K. Batygin, and A. Morbidelli. (2013)cite arxiv:1305.6513Comment: 21 pages, 13 figures, accepted to A&A.
Abstract
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.
%0 Generic
%1 batygin2013analytical
%A Batygin, Konstantin
%A Morbidelli, Alessandro
%D 2013
%K 2013 Batygin Morbidelli
%T Analytical Treatment of Planetary Resonances
%U http://arxiv.org/abs/1305.6513
%X 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.
@misc{batygin2013analytical,
abstract = {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.},
added-at = {2014-08-01T15:45:48.000+0200},
author = {Batygin, Konstantin and Morbidelli, Alessandro},
biburl = {https://www.bibsonomy.org/bibtex/2b254709436ce63f8ac5ceb8d0a8110b6/danielcarrera},
description = {Analytical Treatment of Planetary Resonances},
interhash = {d9301d191e9be418935ba9d483092ca9},
intrahash = {b254709436ce63f8ac5ceb8d0a8110b6},
keywords = {2013 Batygin Morbidelli},
note = {cite arxiv:1305.6513Comment: 21 pages, 13 figures, accepted to A&A},
timestamp = {2014-08-26T22:58:41.000+0200},
title = {Analytical Treatment of Planetary Resonances},
url = {http://arxiv.org/abs/1305.6513},
year = 2013
}