Hostname: page-component-54dcc4c588-2bdfx Total loading time: 0 Render date: 2025-10-06T02:29:03.108Z Has data issue: false hasContentIssue false
  • English
  • Français

A Catalogue of Periodic Orbits in the Elliptic Restricted 3-Body Problem

Published online by Cambridge University Press:  07 August 2017

R. Dvorak  and
J. Kribbel
R. Dvorak
Affiliation:
Institute of Astronomy University if Vienna Türkenschanzstrasse 17 A-1180 Vienna e-mail: DVORAK@AVIA.UNA.AC.AT
J. Kribbel
Affiliation:
Institute of Astronomy University if Vienna Türkenschanzstrasse 17 A-1180 Vienna e-mail: DVORAK@AVIA.UNA.AC.AT

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Results of families of periodic orbits in the elliptic restricted problem are shown for some specific resonances. They are calculated for all mass ratios 0 < μ < 1.0 of the primary bodies and for all values of the eccentricity of the orbit of the primaries e < 1.0. The grid size is of 0.01 for both parameters. The classification of the stability is undertaken according to the usual one and the results are compared with the extensive studies by Contopoulos (1986) in different galactical models.

References

Broucke, R.A.:1969, “Periodic Orbits in the Elliptic Restricted Three Body Problem”, Technical Report 32-1360, NASA CrossRefGoogle Scholar
Contopoulos, G.:1986, “Qualitative changes in 3-dimensional systems”, Astron. Astrophys. 161, p.244 Google Scholar
Deprit, André and Price, J.F.: 1965, “The computation of characteristic exponents in the planar restricted problem of three bodies”,Astron. J. 70,p.10 CrossRefGoogle Scholar
Hadjidemetriou, J.: 1985, “Hamiltonian Perturbations In Dynamical Systems And Applications In Planetary Systems”, in “Stability of the Solar System and its Minor Natural and Artificial Bodies”, Reidel Publishing Company p.213.CrossRefGoogle Scholar
Kribbel, J., Dvorak, R.:1988, “Stability of Periodic Resonance-Orbits in the elliptic restricted 3-body problem”, Cel. Mech. 43, p.391 CrossRefGoogle Scholar
Hénon, M., Guyot, M.: 1970, “Stability of Periodic Orbits in the Restricted Problem” in “Periodic Orbits, Stability and Resonances”, ed. Giacaglia, G.E.O., Reidel,Dordrecht, p.349 CrossRefGoogle Scholar
Poincaré, H.: 1892, “Les méthodes nouvelles de la mécanique céleste”, Gauthier-Villars et Fils, Paris, p.79 Google Scholar
Shelus, P. and Kumar, S.: 1970, “Some periodic orbits in the elliptic problem of three bodies”, Astron. J. 75,p.4 CrossRefGoogle Scholar