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Numerical Experiments on the Motion of the Outer Planets

Published online by Cambridge University Press:  07 August 2017

Gerald D. Quinlan*
Affiliation:
Canadian Institute for Theoretical Astrophysics, University of Toronto

Abstract

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We have integrated the motion of the four Jovian planets on Myr timescales in fictitious solar systems in which the orbits differ from those of the real solar system. A change of ≲1% in the major axis of any one of the planets from its real value can lead to chaotic motion with a Lyapunov exponent larger than 10-5 yr−1. A survey of fifty solar systems with initial conditions chosen at random from a reasonable probability distribution shows the majority of them to be chaotic.

Type
Part I - The Planetary System
Copyright
Copyright © Kluwer 1992 

References

Applegate, J. H., Douglas, M. R., Gürsel, Y., Sussman, G. J., and Wisdom, J. 1986, “The outer solar system for 200 million years”, Astron. J. 92, 176194.CrossRefGoogle Scholar
Benettin, G., Galgani, L., and Strelcyn, J.-M., 1976, “Kolmogorov entropy and numerical experiments”, Phys. Rev. A14, 23382345.Google Scholar
Laskar, J. 1989, “A numerical experiment on the chaotic behaviour of the solar system”, Nature 338, 237238.Google Scholar
Laskar, J. 1990, “The chaotic motion of the solar system: a numerical estimate of the size of the chaotic zones”, Icarus 88, 266291.Google Scholar
Laskar, J., Quinn, T., and Tremaine, S. 1991, “Confirmation of resonant structure”, submitted to Icarus. CrossRefGoogle Scholar
Lissauer, J. 1987, “Timescales for planetary accretion and the structure of the protoplanetary disk”, Icarus 69, 249265.Google Scholar
Milani, A., Nobili, A. M., and Carpino, M. 1989, “Dynamics of Pluto”, Icarus 82, 200217.Google Scholar
Nobili, A. M., Milani, A., and Carpino, M. 1989, “Fundamental frequencies and small divisors in the orbits of the outer planets”, Astron. Astrophys. 210, 313336.Google Scholar
Sussman, G. J. and Wisdom, J. 1988, “Numerical evidence that the motion of Pluto is chaotic”, Science 241, 433437.Google Scholar
Wisdom, J. 1987, “Chaotic dynamics in the solar system”, Icarus 72, 241275.Google Scholar