Spatial resonant periodic orbits in the restricted three-body problem

Research output: Contribution to journalArticle

Abstract

The quest of exo-Earths has become a prominent field. In this work, we study the stability of non-coplanar planetary configurations consisting of an inclined inner terrestrial planet in mean-motion resonance with an outer giant planet. We examine the families of circular and elliptic symmetric periodic orbits with respect to the vertical stability, and identify the vertical critical orbits from which the spatial families emanate. We showcase that stable spatial periodic orbits can exist for both prograde and retrograde motions in 3/2, 2/1, 5/2, 3/1, 4/1, and 5/1 resonances for broad ranges of inclinations, when the giant evolves on a circular orbit. When the orbit of the giant is elliptic, only the 2/1 resonance has stable periodic orbits up to high inclinations, while the 3/1, 4/1, and 5/1 resonances possess segments of stability for low inclinations. Furthermore, we show that regular motion can also take place in the vicinity of both horizontally and vertically stable planar periodic orbits, even for very high inclinations. Finally, the results are discussed in the context of asteroid dynamics.
Original languageEnglish
Pages (from-to)2923-2940
JournalMonthly Notices of the Royal Astronomical Society
Volume483
Issue number3
DOIs
Publication statusPublished - 2019
Externally publishedYes

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three body problem
planet
orbits
asteroid
inclination
terrestrial planets
asteroids
planets
configurations
family

Keywords

  • chaos
  • celestial mechanics
  • planets and satellites: dynamical evolution and stability
  • planets and satellites: terrestrial planets
  • minor planets
  • asteroids: general

Cite this

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title = "Spatial resonant periodic orbits in the restricted three-body problem",
abstract = "The quest of exo-Earths has become a prominent field. In this work, we study the stability of non-coplanar planetary configurations consisting of an inclined inner terrestrial planet in mean-motion resonance with an outer giant planet. We examine the families of circular and elliptic symmetric periodic orbits with respect to the vertical stability, and identify the vertical critical orbits from which the spatial families emanate. We showcase that stable spatial periodic orbits can exist for both prograde and retrograde motions in 3/2, 2/1, 5/2, 3/1, 4/1, and 5/1 resonances for broad ranges of inclinations, when the giant evolves on a circular orbit. When the orbit of the giant is elliptic, only the 2/1 resonance has stable periodic orbits up to high inclinations, while the 3/1, 4/1, and 5/1 resonances possess segments of stability for low inclinations. Furthermore, we show that regular motion can also take place in the vicinity of both horizontally and vertically stable planar periodic orbits, even for very high inclinations. Finally, the results are discussed in the context of asteroid dynamics.",
keywords = "chaos, celestial mechanics, planets and satellites: dynamical evolution and stability, planets and satellites: terrestrial planets, minor planets, asteroids: general",
author = "Antoniadou, {Kyriaki I.} and Anne-Sophie Libert",
year = "2019",
doi = "10.1093/mnras/sty3195",
language = "English",
volume = "483",
pages = "2923--2940",
journal = "Monthly Notices of the Royal Astronomy Society",
issn = "1365-2966",
publisher = "Oxford University Press",
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TY - JOUR

T1 - Spatial resonant periodic orbits in the restricted three-body problem

AU - Antoniadou, Kyriaki I.

AU - Libert, Anne-Sophie

PY - 2019

Y1 - 2019

N2 - The quest of exo-Earths has become a prominent field. In this work, we study the stability of non-coplanar planetary configurations consisting of an inclined inner terrestrial planet in mean-motion resonance with an outer giant planet. We examine the families of circular and elliptic symmetric periodic orbits with respect to the vertical stability, and identify the vertical critical orbits from which the spatial families emanate. We showcase that stable spatial periodic orbits can exist for both prograde and retrograde motions in 3/2, 2/1, 5/2, 3/1, 4/1, and 5/1 resonances for broad ranges of inclinations, when the giant evolves on a circular orbit. When the orbit of the giant is elliptic, only the 2/1 resonance has stable periodic orbits up to high inclinations, while the 3/1, 4/1, and 5/1 resonances possess segments of stability for low inclinations. Furthermore, we show that regular motion can also take place in the vicinity of both horizontally and vertically stable planar periodic orbits, even for very high inclinations. Finally, the results are discussed in the context of asteroid dynamics.

AB - The quest of exo-Earths has become a prominent field. In this work, we study the stability of non-coplanar planetary configurations consisting of an inclined inner terrestrial planet in mean-motion resonance with an outer giant planet. We examine the families of circular and elliptic symmetric periodic orbits with respect to the vertical stability, and identify the vertical critical orbits from which the spatial families emanate. We showcase that stable spatial periodic orbits can exist for both prograde and retrograde motions in 3/2, 2/1, 5/2, 3/1, 4/1, and 5/1 resonances for broad ranges of inclinations, when the giant evolves on a circular orbit. When the orbit of the giant is elliptic, only the 2/1 resonance has stable periodic orbits up to high inclinations, while the 3/1, 4/1, and 5/1 resonances possess segments of stability for low inclinations. Furthermore, we show that regular motion can also take place in the vicinity of both horizontally and vertically stable planar periodic orbits, even for very high inclinations. Finally, the results are discussed in the context of asteroid dynamics.

KW - chaos

KW - celestial mechanics

KW - planets and satellites: dynamical evolution and stability

KW - planets and satellites: terrestrial planets

KW - minor planets

KW - asteroids: general

U2 - 10.1093/mnras/sty3195

DO - 10.1093/mnras/sty3195

M3 - Article

VL - 483

SP - 2923

EP - 2940

JO - Monthly Notices of the Royal Astronomy Society

JF - Monthly Notices of the Royal Astronomy Society

SN - 1365-2966

IS - 3

ER -