Abstract
In several previous papers we had investigated the orbits of the stars that make up galactic satellites and found that many of those orbits were chaotic. In those investigations we made extensive use of the frequency analysis method of Carpintero and Aguilar (1998) to classify the orbits, because that method is much faster than the use of Lyapunov exponents, allows the classification of the regular orbits and our initial comparison of both methods had shown excellent agreement between their results. More recently, we have found some problems with the use of frequency analysis in rotating systems, so that here we present a new investigation of orbits inside galactic satellites using exclusively Lyapunov exponents. Some of our previous conclusions are confirmed, while others are altered. Besides, the Lyapunov times that are now obtained show that the time scales of the chaotic processes are shorter than, or comparable to, other time scales characteristic of galactic satellites.
Similar content being viewed by others
References
Barbanis, B.: 1986, 'Irregular periodic orbits', Cel. Mech. 39, 345-364.
Bennetin, G., Galgani, G. and Strelcyn, J. M.: 1976, 'Kolmogorov entropy and numerical experiments', Phys. Rev. A 14(6), 2338-2345.
Bennetin, G., Galgani, G., Giorgilli, A. and Strelcyn, J. M.: 1980, 'Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems: a method for computing all of them', Meccanica 15, 9.
Binney, J. and Tremaine, S.: 1987, Galactic Dynamics, Princeton University Press.
Carpintero, D. D. and Aguilar, L. A.: 1998, 'Orbit classification in arbitrary 2D and 3D potentials', Monthly Notices Royal Astron. Soc. 298(1), 1-21.
Carpintero, D. D., Muzzio J. C. and Wachlin, F. C.: 1999, 'Regular and chaotic motion in globular clusters', Celest. Mech. Dyn. Astr. 73(1), 159-168.
Cora, S. A., Vergne, M. M. and Muzzio, J. C.: 2001, 'On the effect of chaotic orbits on dynamical friction', Astrophys. J. 546(1), 165-175.
Heggie, D. C. and Ramamani, N.: 1995, 'Approximate self-consistent models for tidally truncated star clusters', Monthly Notices Royal Astron. Soc. 272(2), 317-322.
Hénon, M.: 1966a, 'Exploration numérique du probléme restreint-III Masses égales, orbites non périodiques', Bull. Astron., 3e. ser. 1(1), 57-79.
Hénon, M.: 1966b, 'Exploration numérique du probléme restreint-IV Masses égales, orbites non périodiques (Fin)', Bull. Astron., 3e. ser. 1(2), 49-66.
Hénon, M.: 1970, 'Numerical exploration of the restricted problem. VI. Hills case: non-periodic orbits', Astron. Astrophys. 9(1), 24-36.
Innanen, K. A.: 1979, 'The limiting radii of direct and retrograde satellite orbits, with applications to the solar system and to stellar systems', Astron. J. 84(7), 960-963.
Jefferys, W. H.: 1966, 'Some dynamical systems of two degrees of freedom in celestial mechanics', Astron. J. 71(1), 306-313.
King, I. R.: 1966, 'The structure of star clusters. III. Some simple dynamical models', Astron. J. 71(1), 64-75.
Merritt, D. and Fridman, T.: 1996, 'Triaxial galaxies with cusps', Astrophys. J. 460(1), 136-162.
Miralda-Escudé, J. and Schwarzschild,M.: 1989, 'On the orbit structure of the logarithmic potential', Astrophys. J. 339, 752-762.
Muzzio, J. C.: 2002, 'Chaos in a simple dynamical system', Anales de la Acad. Nac. Cs. Exactas, Físicas y Nat. (in press).
Muzzio, J. C., Carpintero, D. D. and Wachlin, F. C.: 2000a, 'Regular and chaotic motion in galactic satellites', In: V. G. Gurzadyan and R. Ruffini (eds), The Chaotic Universe, Proceedings of the Second ICRA Network Workshop, Rome, Pescara, Italy, February 1999, World Scientific, Singapore, pp. 107-114.
Muzzio, J. C., Wachlin F. C. and Carpintero, D. D.: 2000b, 'Regular and chaotic motion in a restricted three-body problem of astrophysical interest', In: M. Valtonen and C. Flynn (eds), Small Galaxy Groups, IAU Colloquium 174, Turku, Finland, June 1999, Astronomical Society of the Pacific, USA, pp. 281-285.
Muzzio, J. C., Vergne, M. M., Carpintero, D. D. and Wachlin, F. C.: 2001, 'Stellar motion in galactic satellites', Celest. Mech. Dyn. Astr. 81(1), 167-176.
Muzzio, J. C., Wachlin, F. C. and Carpintero, D. D.: 2002, 'Dynamics of galactic satellites on elongated orbits', Rev. Mex. A. A. (Serie de Conferencias) (in press).
Plummer, H. C.: 1911, 'On the problem of distribution in globular star clusters', Monthly Notices Royal Astron. Soc. 71, 460-470.
Rix, H.-W. R. and White, S. D. M.: 1989, 'The dynamical of dum-bell galaxies', Monthly Notices Royal Astron. Soc. 240(4), 941-956.
Satoh, C.: 1980, 'Dynamical models of axisymmetric galaxies and their applications to the elliptical galaxy NGC 4697', Publ. Astron. Soc. Japan 32(1), 41-62.
Stewart, P.: 1993, 'Chaotic behaviour in binary galaxies', Astron. Astrophys. 269(1), 135-144.
Tancredi, G., Sánchez, A. and Roig, F.: 2001, 'A comparison between methods to compute Lyapunov exponents', Astron. J. 121(2), 1171-1179.
Winter, O. C. and Murray, C. D.: 1996, 'The Lyapunov exponent as a tool for exploring phase space', In: J. C. Muzzio, S. Ferraz-Mello and J. Henrard (eds), Chaos in Gravitational N-Body Systems, La Plata, Argentina, August 1995, Kluwer Academic Publishers, The Netherlands, pp. 215-219.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Carpintero, D.D., Muzzio, J.C., Vergne, M.M. et al. Chaotic Orbits in Galactic Satellites. Celestial Mechanics and Dynamical Astronomy 85, 247–267 (2003). https://doi.org/10.1023/A:1022509428034
Issue Date:
DOI: https://doi.org/10.1023/A:1022509428034