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Note About a New Evaluation of the Direct Perturbations of the Planets on the Moon’s Motion

Published online by Cambridge University Press:  12 April 2016

D. Standaert
D. Standaert*
Affiliation:
Dept. of Mathematics, Facultés Universitaires de Namur B-5000 Namur, Belgium

Extract

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The aim of this paper is to present the principal features of a new evaluation of the direct perturbations of the planets on the Moon’s motion. Using the method already published in Celestial Mechanics (Standaert, 1980), we compute “a first-order theory” aiming at an accuracy of the order of the meter for all periodic terms of period less than 3 500 years.

From an external point of view, we mean by that:

  1. a) keplerian orbits for the planets,

  2. b) the ELP-2000 solution of the Main Problem proposed by Mrs. Chapront (Chapront-Touzë, 1980),

  3. c) the first-order derivatives with respect to the constants of motion of the SALE theory of Henrard (Henrard, 1979).

On the other hand, from an internal point of view, the computations include:

  1. d) the development in Legendre polynomials not only to the first-order in (a/a'), but also the following ones (up to the sixth-order for Venus, for example),

  2. e) the contributions of the second-order in the Lie triangle,

  3. f) second-order contributions coming from the corrections of the mean motions due to the planetary action.

Type
Part III
Information
International Astronomical Union Colloquium , Volume 63: High-Precision Earth Rotation and Earth-Moon Dynamics , May 1981 , pp. 265 - 266
Copyright
Copyright © Reidel 1982

References

Brown, E.W. 1891, On the Determination of a Certain Class of Inequalities in the Moon’s Motion, Monthly Notices 52.Google Scholar
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Chapront-Touzé, M. 1980, La Solution ELF du Problème Central de la Lune, Astronomy and Astrophysics 83, p. 86.Google Scholar
Henrard, J. 1978, SALE (Semi-Analytioal-Lunar-Ephemeric) Tables, Internal Report, Dept. of Mathematics, F.N.D.P., Namur.Google Scholar
Henrard, J. 1979, A new solution to the Main Problem of Lunar Theory, Celestial Mechanics 19, pp. 337–355.Google Scholar
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