Ejection-collision orbits in the Restricted three-body problem

In this paper we analyse the ejection-collision (EC) orbits of the planar restricted three body problem. Being µ¿¿¿(0, 0.5] the mass parameter, and taking the big (small) primary with mass (µ), an EC orbit will be an orbit that ejects from the big primary, does an excursion and collides with it. As...

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Detalhes bibliográficos
Autores: Ollé Torner, Mercè|||0000-0002-8050-9055, Rodríguez del Río, Óscar|||0000-0002-4545-5135, Soler Villanueva, Jaume|||0000-0002-6220-5170
Formato: artículo
Fecha de publicación:2017
País:España
Recursos:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/110642
Acesso em linha:https://hdl.handle.net/2117/110642
https://dx.doi.org/10.1016/j.cnsns.2017.07.013
Access Level:acceso abierto
Palavra-chave:Three-body problem
Orbital mechanics
Regularization
Ejection-collision orbits
Invariant manifolds
Bifurcations
Problema dels tres cossos
Mecànica orbital
Àrees temàtiques de la UPC::Matemàtiques i estadística
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spelling Ejection-collision orbits in the Restricted three-body problemOllé Torner, Mercè|||0000-0002-8050-9055Rodríguez del Río, Óscar|||0000-0002-4545-5135Soler Villanueva, Jaume|||0000-0002-6220-5170Three-body problemOrbital mechanicsRegularizationEjection-collision orbitsInvariant manifoldsBifurcationsProblema dels tres cossosMecànica orbitalÀrees temàtiques de la UPC::Matemàtiques i estadísticaIn this paper we analyse the ejection-collision (EC) orbits of the planar restricted three body problem. Being µ¿¿¿(0, 0.5] the mass parameter, and taking the big (small) primary with mass (µ), an EC orbit will be an orbit that ejects from the big primary, does an excursion and collides with it. As it is well known, for any value of the mass parameter µ¿¿¿(0, 0.5] and sufficiently restricted Hill regions (that is, for big enough values of the Jacobi constant C), there are exactly four EC orbits. We check their existence and extend numerically these four orbits for µ¿¿¿(0, 0.5] and for smaller values of the Jacobi constant. We introduce the concept of n-ejection-collision orbits (n-EC orbits) and we explore them numerically for µ¿¿¿(0, 0.5] and values of the Jacobi constant such that the Hill bounded possible region of motion contains the big primary and does not contain the small one. We study the cases 1¿=¿n¿=¿10 and we analyse the continuation of families of such n-EC orbits, varying the energy, as well as the bifurcations that appear.Peer Reviewed20182018-02-0120172017-11-15journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/110642https://dx.doi.org/10.1016/j.cnsns.2017.07.013reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivs 3.0 Spainhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/1106422026-05-27T15:37:01Z
dc.title.none.fl_str_mv Ejection-collision orbits in the Restricted three-body problem
title Ejection-collision orbits in the Restricted three-body problem
spellingShingle Ejection-collision orbits in the Restricted three-body problem
Ollé Torner, Mercè|||0000-0002-8050-9055
Three-body problem
Orbital mechanics
Regularization
Ejection-collision orbits
Invariant manifolds
Bifurcations
Problema dels tres cossos
Mecànica orbital
Àrees temàtiques de la UPC::Matemàtiques i estadística
title_short Ejection-collision orbits in the Restricted three-body problem
title_full Ejection-collision orbits in the Restricted three-body problem
title_fullStr Ejection-collision orbits in the Restricted three-body problem
title_full_unstemmed Ejection-collision orbits in the Restricted three-body problem
title_sort Ejection-collision orbits in the Restricted three-body problem
dc.creator.none.fl_str_mv Ollé Torner, Mercè|||0000-0002-8050-9055
Rodríguez del Río, Óscar|||0000-0002-4545-5135
Soler Villanueva, Jaume|||0000-0002-6220-5170
author Ollé Torner, Mercè|||0000-0002-8050-9055
author_facet Ollé Torner, Mercè|||0000-0002-8050-9055
Rodríguez del Río, Óscar|||0000-0002-4545-5135
Soler Villanueva, Jaume|||0000-0002-6220-5170
author_role author
author2 Rodríguez del Río, Óscar|||0000-0002-4545-5135
Soler Villanueva, Jaume|||0000-0002-6220-5170
author2_role author
author
dc.subject.none.fl_str_mv Three-body problem
Orbital mechanics
Regularization
Ejection-collision orbits
Invariant manifolds
Bifurcations
Problema dels tres cossos
Mecànica orbital
Àrees temàtiques de la UPC::Matemàtiques i estadística
topic Three-body problem
Orbital mechanics
Regularization
Ejection-collision orbits
Invariant manifolds
Bifurcations
Problema dels tres cossos
Mecànica orbital
Àrees temàtiques de la UPC::Matemàtiques i estadística
description In this paper we analyse the ejection-collision (EC) orbits of the planar restricted three body problem. Being µ¿¿¿(0, 0.5] the mass parameter, and taking the big (small) primary with mass (µ), an EC orbit will be an orbit that ejects from the big primary, does an excursion and collides with it. As it is well known, for any value of the mass parameter µ¿¿¿(0, 0.5] and sufficiently restricted Hill regions (that is, for big enough values of the Jacobi constant C), there are exactly four EC orbits. We check their existence and extend numerically these four orbits for µ¿¿¿(0, 0.5] and for smaller values of the Jacobi constant. We introduce the concept of n-ejection-collision orbits (n-EC orbits) and we explore them numerically for µ¿¿¿(0, 0.5] and values of the Jacobi constant such that the Hill bounded possible region of motion contains the big primary and does not contain the small one. We study the cases 1¿=¿n¿=¿10 and we analyse the continuation of families of such n-EC orbits, varying the energy, as well as the bifurcations that appear.
publishDate 2017
dc.date.none.fl_str_mv 2017
2017-11-15
2018
2018-02-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/110642
https://dx.doi.org/10.1016/j.cnsns.2017.07.013
url https://hdl.handle.net/2117/110642
https://dx.doi.org/10.1016/j.cnsns.2017.07.013
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.300719

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