A numerical experiment on the chaotic behaviour of the Solar System

  title={A numerical experiment on the chaotic behaviour of the Solar System},
  author={Jacques Laskar},
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
Due to the chaotic nature of the solar system, the question of its dynamic long-term stability can only be answered in a statistical sense, for instance, based on numerical ensemble integrations ofExpand
On the Dynamical Stability of the Solar System
A long-term numerical integration of the classical Newtonian approximation to the planetary orbital motions of the full solar system (Sun + eight planets), spanning 20 Gyr, was performed. The resultsExpand
The chaotic motion of the solar system: A numerical estimate of the size of the chaotic zones
Abstract In a previous paper (J. Laskar, Nature 338, (237–238)), the chaotic nature of the Solar System excluding Pluto was established by the numerical computation of the maximum Lyapunov exponentExpand
An example of stable chaos in the Solar System
MANY planets have been shown to have chaotic instabilities in their orbital motions, but the long-term significance of this is not fully understood1. The eccentricity of Mercury, for example, changesExpand
Confirmation of resonant structure in the solar system
Abstract Using a semianalytical secular theory, Laskar (1989, Nature 338, 237–238) computed the orbits of the planets over 200 million years and found that their motion, and especially the motion ofExpand
Dynamical Evolution of Multi-Resonant Systems: the Case of GJ876
The GJ876 system was among the earliest multi-planetary detections outside of the Solar System, and has long been known to harbor a resonant pair of giant planets. Subsequent characterization of theExpand
Rapid Dynamical Chaos In An Exoplanetary System
We report on the long-term dynamical evolution of the two-planet Kepler-36 system, which consists of a super-Earth and a sub-Neptune in a tightly packed orbital configuration. The orbits of theExpand
Chaotic diffusion in the Solar System
Abstract The discovery of the chaotic behavior of the planetary orbits in the Solar System [Laskar, J., 1989. Nature 338, 237–238; Laskar, J., 1990. Icarus 88, 266–291] was obtained using numericalExpand
Addressing the statistical mechanics of planet orbits in the solar system
The chaotic nature of planet dynamics in the solar system suggests the relevance of a statistical approach to planetary orbits. In such a statistical description, the time-dependent position andExpand
Dynamic stability of the Solar System: Statistically inconclusive results from ensemble integrations
Due to the chaotic nature of the Solar System, the question of its long-term stability can only be answered in a statistical sense, for instance, based on numerical ensemble integrations of nearbyExpand


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
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