Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-23T19:23:26.683Z Has data issue: false hasContentIssue false
  • English
  • Français

An Iterative Method of General Planetary Theory

Published online by Cambridge University Press:  14 August 2015

V. A. Brumberg
V. A. Brumberg*
Affiliation:
Institute of Theoretical Astronomy, Leningrad, U.S.S.R.

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This paper deals with an iterative version of the general planetary theory. Just as in Airy's Lunar method the series in powers of planetary masses are replaced here by the iterations to achieve improved approximations for the coefficients of planetary inequalities. The right-hand members of the equations of motion are calculated in closed formulas, and no expansion in powers of small corrections to the planetary coordinates is needed. For the N-planet case this method requires the performance of the analytical operations on a computer with power series of 4N polynomial variables, the coefficients being the exponential series of N-1 angular arguments. To obtain numerical series of planetary motion one has to solve the secular system using Birkhoff's normalization or the Taylor series in powers of time. A slight modification of the method in the resonant case makes it valid for the treatment of the main problem of the Galilean satellites of Jupiter.

Type
Research Article
Information
Symposium - International Astronomical Union , Volume 62: The Stability of the Solar System , 1974 , pp. 139 - 155
Copyright
Copyright © Reidel 1974 

References

Broucke, R.: 1969, Celes. Mech. 1, 110.Google Scholar
Broucke, R. and Garthwaite, K.: 1969, Celes. Mech. 1, 271.CrossRefGoogle Scholar
Brumberg, V. A.: 1970, in Giacaglia, G. E. O. (ed.), Periodic Orbits, Stability and Resonances , D. Reidel, Dordrecht, The Netherlands, p. 410.CrossRefGoogle Scholar
Brumberg, V. A. and Chapront, J.: 1974, Celes. Mech. 8, 335.CrossRefGoogle Scholar
Brumberg, V. A. and Egorova, A. V.: 1971, Observations of Artificial Celestial Bodies 62, 42 (in Russian); erratum: Bull. Inst. Theor. Astron. 13 (1972) 336 (in Russian).Google Scholar
Cherniack, J. R.: 1973, Celes. Mech. 7, 107.CrossRefGoogle Scholar
Ferraz-Mello, S.: 1966, Bull. Astron. (3) 1, 287.Google Scholar
Jefferys, W. H.: 1970, Celes. Mech. 2, 474.Google Scholar
Jefferys, W. H.: 1972, Celes. Mech. 6, 117.CrossRefGoogle Scholar
Kovalevsky, J.: 1971, Calculs de mécanique céleste sur ordinateur , São José dos Campos, Brazil.Google Scholar
Krasinsky, G. A. and Pius, L. Yu.: 1971, Observations of Artificial Celestial Bodies 62, 93 (in Russian).Google Scholar
Marsden, B. G.: 1966, The Motions of the Galilean Satellites of Jupiter, Dissertation, Yale University.Google Scholar
Rom, A.: 1970, Celes. Mech. 1, 301.CrossRefGoogle Scholar
Rom, A.: 1971, Celes. Mech. 3, 331.Google Scholar
Sagnier, J. L.: 1972, Séminaires du Bureau des Longitudes , 1 lème Année, No. 9.Google Scholar
Seidelmann, P. K.: 1970, Celes. Mech. 2, 134.CrossRefGoogle Scholar