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The role of chaotic resonances in the Solar System

Nature volume 410, pages 773–779 (2001)Cite this article

Abstract

Our understanding of the Solar System has been revolutionized over the past decade by the finding that the orbits of the planets are inherently chaotic. In extreme cases, chaotic motions can change the relative positions of the planets around stars, and even eject a planet from a system. Moreover, the spin axis of a planet—Earth's spin axis regulates our seasons—may evolve chaotically, with adverse effects on the climates of otherwise biologically interesting planets. Some of the recently discovered extrasolar planetary systems contain multiple planets, and it is likely that some of these are chaotic as well.

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Figure 1: A rigid pendulum, with angle θ measured from the vertical.
Figure 2: The motion of a rigid pendulum traces closed curves on the phase diagram, showing the angle of pendulum, θ, versus its angular momentum, p = ml θ̇.
Figure 6: The location of asteroids in the outer asteroid belt in the (eccentricity, semimajor axis) plane.
Figure 3: The histogram of asteroids as a function of semimajor axis a.
Figure 4: The orbital eccentricity of an object placed in the 3:1 resonance (at 2.5 AU) plotted as a function of time.
Figure 5: The distance between two initially nearly identical initial conditions for two interacting nonlinear oscillators.

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Acknowledgements

We thank P. Goldreich for helpful conversations. This research was supported by NSERC of Canada and NASA.

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Authors and Affiliations

  1. Canadian Institute for Theoretical Astrophysics, 60 St George Street

    N. Murray

  2. University of Toronto, Toronto, M5S 3H8, Ontario, Canada

    N. Murray

  3. Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, 02138, Massachusetts, USA

    M. Holman

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Correspondence to M. Holman.

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Murray, N., Holman, M. The role of chaotic resonances in the Solar System. Nature 410, 773–779 (2001). https://doi.org/10.1038/35071000

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