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On Construction of a Long-Term Moon’s Theory

Published online by Cambridge University Press:  12 April 2016

T.V. Ivanova
T.V. Ivanova*
Affiliation:
Institute of Applied Astronomy of the Russian Academy of Sciences, St.Petersburg, E-mail:itv@ita.spb.su

Extract

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An analytical long-term theory of the motion of the Moon is constructed within the framework of the general planetary theory (Brumberg, 1995). A method, different from the one of (Ivanova, 1997) designated below as (*), for the determination of the perturbations depending on the eccentricities and inclinations of lunar and planetary orbits is used which allows to obtain the solution of the problem in the purely trigonometric form up to any order with respect to the small parameters.

The aim of this paper is to construct the long-term Lunar theory in the form consistent with the general planetary theory (Brumberg, 1995). For this purpose the Moon is considered as an additional planet in the field of eight major planets (Pluto being excluded). In the result the coordinates of the Moon may be represented by means of the power series in the evolutionary eccentric and oblique variables with trigonometric coefficients in mean longitudes of the Moon and the planets. The long-period perturbations are determined by solving a secular system in Laplace-type variables describing the secular motions of the lunar perigee and node and taking into account the secular planetary inequalities.

Type
Extended Abstracts
Information
International Astronomical Union Colloquium , Volume 172: Impact of Modern Dynamics in Astronomy , 1999 , pp. 415 - 416
Copyright
Copyright © Kluwer 1999

References

Brumberg, V.A.: 1995, Analytical Techniques of Celestial Mechanics, Springer, Heidelberg.Google Scholar
Ivanova, T.V.: 1996, “PSP: A New Poisson Series Processor”, in: Dynamics, Ephemerides and Astrometry of the Solar System (eds. Ferraz-Mello, S., Morando, B. and Arlot, J.-E.), 283, Kluwer.Google Scholar
Ivanova, T.V.: 1997, “A Trigonometric Solution of the Secular Lunar System Intended for Long-Term Theory of the Earth’s Rotation”, in: Journees 1997 “Systemes de Reference Spatio-Temporels” (eds. Vondrak, J. and Capitaine, N.), 99, Prague.Google Scholar