Improvement of the theories of Jupiter and Saturn by harmonic analysis

Details Improvement of the theories of Jupiter and Saturn by harmonic analysis Improvement of the theories of Jupiter and Saturn by harmonic analysis

Oct 1982

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982a%26a...114..125s&link_type=abstract

Astronomy and Astrophysics, vol. 114, no. 1, Oct. 1982, p. 125-130. In French.

Astronomy and Astrophysics

Astrophysics

14

Harmonic Analysis, Jupiter (Planet), Planetology, Saturn (Planet), Convergence, Euler-Lagrange Equation, Integral Equations, Iterative Solution, Planetary Mass

Scientific paper

A method is described for the computation of the still-missing terms in the third-order theory of Jupiter and Saturn, where perturbations are found by harmonic analysis using an iterative technique. After ten iterations, the convergence reaches an internal precision better than 0.001 arcsec over 1000 years in the case of a computation for seven time values of the second members of the Lagrange equations under a closed form, which is expanded by harmonic analysis and integrated before iteration. The method is economical as well as precise, and allows the determination of perturbations up to the seventh order with respect to the masses.

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