Stability and secondary resonances in the spatial restricted three-body problem for small mass ratios

R. Schwarz, Á Bazsó, B. Érdi, B. Funk

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

This paper is devoted to the study of secondary resonances and the stability of the Lagrangian point L4 in the spatial restricted three-body problem for moderate mass ratios μ, meaning that μ ≤ 0.0045. However, we concentrated our investigations on small mass ratios μ ≤ 0.001, which represent the mass ratios for stable configurations of tadpole orbits in the Solar system. The stability is investigated by numerical methods, computing stability maps in different parameter planes.We started investigating the mass of the secondary: from Earth-mass bodies up to Jupiter-mass bodies. In addition, we changed the orbital elements (eccentricity and inclination) of the secondary and Trojan body. For this parameter space, we found high-order secondary resonances, which are present for various inclinations. To determine secondary resonances we used Rabe's equation and the frequency analysis. In addition, we investigated the stability in and around these secondary resonances.

Original languageEnglish
Pages (from-to)2437-2443
Number of pages7
JournalMonthly Notices of the Royal Astronomical Society
Volume443
Issue number3
DOIs
Publication statusPublished - 2014

Fingerprint

three body problem
mass ratios
body mass
inclination
orbital elements
frequency analysis
Jupiter (planet)
eccentricity
Jupiter
solar system
numerical method
orbits
configurations
parameter

Keywords

  • Celestial mechanics
  • Methods: numerical
  • Minor planets, asteroids

ASJC Scopus subject areas

  • Space and Planetary Science
  • Astronomy and Astrophysics

Cite this

Stability and secondary resonances in the spatial restricted three-body problem for small mass ratios. / Schwarz, R.; Bazsó, Á; Érdi, B.; Funk, B.

In: Monthly Notices of the Royal Astronomical Society, Vol. 443, No. 3, 2014, p. 2437-2443.

Research output: Contribution to journalArticle

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