Analytical theory of a lunar artificial satellite with third body perturbations

  • Bernard De Saedeleer
Conference 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 n), the oblateness J 2 of the Moon, the triaxiality C 22 of the Moon (C 22J 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.


Lunar artificial satellite Third body Lie Hamiltonian C22 Earth 


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Copyright information

© Springer Science+Business Media B.V. 2006

Authors and Affiliations

  • Bernard De Saedeleer
    • 1
  1. 1.Département de MathématiqueUniversity of NamurNamurBelgium

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