harvard-Smithsonian Center for Astrophysics.
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Harvard-Smithsonian Center for AstrophysicsUNSPECIFIED
Subject Keywords:celestial mechanics – planets and satellites: dynamical evolution and stability – chaos
Record Number:CaltechAUTHORS:20140805-130323955
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Official Citation:Analytical treatment of planetary resonances K. Batygin, A. Morbidelli A&A 556 A28 (2013) DOI: 10.1051/0004-6361/201220907
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:47991
Deposited By: Tony Diaz
Deposited On:05 Aug 2014 20:10
Last Modified:10 Nov 2021 17:52

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