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\centerline{\bf An analytical theory for a low-altitude lunar polar
orbiter} 

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\centerline {Zoran Kne\v zevi\'c}
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\centerline {\it Astronomical Observatory, Belgrade}
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\centerline{and}
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\centerline {Andrea Milani}
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\centerline {\it Department of Mathematics, Pisa}
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We have developed a fully analytical perturbation theory to compute
proper elements for low-altitude (100 km) lunar satellites 
orbiting the Moon on nearly polar orbits. We used a mixed
Lagrangian-Hamiltonian formalism, and separately accounted for the
very short periodic perturbations (associated with the revolution of
the satellite around the Moon), the medium periodic perturbations
(associated with the rotation of the Moon), and the long periodic
ones. Two contemporary models of the lunar gravity field were used to
show that the difference in location of even the "frozen orbit"
changes by a significant amount when the solution is pushed to
comprise the high degree and order coefficients in the two models.

The algorithm based on the theory proved to be very efficient in
computing and propagating the satellite orbits, because it explicitly
computes the orbital elements for any time. The reliability of
the software has been tested internally and externally, against the
numerical integrations. A total of 52 different options of element
transformations and outputs are implemented and available by making
appropriate choices in a single and simple option file.

The accuracy of the achieved results is inferred using again the
numerical integration. We have shown that the need for a second order
(in terms of the perturbation size) solution arises in case the
accuracy requirements are strict.

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