Abstract
We consider the trajectories in the neighborhood of a 2: 1 resonance (in periods of osculating motions of the outer and inner binaries) in the plane equal-mass three-body problem. We identified the zones of motions that are stable on limited time intervals. All of them correspond to the retrograde motions of the outer and inner subsystems. The prograde motions are unstable: the triple system breaks up into a final binary and an escaping component. In the barycentric nonrotating coordinate system, the trajectories occasionally form symmetric structures composed of several leaves. These structures persist for a long time, and, subsequently, the trajectories of the bodies fill compact regions in coordinate space.
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References
S. J. Aarseth, Gravitational N-Body Simulations (Cambridge Univ. Press, Cambridge, 2003).
S. J. Aarseth and K. Zare, Celest. Mech. 10, 185 (1974).
V. V. Beletskii, Sketchs on the Motion of Cosmic Bodies (Nauka, Moscow, 1972) [in Russian].
R. Brasser, D. C. Heggie, and S. Mikkola, Celest. Mech. Dyn. Astron. 88, 123 (2004).
D. Brower, Astron. J. 68, 152 (1963).
A. D. Bryuno, Mat. Sbornik 83(125), 273 (1970).
R. Bulirsch and J. Stoer, Num. Math. 8, 1 (1966).
S. Ferraz Mellu, Dynamics of Jupiter’s Galilean Satellites (Mir, Moscow, 1983) [in Russian].
K. Gozdziewsky and A. J. Maciejewski, Astrophys. J. 563, L81 (2001).
N. N. Gor’kavyi and A. M. Fridman, Physics of Planetary Rings (Nauka, Moscow, 1994) [in Russian].
E. A. Grebenikov and Yu. A. Ryabov, New Qualitative Methods in Celestial Mechanics (Nauka, Moscow, 1971) [in Russian].
G. W. Marcy, R. P. Butler, D. A. Fisher, et al., Astrophys. J. 556, 296 (2001).
G. W. Marcy, R. P. Butler, D. A. Fisher, et al., Astrophys. J. 581, 1375 (2002).
C. Moore, Phys. Rev. Lett. 70, 3675 (1993).
N. P. Pitjev and L. L. Sokolov, Abstracts of the Conf. “Order and Chaos in Stellar and Planetary Systems,” St. Petersburg, 2003, p. 46.
N. C. Santos, G. Israelian, and M. Mayor, Astron. Astrophys. 363, 228 (2000).
K. Simo, Up-to-date Chaos and Nonlinearity Problems, Ed. by A. V. Borisov and A. A. Kilin (Inst. Comp. Res., Izhevsk, 2002), p. 252 [in Russian].
R. J. Vanderbei, astro-ph/0303153 (2003).
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Translated from Pis’ma v Astronomicheski\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l}\) Zhurnal, Vol. 31, No. 3, 2005, pp. 234–240.
Original Russian Text Copyright © 2005 by Martynova, Orlov, Sokolov.
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Martynova, A.I., Orlov, V.V. & Sokolov, L.L. Analysis of the neighborhood of the 2: 1 resonance in the equal-mass three-body problem. Astron. Lett. 31, 213–219 (2005). https://doi.org/10.1134/1.1883353
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DOI: https://doi.org/10.1134/1.1883353