Abstract
With a simple map model, derived within the framework of the planar circular restricted three-body problem (SunuuJupiteruucomet), we study the dynamical evolution of near-parabolic comets under the perturbation of Jupiter. The commonly adopted random walk assumption about the energy evolution of the comets is examined. Numerical results show that for the comets on Jupiter-crossing orbits, due to the large energy changes with Jupiter per passage, the statistical evolution of the cometary energy follows a Lévy random walk, thus statistically the final energy parameter that a comet reaches is linked to the number of passages by a power law K f ∼ n f. The mechanism that generates the Lévy random walk is explained in this model.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Efthymiopoulos, C., Contopoulos, G., Voglis, N. and Dvorak, R.: 1997, 'Stickiness and cantori', J. Phys. A: Math. Gen. 30, 8167uu8186.
Everhart, E.: 1967, 'Intrinsic distributions of cometary perihelia magnitudes', Astron. J. 72, 1002uu1011.
Fernández, J. A. and Gallardo, T.: 1994, 'The transfer of comets from parabolic to short-period orbits: numerical studies', Astron. Astrophys. 281, 911uu922.
Geisel, T., Nierwetberg and Zacherl, A.: 1985, 'Accelerated diffusion in Josephson junctions and related chaotic systems', Phys. Rev. Lett. 54, 616uu619.
Klafter, J., Shlesinger, M. F. and Zumofen, G.: 1996, 'Beyond Brownian motion', Phys. Today February, 33uu39.
Liu, J. and Sun, Y. S.: 1994, 'Chaotic motions of comets in near-parabolic orbits: mapping approaches', Celest. Mech. & Dyn. Astron. 60, 3uu28.
Oort, J. H.: 1950, 'The structure of the cloud of comets surrounding the solar system and a hypothesis concerning its origin', Bull. Astro. Inst. Netherlands 11, 259uu269.
Malyshkin, L. and Tremaine, S.: 1999, 'The Keplerian map for the planar restricted three-body problem as a model of comet evolution', Icarus 142, 341uu353.
Petrosky, T. Y. and Broucke, R.: 1988, 'Area-preserving mappings and deterministic chaos for nearly parabolic motions', Celest. Mech. & Dyn. Astr. 42, 53uu79.
Shlesinger, M. F., West, B. J. and Klafter, J.: 1987, 'Lévy dynamics of enhanced diffusion: Application to turbulence', Phys. Rev. Lett. 58, 1100uu1103.
Yabushita, S.: 1979, 'A statistical study of the evolution of the orbits of long-periodic comets', Mon. Not. R. Astr. Soc. 187, 445uu462.
Zhou, J. L., Sun, Y. S., Zheng, J. Q. and Valtonen, M. J.: 2000, 'The transfer of comets from nearparabolic to short-period orbits: map approach', Astron. Astrophys. 364, 887uu893.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Zhou, JL., Sun, YS. & Zhou, LY. Evidence for Lévy Random Walks in the Evolution of Comets from the Oort Cloud. Celestial Mechanics and Dynamical Astronomy 84, 409–427 (2002). https://doi.org/10.1023/A:1021156112825
Issue Date:
DOI: https://doi.org/10.1023/A:1021156112825