Astronomy and Astrophysics – Astronomy
Scientific paper
May 2006
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006cemda..95..407d&link_type=abstract
Celestial Mechanics and Dynamical Astronomy, Volume 95, Issue 1-4, pp. 407-423
Astronomy and Astrophysics
Astronomy
4
Scientific paper
We present here the first numerical results of our analytical theory of an artificial satellite of the Moon. The perturbation method used is the Lie Transform for averaging the Hamiltonian of the problem, in canonical variables: short-period terms (linked to l, the mean anomaly) are eliminated first. We achieved a quite complete averaged model with the main four perturbations, which are: the synchronous rotation of the Moon (rate [InlineMediaObject not available: see fulltext.]), the oblateness J 2 of the Moon, the triaxiality C 22 of the Moon ( C_{22} ≈ J_2/10) and the major third body effect of the Earth (ELP2000). The solution is developed in powers of small factors linked to these perturbations up to second-order; the initial perturbations being sorted ([InlineMediaObject not available: see fulltext.] is first-order while the others are second-order). The results are obtained in a closed form, without any series developments in eccentricity nor inclination, so the solution apply for a wide range of values. Numerical integrations are performed in order to validate our analytical theory. The effect of each perturbation is presented progressively and separately as far as possible, in order to achieve a better understanding of the underlying mechanisms. We also highlight the important fact that it is necessary to adapt the initial conditions from averaged to osculating values in order to validate our averaged model dedicated to mission analysis purposes.
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