Oscillatory motions, parabolic orbits and collision orbits in the planar circular restricted three-body problem

In this paper we consider the planar circular restricted three body problem (PCRTBP), which models the motion of a massless body under the attraction of other two bodies, the primaries, which describe circular orbits around their common center of mass. In a suitable system of coordinates, this is a...

Descripción completa

Detalles Bibliográficos
Autores: Lamas Rodríguez, José|||0000-0002-1809-1823, Guàrdia Munarriz, Marcel|||0000-0002-4802-3151, Martínez-Seara Alonso, M. Teresa|||0000-0001-8421-8717
Tipo de recurso: artículo
Fecha de publicación:2025
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/429624
Acceso en línea:https://hdl.handle.net/2117/429624
https://dx.doi.org/10.1007/s00220-025-05283-9
Access Level:acceso abierto
Palabra clave:Restricted three-body problem
Parabolic orbits
Oscillatory motions
Orbital collisions
Final motions
Gravitational interaction
Ejection-collision trajectories
Periodic orbits
Àrees temàtiques de la UPC::Aeronàutica i espai::Astronàutica::Navegació espacial
Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals
id ES_d809e2fed0175d9dafd47643a86a3d82
oai_identifier_str oai:upcommons.upc.edu:2117/429624
network_acronym_str ES
network_name_str España
repository_id_str
spelling Oscillatory motions, parabolic orbits and collision orbits in the planar circular restricted three-body problemLamas Rodríguez, José|||0000-0002-1809-1823Guàrdia Munarriz, Marcel|||0000-0002-4802-3151Martínez-Seara Alonso, M. Teresa|||0000-0001-8421-8717Restricted three-body problemParabolic orbitsOscillatory motionsOrbital collisionsFinal motionsGravitational interactionEjection-collision trajectoriesPeriodic orbitsÀrees temàtiques de la UPC::Aeronàutica i espai::Astronàutica::Navegació espacialÀrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integralsIn this paper we consider the planar circular restricted three body problem (PCRTBP), which models the motion of a massless body under the attraction of other two bodies, the primaries, which describe circular orbits around their common center of mass. In a suitable system of coordinates, this is a two degrees of freedom Hamiltonian system. The orbits of this system are either defined for all (future or past) time or eventually go to collision with one of the primaries. For orbits defined for all time, Chazy provided a classification of all possible asymptotic behaviors, usually called final motions. By considering a sufficiently small mass ratio between the primaries, we analyze the interplay between collision orbits and various final motions and construct several types of dynamics. In particular, we show that orbits corresponding to any combination of past and future final motions can be created to pass arbitrarily close to the massive primary. Additionally, we construct arbitrarily large ejection-collision orbits (orbits which experience collision in both past and future times) and periodic orbits that are arbitrarily large and get arbitrarily close to the massive primary. Furthermore, we also establish oscillatory motions in both position and velocity, meaning that as time tends to infinity, the superior limit of the position or velocity is infinity while the inferior limit remains a real number.This work was partially supported by the grant PID-2021-122954NB-100 funded by MCIN/AEI/10. 13039/501100011033 and “ERDF A way of making Europe”. M.Guardia has been supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 757802). M.Guardia was also supported by the Catalan Institution for Research and Advanced Studies via an ICREA Academia Prizes 2018 and 2023. J.Lamas has been supported by grant 2021 FI_B 00117 under the European Social Fund. Tere M.Seara has been supported by the Catalan Institution for Research and Advanced Studies via an ICREA Academia Prize 2018. This work was also supported by the Spanish State Research Agency through the Severo Ochoa and María de Maeztu Program for Centers and Units of Excellence in R&D(CEX2020-001084-M)Peer ReviewedSpringer20252025-04-1020252025-05-15journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/429624https://dx.doi.org/10.1007/s00220-025-05283-9reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)InglésengAgencia Estatal de Investigación http://doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023 PID2021-122954NB-I00 INVARIANT MANIFOLDS, HAMILTONIAN SYSTEMS AND DYNAMICS IN NEUROSCIENCE, EPIDEMIOLOGY AND ATMOSPHEREopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/4296242026-05-27T15:37:01Z
dc.title.none.fl_str_mv Oscillatory motions, parabolic orbits and collision orbits in the planar circular restricted three-body problem
title Oscillatory motions, parabolic orbits and collision orbits in the planar circular restricted three-body problem
spellingShingle Oscillatory motions, parabolic orbits and collision orbits in the planar circular restricted three-body problem
Lamas Rodríguez, José|||0000-0002-1809-1823
Restricted three-body problem
Parabolic orbits
Oscillatory motions
Orbital collisions
Final motions
Gravitational interaction
Ejection-collision trajectories
Periodic orbits
Àrees temàtiques de la UPC::Aeronàutica i espai::Astronàutica::Navegació espacial
Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals
title_short Oscillatory motions, parabolic orbits and collision orbits in the planar circular restricted three-body problem
title_full Oscillatory motions, parabolic orbits and collision orbits in the planar circular restricted three-body problem
title_fullStr Oscillatory motions, parabolic orbits and collision orbits in the planar circular restricted three-body problem
title_full_unstemmed Oscillatory motions, parabolic orbits and collision orbits in the planar circular restricted three-body problem
title_sort Oscillatory motions, parabolic orbits and collision orbits in the planar circular restricted three-body problem
dc.creator.none.fl_str_mv Lamas Rodríguez, José|||0000-0002-1809-1823
Guàrdia Munarriz, Marcel|||0000-0002-4802-3151
Martínez-Seara Alonso, M. Teresa|||0000-0001-8421-8717
author Lamas Rodríguez, José|||0000-0002-1809-1823
author_facet Lamas Rodríguez, José|||0000-0002-1809-1823
Guàrdia Munarriz, Marcel|||0000-0002-4802-3151
Martínez-Seara Alonso, M. Teresa|||0000-0001-8421-8717
author_role author
author2 Guàrdia Munarriz, Marcel|||0000-0002-4802-3151
Martínez-Seara Alonso, M. Teresa|||0000-0001-8421-8717
author2_role author
author
dc.subject.none.fl_str_mv Restricted three-body problem
Parabolic orbits
Oscillatory motions
Orbital collisions
Final motions
Gravitational interaction
Ejection-collision trajectories
Periodic orbits
Àrees temàtiques de la UPC::Aeronàutica i espai::Astronàutica::Navegació espacial
Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals
topic Restricted three-body problem
Parabolic orbits
Oscillatory motions
Orbital collisions
Final motions
Gravitational interaction
Ejection-collision trajectories
Periodic orbits
Àrees temàtiques de la UPC::Aeronàutica i espai::Astronàutica::Navegació espacial
Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals
description In this paper we consider the planar circular restricted three body problem (PCRTBP), which models the motion of a massless body under the attraction of other two bodies, the primaries, which describe circular orbits around their common center of mass. In a suitable system of coordinates, this is a two degrees of freedom Hamiltonian system. The orbits of this system are either defined for all (future or past) time or eventually go to collision with one of the primaries. For orbits defined for all time, Chazy provided a classification of all possible asymptotic behaviors, usually called final motions. By considering a sufficiently small mass ratio between the primaries, we analyze the interplay between collision orbits and various final motions and construct several types of dynamics. In particular, we show that orbits corresponding to any combination of past and future final motions can be created to pass arbitrarily close to the massive primary. Additionally, we construct arbitrarily large ejection-collision orbits (orbits which experience collision in both past and future times) and periodic orbits that are arbitrarily large and get arbitrarily close to the massive primary. Furthermore, we also establish oscillatory motions in both position and velocity, meaning that as time tends to infinity, the superior limit of the position or velocity is infinity while the inferior limit remains a real number.
publishDate 2025
dc.date.none.fl_str_mv 2025
2025-04-10
2025
2025-05-15
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/2117/429624
https://dx.doi.org/10.1007/s00220-025-05283-9
url https://hdl.handle.net/2117/429624
https://dx.doi.org/10.1007/s00220-025-05283-9
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación http://doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023 PID2021-122954NB-I00 INVARIANT MANIFOLDS, HAMILTONIAN SYSTEMS AND DYNAMICS IN NEUROSCIENCE, EPIDEMIOLOGY AND ATMOSPHERE
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
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
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
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
_version_ 1869421063487619073
score 15,812429

Similares en LA Referencia