Advertisement

Astrophysics and Space Science

, Volume 266, Issue 4, pp 557–567 | Cite as

Simple Simulation of Solar System

  • Jan Vrbik
Article
  • 52 Downloads

Abstract

The article presents a simple derivation of a set of approximate formulas for the rate of change of orbital elements of a planet, perturbed by a time-averaged gravitational force due to the remaining planets of the solar system. The corresponding set of differential equations for long-time development of planetary orbits is then numerically integrated and the results are shown to be consistent with Milankovitch theory of climatic cycles.

Keywords

Solar System Orbital Element Planetary Orbit Climatic Cycle Simple Simulation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Berger, A., Loutre, M.F. and Laskar, J.: 1992, Stability of the Astronomical Frequencies Over the Earth's History for Paleoclimate Studies, Science 255, 560-565.ADSGoogle Scholar
  2. 2.
    Brumberg, V.A.: 1967, A numerical development of a generalized planetary theory, Soviet Astron. 11,No. 1, 156-165.ADSGoogle Scholar
  3. 3.
    Milankovitch, M.: 1920, Théorie Mathématique des Phénomènes Thermiques Produits par la Radiation Solaire, Gauthier-Villars, Paris.Google Scholar
  4. 4.
    Green, R.M.: 1985, Spherical Astronomy, Cambridge University Press, Cambridge.Google Scholar
  5. 5.
    Vrbik, J.: 1995, Perturbed Kepler problem in quaternionic form, J. Phys. A 28, 6245-6252.zbMATHMathSciNetCrossRefADSGoogle Scholar
  6. 6.
    Vrbik, J.: 1997, Oblateness perturbations to fourth order, Mon. Not. R. Astron. Soc. 291, 65-70.ADSGoogle Scholar
  7. 7.
    Wolfram, S.: 1996, The Mathematica Book, Cambridge University Press, Cambridge.Google Scholar

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • Jan Vrbik
    • 1
  1. 1.Department of MathematicsBrock UniversitySt. CatharinesCanada

Personalised recommendations