Astronomy and Astrophysics – Astrophysics
Scientific paper
Apr 1977
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977a%26a....56..333l&link_type=abstract
Astronomy and Astrophysics, vol. 56, no. 3, Apr. 1977, p. 333-352.
Astronomy and Astrophysics
Astrophysics
47
Celestial Mechanics, Galilean Satellites, Librational Motion, Orbital Mechanics, Satellite Orbits, Analytic Functions, Computer Programs, Equations Of Motion, Error Analysis, Jupiter (Planet), Orbit Calculation, Position Errors
Scientific paper
Final results are presented for a theory enabling one to calculate the positions of the Galilean satellites and their partial derivatives. Extensive use of algebraic manipulation software on a digital computer is made to generate the final expressions. The theory is, in effect, a revitalization of Sampson's (1921) theory. Algebraic and mathematical errors existing in Sampson's work are removed, some neglected effects due to solar interactions and the 3-7 commensurability are introduced, allowance is made for nonzero amplitude and phase of the free libration, and the final results are expressed as analytic functions of variations in 49 arbitrary constants of integration and physical parameters. The theory is constructed in a manner which readily allows for future revision, and analytic expressions are provided for the partial derivatives with respect to the 49 parameters.
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