Astronomy and Astrophysics – Astrophysics
Scientific paper
May 1990
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990a%26a...231..561b&link_type=abstract
Astronomy and Astrophysics (ISSN 0004-6361), vol. 231, no. 2, May 1990, p. 561-570. In French.
Astronomy and Astrophysics
Astrophysics
10
Celestial Mechanics, Iterative Solution, Planetary Evolution, Solar System, Numerical Integration, Periodic Variations, Planetary Mass
Scientific paper
An iterative method is developed in the construction of general planetary theories. Due to the speed of computers, the study of long-period variations of planetary orbits can now be done by numerical integration over multimillion-year time spans. The iterative method enables the development of higher-order perturbations with respect to the planetary masses. The advantages and disadvantages presented by both numerical integration methods and by analytical methods are described. The equations of motion of the system of eight planets from Mercury to Neptune are considered along with the relevant forces. The iterative method is then developed from the solution of the Lagrange-Laplace system of equations. With the help of each preceding iteration the complete 48 second terms of the Lagrange equations are then calculated, with the only limitations on precision appearing in the truncation of the Fourier series. Finally, results are presented on the application of the method to the Jupiter-Saturn system.
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