Construction of a theory of the outer planets through an iterative method

Details Construction of a theory of the outer planets through an iterative method Construction of a theory of the outer planets through an iterative method

Sep 1981

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981a%26a...101..342b&link_type=abstract

Astronomy and Astrophysics, vol. 101, no. 3, Sept. 1981, p. 342-349. In French.

Astronomy and Astrophysics

Astrophysics

13

Celestial Mechanics, Gas Giant Planets, Iterative Solution, Planetology, Numerical Integration, Planetary Mass, Precision, Space Exploration, Planets, Jovian Planets, Theoretical Studies, Longitude, Jupiter, Uranus, Techniques, Mass, Saturn, Neptune, Comparisons, Celestial Mechanics, Mathematical Models, Data

Scientific paper

Together with a solution working order after order with respect to the masses, we have undertaken, at the Bureau des Longitudes, the construction of a theory for the outer planets Jupiter, Saturn, Uranus, and Neptune through an iterative method.
This method makes it possible to reach a high order with respect to the masses, particularly for Jupiter and Saturn (6Sh order), which is necessary, as shown in Figs. 1 and 2. The variables we use are α, λ, k, h, q, p. The solutions are analytical functions of the mean longitudes of the eight planets and are numerical with respect to other integration constants.
We develop the formulae we need and illustrate the difficulties of convergence appearing in the iterations for the variables α and λ of Uranus and Neptune. For the other variables of Uranus and Neptune and for the 6 variables of Jupiter and Saturn, the convergence works at the precision of 0".001 for the short period arguments (about some 10 yr) and around 0".01 or 0".1 for the long period arguments (1000 yr and over).
The precision as a whole for the solutions is shown (Figs. 36) by comparisons to numerical integrations over 1000 yr. Except for very long period terms in the longitudes of Uranus and Neptune, the residuals are about 0".3 in the mean longitudes and 0".1 in the other variables.

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