Statistics – Computation
Scientific paper
Mar 1985
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985a%26a...144..133l&link_type=abstract
Astronomy and Astrophysics (ISSN 0004-6361), vol. 144, no. 1, March 1985, p. 133-146.
Statistics
Computation
43
Celestial Mechanics, Computational Astrophysics, Orbital Mechanics, Planetary Mass, Solar Orbits, Eccentric Orbits, Euler-Lagrange Equation, Secular Variations, Solar System, Planets, Techniques, Procedure, Computer Methods, Period, Parameters, Orbits, Eccentricity, Inclination, Description, Celestial Mechanics, Mass, Astronomy, Theoretical Studies
Scientific paper
The author develops a formalism and an algorithm which allow to compute with great relative precision (10-6) the autonomous system which regulates the very long period (>50,000 yr) variations of the 8 planets' orbital elements, up to degree 5 in eccentricity-inclination and up to 2nd order with respect to the masses. In particular, the author studies the convergence of the series giving the coefficients of this system. The computations are optimized thanks to a particular organization of the series which enables to establish beforehand a unique address table for all the products to be made in the computations of the second order. The author also presents here the first results he obtained by the application of the algorithm in the computation of a Lagrange solution up to the second order with respect to the masses.
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