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Numerical efficiency of the elliptic function expansions of the first-order intermediary for general planetary theory

Published online by Cambridge University Press:  25 May 2016

Victor A. Brumberg  and
Sergei A. Klioner
Victor A. Brumberg
Affiliation:
Institute of Applied Astronomy, 197042, St. Petersburg, Russia
Sergei A. Klioner
Affiliation:
Institute of Applied Astronomy, 197042, St. Petersburg, Russia

Abstract

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We compare numerical efficiency of the two kinds of series for the first-order intermediate orbit for general planetary theory: (1) the classical expansion involving mean longitudes of the planets; (2) an expansion resulting from the theory of elliptic functions. We conclude that mutual perturbations of close couples of planets (the ratio of major semi-axes ∼ 1) can be represented in more compact form with the aid of the second kind of series.

Type
Part II - Planets and Moon: Theory and Ephemerides
Information
Symposium - International Astronomical Union , Volume 172: Dynamics, Ephemerides and Astrometry of the Solar System , 1996 , pp. 101 - 104
Copyright
Copyright © Kluwer 1996 

References

Brumberg, V.A. (1994) General Planetary Theory in Elliptic Functions, Celes. Mech., 59, 1 CrossRefGoogle Scholar
Brumberg, V.A. (1996) Theory Compression with Elliptic Functions. In: Ferraz-Mello, S., Morando, B., Arlot, J. E. (eds.), Dynamics, ephemerides and astrometry of the solar system, Kluwer, Dordrecht Google Scholar