A numerical experiment on the chaotic behaviour of the Solar System

@article{Laskar1989ANE,
  title={A numerical experiment on the chaotic behaviour of the Solar System},
  author={Jacques Laskar},
  journal={Nature},
  year={1989},
  volume={338},
  pages={237-238}
}
LAPLACE and Lagrange made an essential contribution to the study of the stability of the Solar System by proving analytically that, to first order in the masses, inclinations and eccentricities of their orbits, the planets move quasiperiodically. Since then, many analytic quasiperiodic solutions have been sought to higher order1–10.1 have recently constructed an extensive analytic system of averaged differential equations containing the secular evolution of the orbits of the eight main planets… Expand
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References

SHOWING 1-10 OF 11 REFERENCES
Long-term changes in the semimajor axes of the outer planets
One of the oldest problems of celestial mechanics is that of the long-term behaviour of the semimajor axes a of the planetary orbits. Analytical theories1,2 predict periodic variations in a, some ofExpand
Asymptotic series for planetary motion in periodic terms in three dimensions
For the ‘planetary case’ of the gravitationaln-body problem in three dimensions, a sequence of Lie series contact transformations is used to construct asymptotic series representations for theExpand
Stability of the solar system and its minor natural and artificial bodies. Proceedings of a NATO Advanced Study Institute, held at Cortina d'Ampezzo, Italy, 6 - 18 August 1984.
I: Dynamics of Natural and Artificial Satellites.- The Tiny Satellites of Jupiter and Saturn and Their Interactions with the Rings.- Motion of a Geo-Centric Synchronous Satellite.- On the BrownExpand
Motions of the perihelions of Neptune and Pluto
Five outer planets are numerically integrated over five million years in the Newtonian frame. The argument of Pluto's perihelion librates about 90 degrees with an amplitude of about 23 degrees. TheExpand
Numerical Evidence That the Motion of Pluto Is Chaotic
TLDR
This integration indicates that the long-term motion of the planet Pluto is chaotic, and nearby trajectories diverge exponentially with an e-folding time of only about 20 million years. Expand
Milankovitch and Climate
1 2 2 . 2 d J. Adem , A· Bergzr , Ph. Gaspar , P. Pest1aux an J.P. van Ypersele 1 Centro de Ciencias de la Atmosfera, UNAM, 04510 ~exico D.F. Universit~ Catholique de Louvain, Institut d 'AstronomieExpand
The Lyapunov Characteristic Exponents and Applications to the Dimension of the Invariant Manifolds and Chaotic Attractors
After a presentation of Lyapunov characteristic exponents (LCE) we recall their basic properties and numerical methods of computation. We review some numerical computations which are concerned withExpand
Lyapunov Characteristic Exponents for smooth dynamical systems and for hamiltonian systems; a method for computing all of them. Part 1: Theory
SommarioDa diversi anni gli esponenti caratteristici di Lyapunov sono divenuti di notevole interesse nello studio dei sistemi dinamici al fine di caratterizzare quantitativamente le proprietà diExpand
...
1
2
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