Computer assisted expansion of 1/Delta series with Newton iteration

Details Computer assisted expansion of 1/Delta series with Newton iteration Computer assisted expansion of 1/Delta series with Newton iteration

Aug 1976

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976aaas.conft....c&link_type=abstract

American Institute of Aeronautics and Astronautics and American Astronautical Society, Astrodynamics Conference, San Diego, Cali

Astronomy and Astrophysics

Astronomy

Computer Techniques, Fourier Series, Newton Methods, Newton-Raphson Method, Satellite Perturbation, Callisto, Eccentricity, Europa, Ganymede, Io, Orbit Perturbation, Perturbation Theory, Tables (Data)

Scientific paper

The Newton iteration method has been widely applied to the solution of various equations such as Kepler's equation. In this study it is used in planetary and satellite theory as a general procedure for Fourier series inversion. The method is used for the construction of the 1/Delta series either in literal form or in numerical form with small eccentricities and inclinations substituted in advance. This usually results in very compact series. With the Newton iteration procedure and a computerized series manipulation technique, the Fourier series of 1/Delta of the mutual perturbations among most natural satellites can be easily constructed.

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