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Marginal stability and chaos in the solar system

Published online by Cambridge University Press:  25 May 2016

Jacques Laskar*
Affiliation:
CNRS–Astronomie et Systèmes Dynamiques, Bureau des Longitudes, 3, rue Mazarine, 75006 Paris

Extract

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The motion of the planets is one of the best modelized problems in physics, and its study can be practically reduced to the study of the behavior of the solutions of the well known gravitational equations, neglecting all dissipation, and treating the planets as mass points. In fact, the mathematical complexity of this problem, despites its apparent simplicity is daunting and has been a challenge for mathematicians and astronomers since its formulation three centuries ago.

Type
Part II - Planets and Moon: Theory and Ephemerides
Copyright
Copyright © Kluwer 1996 

References

Applegate, J.H., Douglas, M.R., Gursel, Y., Sussman, G.J. and Wisdom, J.: 1986, ‘The solar system for 200 million years,’ Astron. J. 92, 176194 CrossRefGoogle Scholar
Bretagnon, P.: 1974, Termes à longue périodes dans le système solaire, Astron. Astrophys 30 341362 Google Scholar
Brumberg, V.A., Chapront, J.: 1973, Construction of a general planetary theory of the first order, Cel. Mech. 8 335355 CrossRefGoogle Scholar
Carpino, M., Milani, A. and Nobili, A.M.: 1987, Long-term numerical integrations and synthetic theories for the motion of the outer planets, Astron. Astrophys 181 182194 Google Scholar
Cohen, C.J., Hubbard, E.C., Oesterwinter, C.: 1973, Astron. Papers Am. Ephemeris XXII 1.Google Scholar
Duriez, L.: 1979, ‘Approche d'une théorie générale planétaire en variable elliptiques héliocentriques, thèse Lille Google Scholar
Gladman, B., Duncan, M.: 1990, On the fates of minor bodies in the outer solar system Astron. J., 100(5).CrossRefGoogle Scholar
Holman, M.J., Wisdom, J.: 1993, Dynamical stability in the outer solar system and the delivery of short period comets Astron. J., 105(5).CrossRefGoogle Scholar
Kinoshita, H., Nakai, H.: 1984, Motions of the perihelion of Neptune and Pluto, Cel. Mech. 34 203 CrossRefGoogle Scholar
Laskar, J.: 1984, , Google Scholar
Laskar, J.: 1986, Secular terms of classical planetary theories using the results of general theory, Astron. Astrophys. 157 5970 Google Scholar
Laskar, J.: 1989, A numerical experiment on the chaotic behaviour of the Solar System Nature, 338, 237238 CrossRefGoogle Scholar
Laskar, J.: 1990, The chaotic motion of the solar system. A numerical estimate of the size of the chaotic zones, Icarus, 88, 266291 CrossRefGoogle Scholar
Laskar, J.: 1992a, A few points on the stability of the solar system, in Symposium IAU 152, Ferraz-Mello, S. ed., 116, Kluwer, Dordrecht Google Scholar
Laskar, J.: 1992b, La stabilité du Système Solaire, in Chaos et Déteminisme, Dahan, A. et al., eds., Seuil, Paris Google Scholar
Laskar, J.: 1993, La Lune et l'origine de l'homme, Pour La Science, 186, avril 1993 .Google Scholar
Laskar, J.: 1994, Large scale chaos in the solar system, Astron. Astrophys. 287 L9L12 Google Scholar
Laskar, J.: 1995, Large scale chaos and Marginal stability of the solar system, XIème Colloque ICMP, Paris july, 1994, International Press, p. 75120 Google Scholar
Laskar, J., Quinn, T., Tremaine, S.: 1992a, Confirmation of Resonant Structure in the Solar System, Icarus, 95, 148152 CrossRefGoogle Scholar
Laskar, J. Robutel, P.: 1993, The chaotic obliquity of the planets, Nature, 361, 608612 CrossRefGoogle Scholar
Laskar, J., Joutel, F., Robutel, P.: 1993, Stabilization of the Earth's obliquity by the Moon, Nature, 361, 615617 CrossRefGoogle Scholar
Levison, H.F., Duncan, M.J.: 1993, The gravitational sculpting of the Kuiper belt, Astrophys. J. Lett., 406, L35L38 CrossRefGoogle Scholar
Newhall, X. X., Standish, E. M., Williams, J. G.: 1983, DE102: a numerically integrated ephemeris of the Moon and planets spanning forty-four centuries, Astron. Astrophys. 125 150167 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
Quinn, T.R., Tremaine, S., Duncan, M.: 1991, ‘A three million year integration of the Earth's orbit,’ Astron. J. 101, 22872305 CrossRefGoogle Scholar
Sussman, G.J., and Wisdom, J.: 1988, ‘Numerical evidence that the motion of Pluto is chaotic.’ Science 241, 433437 CrossRefGoogle ScholarPubMed
Sussman, G.J., and Wisdom, J.: 1992, ‘Chaotic evolution of the solar system’, Science 257, 5662 CrossRefGoogle ScholarPubMed