Analytical theory of a lunar artificial satellite with third body perturbations
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 n), 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 (n 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.
KeywordsLunar artificial satellite Third body Lie Hamiltonian C22 Earth
Unable to display preview. Download preview PDF.
- Chapront-Touzé, M., Chapront, J.: Lunar Tables and Programs 4000 BC to AD 8000. Willmann-Bell. (1991)Google Scholar
- De Saedeleer, B., Henrard, J.: Orbit of a lunar artificial satellite: analytical theory of perturbations. IAU Colloq. 196: Transits of Venus: New Views of the Solar System and Galaxy. pp. 254–262 (2005)Google Scholar
- De Saedeleer, B.: Analytical theory of an artificial satellite of the Moon. In: Belbruno, E., Gurfil, P. (eds.) Astrodynamics, Space Missions, and Chaos, of the Annals of the New York Academy of Sciences. Proceedings of the Conference New Trends in Astrodynamics and Applications, January 20–22, 2003, Vol. 1017, pp. 434–449. Washington (2004)Google Scholar
- Henrard, J.: The algorithm of the inverse for Lie transform. In: Szebehely, V., Tapley, B. (eds.) ASSL: Recent Advances in Dynamical Astronomy, Vol. 39, pp. 248–257. Dordrecht (1973)Google Scholar
- Konopliv, A. S., Sjogren, W.L., Wimberly, R.N., Cook, R.A., Vijayaraghavan, A.: A high resolution lunar gravity field and predicted orbit behavior. In Advances in the Astronautical Sciences, Astrodynamics (AAS/AIAA Astrodynamics Specialist Conference, Pap. # AAS 93–622, Victoria, B.C.), Vol. 85, pp. 1275–1295 (1993)Google Scholar
- Milani, A., Knežević, Z.: Selenocentric proper elements: A tool for lunar satellite mission analysis. Final Report of a study conducted for ESA, ESTEC, Noordwijk (1995)Google Scholar
- Press, W. H., Teukolsky, S. A., Vetterling, W. T., Flannery, B. P.: Numerical Recipes in Fortran 77-The Art of Scientific Computing. Cambridge University Press, Cambridge (1986)Google Scholar