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{\Large Numerical mean elements for asteroid orbits}
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Anne Lemaitre \\
Facult\'es Universitaires Notre-Dame de la Paix \\
D\'epartement de Math\'ematique \\
Rempart de la Vierge, 8 B 5000 Namur Belgium \\
T\'el.: (32-81) 72 49 08  Fax : (32-81) 72 49 14  \\
E-mail: alemaitr@math.fundp.ac.be

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The calculation of proper elements for asteroid orbits refers presently to two
different computations; a powerful analytical theory, developed by Milani and
Kne\v zevi\'c (1990, 1992, 1994) and  a semi-numerical approach due to
Lemaitre and Morbidelli (1994). The analytical theory, based on series
expansions in eccentricity and inclination, is particularly suitable for low
inclination and low eccentricity orbits, while the semi-numerical one refers
to orbits with either large eccentricities or large inclinations. The
superposition region has been tested and is situated about $17^\circ$ in
inclination.

Up to now even the semi-numerical approach has used the \underline{analytical}
mean  elements as initial conditions for the computation of the proper
elements; those mean elemnts, also obtained by series expansions by Milani and
Kne\v zevi\'c,  could
be sources of errors in the calculation of the proper ones for highly inclined
or eccentric orbits. The purpose of this paper is to compare, for the numbered
asteroids, the analytical mean elements with a complete set of numerical mean
ones. For significative differences in the results, proper elements are
then  recalculated with the numerical initial conditions and compared to their
previous values. Consequences on the presence of new high inclination  families
of asteroids are analyzed.
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