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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
Standaert, D. l980, Direct Perturbations of the Planets on the Moon’s Motion, Celestial Mechanics 22, pp. 357–369.Google Scholar
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