Inclined asymmetric librations in exterior resonances

G. Voyatzis, K. Tsiganis, K. I. Antoniadou

Research output: Contribution to journalArticle

Abstract

Librational motion in Celestial Mechanics is generally associated with the existence of stable resonant configurations and signified by the existence of stable periodic solutions and oscillation of critical (resonant) angles. When such an oscillation takes place around a value different than 0 or π, the libration is called asymmetric. In the context of the planar circular restricted three-body problem, asymmetric librations have been identified for the exterior mean motion resonances (MMRs) 1:2, 1:3, etc., as well as for co-orbital motion (1:1). In exterior MMRs the massless body is the outer one. In this paper, we study asymmetric librations in the three-dimensional space. We employ the computational approach of Markellos (Mon Not R Astron Soc 184:273–281, https://doi.org/10.1093/mnras/184.2. 273, 1978) and compute families of asymmetric periodic orbits and their stability. Stable asymmetric periodic orbits are surrounded in phase space by domains of initial conditions which correspond to stable evolution and librating resonant angles. Our computations were focused on the spatial circular restricted three-body model of the Sun–Neptune–TNO system (TNO = trans-Neptunian object).We compare our results with numerical integrations of observed TNOs, which reveal that some of them perform 1:2 resonant, inclined asymmetric librations. For the stable 1:2 TNO librators, we find that their libration seems to be related to the vertically stable planar asymmetric orbits of our model, rather than the three-dimensional ones found in the present study.

LanguageEnglish
Article number29
JournalCelestial Mechanics and Dynamical Astronomy
Volume130
Issue number4
DOIs
Publication statusPublished - 2018

Fingerprint

trans-Neptunian objects
libration
Inclined
Orbits
oscillation
Neptune
orbits
mechanics
Motion
Sun
celestial mechanics
librational motion
Mechanics
Periodic Orbits
oscillations
Neptune (planet)
three body problem
Oscillation
numerical integration
Celestial Mechanics

Keywords

  • Circular restricted TBP
  • Exterior resonances
  • Spatial asymmetric periodic orbits
  • Trans-Neptunian object dynamics

Cite this

@article{d33535322c854326908bdadc31cb0576,
title = "Inclined asymmetric librations in exterior resonances",
abstract = "Librational motion in Celestial Mechanics is generally associated with the existence of stable resonant configurations and signified by the existence of stable periodic solutions and oscillation of critical (resonant) angles. When such an oscillation takes place around a value different than 0 or π, the libration is called asymmetric. In the context of the planar circular restricted three-body problem, asymmetric librations have been identified for the exterior mean motion resonances (MMRs) 1:2, 1:3, etc., as well as for co-orbital motion (1:1). In exterior MMRs the massless body is the outer one. In this paper, we study asymmetric librations in the three-dimensional space. We employ the computational approach of Markellos (Mon Not R Astron Soc 184:273–281, https://doi.org/10.1093/mnras/184.2. 273, 1978) and compute families of asymmetric periodic orbits and their stability. Stable asymmetric periodic orbits are surrounded in phase space by domains of initial conditions which correspond to stable evolution and librating resonant angles. Our computations were focused on the spatial circular restricted three-body model of the Sun–Neptune–TNO system (TNO = trans-Neptunian object).We compare our results with numerical integrations of observed TNOs, which reveal that some of them perform 1:2 resonant, inclined asymmetric librations. For the stable 1:2 TNO librators, we find that their libration seems to be related to the vertically stable planar asymmetric orbits of our model, rather than the three-dimensional ones found in the present study.",
keywords = "Circular restricted TBP, Exterior resonances, Spatial asymmetric periodic orbits, Trans-Neptunian object dynamics",
author = "G. Voyatzis and K. Tsiganis and Antoniadou, {K. I.}",
year = "2018",
doi = "10.1007/s10569-018-9821-0",
language = "English",
volume = "130",
journal = "Celest. Mech & Dyn. Astron.",
issn = "0923-2958",
publisher = "Springer Netherlands",
number = "4",

}

Inclined asymmetric librations in exterior resonances. / Voyatzis, G.; Tsiganis, K.; Antoniadou, K. I.

In: Celestial Mechanics and Dynamical Astronomy, Vol. 130, No. 4, 29, 2018.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Inclined asymmetric librations in exterior resonances

AU - Voyatzis, G.

AU - Tsiganis, K.

AU - Antoniadou, K. I.

PY - 2018

Y1 - 2018

N2 - Librational motion in Celestial Mechanics is generally associated with the existence of stable resonant configurations and signified by the existence of stable periodic solutions and oscillation of critical (resonant) angles. When such an oscillation takes place around a value different than 0 or π, the libration is called asymmetric. In the context of the planar circular restricted three-body problem, asymmetric librations have been identified for the exterior mean motion resonances (MMRs) 1:2, 1:3, etc., as well as for co-orbital motion (1:1). In exterior MMRs the massless body is the outer one. In this paper, we study asymmetric librations in the three-dimensional space. We employ the computational approach of Markellos (Mon Not R Astron Soc 184:273–281, https://doi.org/10.1093/mnras/184.2. 273, 1978) and compute families of asymmetric periodic orbits and their stability. Stable asymmetric periodic orbits are surrounded in phase space by domains of initial conditions which correspond to stable evolution and librating resonant angles. Our computations were focused on the spatial circular restricted three-body model of the Sun–Neptune–TNO system (TNO = trans-Neptunian object).We compare our results with numerical integrations of observed TNOs, which reveal that some of them perform 1:2 resonant, inclined asymmetric librations. For the stable 1:2 TNO librators, we find that their libration seems to be related to the vertically stable planar asymmetric orbits of our model, rather than the three-dimensional ones found in the present study.

AB - Librational motion in Celestial Mechanics is generally associated with the existence of stable resonant configurations and signified by the existence of stable periodic solutions and oscillation of critical (resonant) angles. When such an oscillation takes place around a value different than 0 or π, the libration is called asymmetric. In the context of the planar circular restricted three-body problem, asymmetric librations have been identified for the exterior mean motion resonances (MMRs) 1:2, 1:3, etc., as well as for co-orbital motion (1:1). In exterior MMRs the massless body is the outer one. In this paper, we study asymmetric librations in the three-dimensional space. We employ the computational approach of Markellos (Mon Not R Astron Soc 184:273–281, https://doi.org/10.1093/mnras/184.2. 273, 1978) and compute families of asymmetric periodic orbits and their stability. Stable asymmetric periodic orbits are surrounded in phase space by domains of initial conditions which correspond to stable evolution and librating resonant angles. Our computations were focused on the spatial circular restricted three-body model of the Sun–Neptune–TNO system (TNO = trans-Neptunian object).We compare our results with numerical integrations of observed TNOs, which reveal that some of them perform 1:2 resonant, inclined asymmetric librations. For the stable 1:2 TNO librators, we find that their libration seems to be related to the vertically stable planar asymmetric orbits of our model, rather than the three-dimensional ones found in the present study.

KW - Circular restricted TBP

KW - Exterior resonances

KW - Spatial asymmetric periodic orbits

KW - Trans-Neptunian object dynamics

UR - http://www.scopus.com/inward/record.url?scp=85047817691&partnerID=8YFLogxK

U2 - 10.1007/s10569-018-9821-0

DO - 10.1007/s10569-018-9821-0

M3 - Article

VL - 130

JO - Celest. Mech & Dyn. Astron.

T2 - Celest. Mech & Dyn. Astron.

JF - Celest. Mech & Dyn. Astron.

SN - 0923-2958

IS - 4

M1 - 29

ER -