Secular evolution of resonant small bodies: semi-analytical approach for arbitrary eccentricities in the coplanar case

Pons Vuolo, Juan Andrés - Gallardo, Tabaré

Resumen:

We study the secular evolution of a particle in deep mean motion resonance (MMR) with a planet in the planar elliptic restricted three body problem. We do not consider any restriction neither in the planet’s eccentricity ep nor in the particle’s eccentricity e. The methodology used is based on a semi-analytical model that consists on calculating the averaged resonant disturbing function numerically, assuming for this that in the resonant scale of time all the orbital elements of the particle are constant. In order to obtain the secular evolution inside the MMR, we make use of the adiabatic invariance principle, assuming a zero-amplitude resonant libration. We construct two-dimensional surfaces (called H surfaces) in the three-dimensional space (σ , e, ) that allow us to predict the secular evolution of these three variables. The 2:1 MMR is used as example to show some results. We found four apsidal corotation resonance (ACR) families, two symmetric and two asymmetric. One of the symmetric families exists for almost any ep value. The other one for ep > 0.3 and the asymmetric ones for ep > 0.44. We corroborate the secular variations in e and predicted by the model through numerical integrations even when the initial conditions are displaced from those ACR. Some peculiar examples are presented for the 3:1 and 3:2 MMR showing large excursions in eccentricity. As an application, the Planet 9 is investigated as a possible responsible of high eccentric distant TNOs.


Detalles Bibliográficos
2022
ANII y PEDECIBA
Methods: numerical
Celestial mechanics
Planets and satellites: dynamical evolution and stability
Inglés
Universidad de la República
COLIBRI
https://hdl.handle.net/20.500.12008/39677
Acceso abierto
Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)
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author Pons Vuolo, Juan Andrés
author2 Gallardo, Tabaré
author2_role author
author_facet Pons Vuolo, Juan Andrés
Gallardo, Tabaré
author_role author
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collection COLIBRI
dc.contributor.filiacion.none.fl_str_mv Pons Vuolo Juan Andrés, Universidad de la República (Uruguay). Facultad de Ciencias. Instituto de Física.
Gallardo Tabaré, Universidad de la República (Uruguay). Facultad de Ciencias. Instituto de Física.
dc.creator.none.fl_str_mv Pons Vuolo, Juan Andrés
Gallardo, Tabaré
dc.date.accessioned.none.fl_str_mv 2023-08-24T12:09:01Z
dc.date.available.none.fl_str_mv 2023-08-24T12:09:01Z
dc.date.issued.none.fl_str_mv 2022
dc.description.abstract.none.fl_txt_mv We study the secular evolution of a particle in deep mean motion resonance (MMR) with a planet in the planar elliptic restricted three body problem. We do not consider any restriction neither in the planet’s eccentricity ep nor in the particle’s eccentricity e. The methodology used is based on a semi-analytical model that consists on calculating the averaged resonant disturbing function numerically, assuming for this that in the resonant scale of time all the orbital elements of the particle are constant. In order to obtain the secular evolution inside the MMR, we make use of the adiabatic invariance principle, assuming a zero-amplitude resonant libration. We construct two-dimensional surfaces (called H surfaces) in the three-dimensional space (σ , e, ) that allow us to predict the secular evolution of these three variables. The 2:1 MMR is used as example to show some results. We found four apsidal corotation resonance (ACR) families, two symmetric and two asymmetric. One of the symmetric families exists for almost any ep value. The other one for ep > 0.3 and the asymmetric ones for ep > 0.44. We corroborate the secular variations in e and predicted by the model through numerical integrations even when the initial conditions are displaced from those ACR. Some peculiar examples are presented for the 3:1 and 3:2 MMR showing large excursions in eccentricity. As an application, the Planet 9 is investigated as a possible responsible of high eccentric distant TNOs.
dc.description.sponsorship.none.fl_txt_mv ANII y PEDECIBA
dc.format.extent.es.fl_str_mv 14 h.
dc.format.mimetype.es.fl_str_mv application/pdf
dc.identifier.citation.es.fl_str_mv Pons Vuolo, J y Gallardo, T. "Secular evolution of resonant small bodies: semi-analytical approach for arbitrary eccentricities in the coplanar case". Monthly Notices of the Royal Astronomical Society. [en línea] 2022, 511(1): 1153–1166. 14 h. DOI: 10.1093/mnras/stac018
dc.identifier.doi.none.fl_str_mv 10.1093/mnras/stac018
dc.identifier.issn.none.fl_str_mv 1745-3933
dc.identifier.uri.none.fl_str_mv https://hdl.handle.net/20.500.12008/39677
dc.language.iso.none.fl_str_mv en_US
eng
dc.publisher.es.fl_str_mv Oxford University Press
dc.relation.ispartof.es.fl_str_mv Monthly Notices of the Royal Astronomical Society, 2022, 511(1): 1153–1166.
dc.rights.license.none.fl_str_mv Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
dc.source.none.fl_str_mv reponame:COLIBRI
instname:Universidad de la República
instacron:Universidad de la República
dc.subject.es.fl_str_mv Methods: numerical
Celestial mechanics
Planets and satellites: dynamical evolution and stability
dc.title.none.fl_str_mv Secular evolution of resonant small bodies: semi-analytical approach for arbitrary eccentricities in the coplanar case
dc.type.es.fl_str_mv Artículo
dc.type.none.fl_str_mv info:eu-repo/semantics/article
dc.type.version.none.fl_str_mv info:eu-repo/semantics/publishedVersion
description We study the secular evolution of a particle in deep mean motion resonance (MMR) with a planet in the planar elliptic restricted three body problem. We do not consider any restriction neither in the planet’s eccentricity ep nor in the particle’s eccentricity e. The methodology used is based on a semi-analytical model that consists on calculating the averaged resonant disturbing function numerically, assuming for this that in the resonant scale of time all the orbital elements of the particle are constant. In order to obtain the secular evolution inside the MMR, we make use of the adiabatic invariance principle, assuming a zero-amplitude resonant libration. We construct two-dimensional surfaces (called H surfaces) in the three-dimensional space (σ , e, ) that allow us to predict the secular evolution of these three variables. The 2:1 MMR is used as example to show some results. We found four apsidal corotation resonance (ACR) families, two symmetric and two asymmetric. One of the symmetric families exists for almost any ep value. The other one for ep > 0.3 and the asymmetric ones for ep > 0.44. We corroborate the secular variations in e and predicted by the model through numerical integrations even when the initial conditions are displaced from those ACR. Some peculiar examples are presented for the 3:1 and 3:2 MMR showing large excursions in eccentricity. As an application, the Planet 9 is investigated as a possible responsible of high eccentric distant TNOs.
eu_rights_str_mv openAccess
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identifier_str_mv Pons Vuolo, J y Gallardo, T. "Secular evolution of resonant small bodies: semi-analytical approach for arbitrary eccentricities in the coplanar case". Monthly Notices of the Royal Astronomical Society. [en línea] 2022, 511(1): 1153–1166. 14 h. DOI: 10.1093/mnras/stac018
1745-3933
10.1093/mnras/stac018
instacron_str Universidad de la República
institution Universidad de la República
instname_str Universidad de la República
language eng
language_invalid_str_mv en_US
network_acronym_str COLIBRI
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publishDate 2022
reponame_str COLIBRI
repository.mail.fl_str_mv mabel.seroubian@seciu.edu.uy
repository.name.fl_str_mv COLIBRI - Universidad de la República
repository_id_str 4771
rights_invalid_str_mv Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)
spelling Pons Vuolo Juan Andrés, Universidad de la República (Uruguay). Facultad de Ciencias. Instituto de Física.Gallardo Tabaré, Universidad de la República (Uruguay). Facultad de Ciencias. Instituto de Física.2023-08-24T12:09:01Z2023-08-24T12:09:01Z2022Pons Vuolo, J y Gallardo, T. "Secular evolution of resonant small bodies: semi-analytical approach for arbitrary eccentricities in the coplanar case". Monthly Notices of the Royal Astronomical Society. [en línea] 2022, 511(1): 1153–1166. 14 h. DOI: 10.1093/mnras/stac0181745-3933https://hdl.handle.net/20.500.12008/3967710.1093/mnras/stac018We study the secular evolution of a particle in deep mean motion resonance (MMR) with a planet in the planar elliptic restricted three body problem. We do not consider any restriction neither in the planet’s eccentricity ep nor in the particle’s eccentricity e. The methodology used is based on a semi-analytical model that consists on calculating the averaged resonant disturbing function numerically, assuming for this that in the resonant scale of time all the orbital elements of the particle are constant. In order to obtain the secular evolution inside the MMR, we make use of the adiabatic invariance principle, assuming a zero-amplitude resonant libration. We construct two-dimensional surfaces (called H surfaces) in the three-dimensional space (σ , e, ) that allow us to predict the secular evolution of these three variables. The 2:1 MMR is used as example to show some results. We found four apsidal corotation resonance (ACR) families, two symmetric and two asymmetric. One of the symmetric families exists for almost any ep value. The other one for ep > 0.3 and the asymmetric ones for ep > 0.44. We corroborate the secular variations in e and predicted by the model through numerical integrations even when the initial conditions are displaced from those ACR. Some peculiar examples are presented for the 3:1 and 3:2 MMR showing large excursions in eccentricity. As an application, the Planet 9 is investigated as a possible responsible of high eccentric distant TNOs.Submitted by Farías Verónica (vfarias@fcien.edu.uy) on 2023-08-23T14:03:47Z No. of bitstreams: 2 license_rdf: 23149 bytes, checksum: 1996b8461bc290aef6a27d78c67b6b52 (MD5) 101093mnrasstac018.pdf: 3521072 bytes, checksum: 084b91e169e2135862d8c009b9aeea7e (MD5)Approved for entry into archive by Faget Cecilia (lfaget@fcien.edu.uy) on 2023-08-23T14:06:19Z (GMT) No. of bitstreams: 2 license_rdf: 23149 bytes, checksum: 1996b8461bc290aef6a27d78c67b6b52 (MD5) 101093mnrasstac018.pdf: 3521072 bytes, checksum: 084b91e169e2135862d8c009b9aeea7e (MD5)Made available in DSpace by Luna Fabiana (fabiana.luna@seciu.edu.uy) on 2023-08-24T12:09:01Z (GMT). No. of bitstreams: 2 license_rdf: 23149 bytes, checksum: 1996b8461bc290aef6a27d78c67b6b52 (MD5) 101093mnrasstac018.pdf: 3521072 bytes, checksum: 084b91e169e2135862d8c009b9aeea7e (MD5) Previous issue date: 2022ANII y PEDECIBA14 h.application/pdfen_USengOxford University PressMonthly Notices of the Royal Astronomical Society, 2022, 511(1): 1153–1166.Las obras depositadas en el Repositorio se rigen por la Ordenanza de los Derechos de la Propiedad Intelectual de la Universidad de la República.(Res. Nº 91 de C.D.C. de 8/III/1994 – D.O. 7/IV/1994) y por la Ordenanza del Repositorio Abierto de la Universidad de la República (Res. Nº 16 de C.D.C. de 07/10/2014)info:eu-repo/semantics/openAccessLicencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)Methods: numericalCelestial mechanicsPlanets and satellites: dynamical evolution and stabilitySecular evolution of resonant small bodies: semi-analytical approach for arbitrary eccentricities in the coplanar caseArtículoinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionreponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaPons Vuolo, Juan AndrésGallardo, TabaréLICENSElicense.txtlicense.txttext/plain; charset=utf-84267http://localhost:8080/xmlui/bitstream/20.500.12008/39677/5/license.txt6429389a7df7277b72b7924fdc7d47a9MD55CC-LICENSElicense_urllicense_urltext/plain; charset=utf-850http://localhost:8080/xmlui/bitstream/20.500.12008/39677/2/license_urla006180e3f5b2ad0b88185d14284c0e0MD52license_textlicense_texttext/html; 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- Universidad de la Repúblicafalse
spellingShingle Secular evolution of resonant small bodies: semi-analytical approach for arbitrary eccentricities in the coplanar case
Pons Vuolo, Juan Andrés
Methods: numerical
Celestial mechanics
Planets and satellites: dynamical evolution and stability
status_str publishedVersion
title Secular evolution of resonant small bodies: semi-analytical approach for arbitrary eccentricities in the coplanar case
title_full Secular evolution of resonant small bodies: semi-analytical approach for arbitrary eccentricities in the coplanar case
title_fullStr Secular evolution of resonant small bodies: semi-analytical approach for arbitrary eccentricities in the coplanar case
title_full_unstemmed Secular evolution of resonant small bodies: semi-analytical approach for arbitrary eccentricities in the coplanar case
title_short Secular evolution of resonant small bodies: semi-analytical approach for arbitrary eccentricities in the coplanar case
title_sort Secular evolution of resonant small bodies: semi-analytical approach for arbitrary eccentricities in the coplanar case
topic Methods: numerical
Celestial mechanics
Planets and satellites: dynamical evolution and stability
url https://hdl.handle.net/20.500.12008/39677