The periodic and chaotic regimes of motion in the exoplanet 2/1 mean-motion resonance

Autores
Michtchenko, Tatiana Alexandrovna; Ferraz-Mello, Sylvio; Beaugé, Cristian
Año de publicación
2011
Idioma
inglés
Tipo de recurso
documento de conferencia
Estado
versión publicada
Descripción
We present the dynamical structure of the phase space of the planar planetary 2/1 mean-motion resonance (MMR). Inside the resonant domain, there exist two families of periodic orbits, one associated to the librational motion of the critical angle (c-family) and the other related to the circulatory motion of the angle between the pericentres (Aw-family). The well-known apsidal corotation resonances (ACR) appear at the intersections of these families. A complex web of secondary resonances exists also for low eccentricities, whose strengths and positions are dependent on the individual masses and spatial scale of the system. Depending on initial conditions, a resonant system is found in one of the two topologically different states, referred to as internal and external resonances. The internal resonance is characterized by symmetric ACR and its resonant angle is 2 λ₂ — λ₁— ͞ω₁, where λᵢ and Wi stand for the planetary mean longitudes and longitudes of pericentre, respectively. In contrast, the external resonance is characterized by asymmetric ACR and the resonant angle is 2 λ₂ — λ₁ — ͞ω₂. We show that systems with more massive outer planets always envolve inside internal resonances. The limit case is the well-known asteroidal resonances with Jupiter. At variance, systems with more massive inner planets may evolve in either internal or external resonances; the internal resonances are typical for low-to- moderate eccentricity configurations, whereas the external ones for high eccentricity configurations of the systems. In the limit case, analogous to Kuiper belt objects in resonances with Neptune, the systems are always in the external resonances characterized by asymmetric equilibria.
Facultad de Ciencias Astronómicas y Geofísicas
Materia
Ciencias Astronómicas
mean-motion resonance
chaotic motions
apsidal corotation resonances
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by-nc-sa/4.0/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/167657

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network_name_str SEDICI (UNLP)
spelling The periodic and chaotic regimes of motion in the exoplanet 2/1 mean-motion resonanceMichtchenko, Tatiana AlexandrovnaFerraz-Mello, SylvioBeaugé, CristianCiencias Astronómicasmean-motion resonancechaotic motionsapsidal corotation resonancesWe present the dynamical structure of the phase space of the planar planetary 2/1 mean-motion resonance (MMR). Inside the resonant domain, there exist two families of periodic orbits, one associated to the librational motion of the critical angle (c-family) and the other related to the circulatory motion of the angle between the pericentres (Aw-family). The well-known apsidal corotation resonances (ACR) appear at the intersections of these families. A complex web of secondary resonances exists also for low eccentricities, whose strengths and positions are dependent on the individual masses and spatial scale of the system. Depending on initial conditions, a resonant system is found in one of the two topologically different states, referred to as internal and external resonances. The internal resonance is characterized by symmetric ACR and its resonant angle is 2 λ₂ — λ₁— ͞ω₁, where λᵢ and Wi stand for the planetary mean longitudes and longitudes of pericentre, respectively. In contrast, the external resonance is characterized by asymmetric ACR and the resonant angle is 2 λ₂ — λ₁ — ͞ω₂. We show that systems with more massive outer planets always envolve inside internal resonances. The limit case is the well-known asteroidal resonances with Jupiter. At variance, systems with more massive inner planets may evolve in either internal or external resonances; the internal resonances are typical for low-to- moderate eccentricity configurations, whereas the external ones for high eccentricity configurations of the systems. In the limit case, analogous to Kuiper belt objects in resonances with Neptune, the systems are always in the external resonances characterized by asymmetric equilibria.Facultad de Ciencias Astronómicas y Geofísicas2011-07info:eu-repo/semantics/conferenceObjectinfo:eu-repo/semantics/publishedVersionObjeto de conferenciahttp://purl.org/coar/resource_type/c_5794info:ar-repo/semantics/documentoDeConferenciaapplication/pdf247-262http://sedici.unlp.edu.ar/handle/10915/167657enginfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-sa/4.0/Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-09-29T11:44:40Zoai:sedici.unlp.edu.ar:10915/167657Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-29 11:44:40.835SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv The periodic and chaotic regimes of motion in the exoplanet 2/1 mean-motion resonance
title The periodic and chaotic regimes of motion in the exoplanet 2/1 mean-motion resonance
spellingShingle The periodic and chaotic regimes of motion in the exoplanet 2/1 mean-motion resonance
Michtchenko, Tatiana Alexandrovna
Ciencias Astronómicas
mean-motion resonance
chaotic motions
apsidal corotation resonances
title_short The periodic and chaotic regimes of motion in the exoplanet 2/1 mean-motion resonance
title_full The periodic and chaotic regimes of motion in the exoplanet 2/1 mean-motion resonance
title_fullStr The periodic and chaotic regimes of motion in the exoplanet 2/1 mean-motion resonance
title_full_unstemmed The periodic and chaotic regimes of motion in the exoplanet 2/1 mean-motion resonance
title_sort The periodic and chaotic regimes of motion in the exoplanet 2/1 mean-motion resonance
dc.creator.none.fl_str_mv Michtchenko, Tatiana Alexandrovna
Ferraz-Mello, Sylvio
Beaugé, Cristian
author Michtchenko, Tatiana Alexandrovna
author_facet Michtchenko, Tatiana Alexandrovna
Ferraz-Mello, Sylvio
Beaugé, Cristian
author_role author
author2 Ferraz-Mello, Sylvio
Beaugé, Cristian
author2_role author
author
dc.subject.none.fl_str_mv Ciencias Astronómicas
mean-motion resonance
chaotic motions
apsidal corotation resonances
topic Ciencias Astronómicas
mean-motion resonance
chaotic motions
apsidal corotation resonances
dc.description.none.fl_txt_mv We present the dynamical structure of the phase space of the planar planetary 2/1 mean-motion resonance (MMR). Inside the resonant domain, there exist two families of periodic orbits, one associated to the librational motion of the critical angle (c-family) and the other related to the circulatory motion of the angle between the pericentres (Aw-family). The well-known apsidal corotation resonances (ACR) appear at the intersections of these families. A complex web of secondary resonances exists also for low eccentricities, whose strengths and positions are dependent on the individual masses and spatial scale of the system. Depending on initial conditions, a resonant system is found in one of the two topologically different states, referred to as internal and external resonances. The internal resonance is characterized by symmetric ACR and its resonant angle is 2 λ₂ — λ₁— ͞ω₁, where λᵢ and Wi stand for the planetary mean longitudes and longitudes of pericentre, respectively. In contrast, the external resonance is characterized by asymmetric ACR and the resonant angle is 2 λ₂ — λ₁ — ͞ω₂. We show that systems with more massive outer planets always envolve inside internal resonances. The limit case is the well-known asteroidal resonances with Jupiter. At variance, systems with more massive inner planets may evolve in either internal or external resonances; the internal resonances are typical for low-to- moderate eccentricity configurations, whereas the external ones for high eccentricity configurations of the systems. In the limit case, analogous to Kuiper belt objects in resonances with Neptune, the systems are always in the external resonances characterized by asymmetric equilibria.
Facultad de Ciencias Astronómicas y Geofísicas
description We present the dynamical structure of the phase space of the planar planetary 2/1 mean-motion resonance (MMR). Inside the resonant domain, there exist two families of periodic orbits, one associated to the librational motion of the critical angle (c-family) and the other related to the circulatory motion of the angle between the pericentres (Aw-family). The well-known apsidal corotation resonances (ACR) appear at the intersections of these families. A complex web of secondary resonances exists also for low eccentricities, whose strengths and positions are dependent on the individual masses and spatial scale of the system. Depending on initial conditions, a resonant system is found in one of the two topologically different states, referred to as internal and external resonances. The internal resonance is characterized by symmetric ACR and its resonant angle is 2 λ₂ — λ₁— ͞ω₁, where λᵢ and Wi stand for the planetary mean longitudes and longitudes of pericentre, respectively. In contrast, the external resonance is characterized by asymmetric ACR and the resonant angle is 2 λ₂ — λ₁ — ͞ω₂. We show that systems with more massive outer planets always envolve inside internal resonances. The limit case is the well-known asteroidal resonances with Jupiter. At variance, systems with more massive inner planets may evolve in either internal or external resonances; the internal resonances are typical for low-to- moderate eccentricity configurations, whereas the external ones for high eccentricity configurations of the systems. In the limit case, analogous to Kuiper belt objects in resonances with Neptune, the systems are always in the external resonances characterized by asymmetric equilibria.
publishDate 2011
dc.date.none.fl_str_mv 2011-07
dc.type.none.fl_str_mv info:eu-repo/semantics/conferenceObject
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url http://sedici.unlp.edu.ar/handle/10915/167657
dc.language.none.fl_str_mv eng
language eng
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
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Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
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Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
dc.format.none.fl_str_mv application/pdf
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