Orbit of a lunar artificial satellite: Analytical theory of perturbations
(2005) International Astronomical Union. Proceedings — Vol. IAU Colloquium No., n° 196, p. 254-262 (2005)
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- Abstract
- We are currently developing an analytical theory of an artificial satellite of the Moon. It is an interesting problem because the dynamics of a lunar orbiter is quite different from that of an artificial satellite of the Earth, by at least two aspects: the J2 lunar gravity term is only 1/10 of the C22 term and the third body effect of the Earth on the lunar satellite is much larger than the effect of the Moon on a terrestrial satellite. So we have to account at least for these larger perturbations. We use here the method of the Lie Transform as perturbation method. The Hamiltonian of the problem is first averaged over the fast angle, in canonical variables. The solution is developed in powers of the small factors linked to n_M, J2, C22 and to the Earth’s position. The Earth location is determined by the lunar theory ELP2000 (Chapront-Touze & Chapront 1991) from which we take the leading terms. Series developments are made with our home-made Algebraic Manipulator, the MM (standing for “Moon’s series Manipulator”). The results are obtained in a closed form, without any series developments in eccentricity or inclination. So the solution applies for a wide range of values, except for few isolated critical values. We Achieved, among others, second order results for the combined effect of J2 and C22. As a side result, we were able to check the second order generator W2 given by Kozai for the effect of the J2 term on an artificial satellite.
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De Saedeleer, B., & Henrard, J. (2005). Orbit of a lunar artificial satellite: Analytical theory of perturbations. International Astronomical Union. Proceedings, IAU Colloquium No.(196), 254-262. https://doi.org/10.1017/S1743921305001432 (Original work published 2005)