Stability of librational motion in the spatial circular restricted three-body problem for high inclinations and mass ratios

A. Bazsó, R. Schwarz, B. Érdi, B. Funk

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

In the spatial circular restricted three-body problem librational motion around the Lagrangian points L4 and L5 exists up to high inclinations of the massless object. We report the results of numerical investigations on the stability of this librational motion for systematic variations in the inclination of the Trojan and the mass-ratio μ of the two massive bodies. We show that stable motion prevails for inclinations below 60 degrees and mass-ratios μ <0.04 for typical integration times up to 106 revolution periods. At even higher mass-ratios - beyond the critical mass-ratio for the planar case - stable orbits were found to exist for up to 107 periods at moderate inclinations. We extracted the librational frequencies on a grid in the parameter space from the Fourier spectra and traced their variation. Several resonances between the short and long period librational frequency as well as the vertical frequency lie inside the investigated region. The application of the Lyapunov characteristic indicator and spectral number methods also reveals the chaotic regions. This simple model is equally applicable in the Solar system for low mass ratios for Trojans of the planets, as well as to Trojan-type exoplanets in binary star systems at high mass-ratios.

Original languageEnglish
Pages (from-to)1008-1011
Number of pages4
JournalAstronomische Nachrichten
Volume334
Issue number9
DOIs
Publication statusPublished - Nov 2013

Fingerprint

librational motion
three body problem
mass ratios
inclination
critical mass
binary stars
extrasolar planets
solar system
planets
planet
grids
orbits

Keywords

  • Celestial mechanics, stellar dynamics
  • Methods: numerical
  • Minor planets, asteroids
  • Planets and satellites: dynamical evolution and stability

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science

Cite this

Stability of librational motion in the spatial circular restricted three-body problem for high inclinations and mass ratios. / Bazsó, A.; Schwarz, R.; Érdi, B.; Funk, B.

In: Astronomische Nachrichten, Vol. 334, No. 9, 11.2013, p. 1008-1011.

Research output: Contribution to journalArticle

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