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PERTURBATIONS OF A HIGHLY ECCENTRIC SATELLITE ORBITS
DUE TO THE GRAVITY POTENTIAL OF A CENTRAL PLANET

Edwin Wnuk
Astronomical Observatory of the A.Mickiewicz University
ul. Sloneczna 36, 60-286 Poznan, Poland
e-mail: wnuk@phys.amu.edu.pl

ABSTRACT: The precise calculations of a close natural and artificial 
planet's satellite motion must take into account spherical coefficients 
of the central planet gravity potential up to a high degree and order. 
Some difficulties occur when an analytical theory of a planet's satellite 
motion is used in calculations of  precise positions of a satellite on 
a highly eccentric orbit, like for example the Mars 96 mission orbit. 
The source of these difficulties is the calculation of the eccentricity 
function (Hansen's coefficients), values of which are calculated in order 
to obtain perturbations due to the non-spherical gravity field of a cen-
tral planet. The Kaula's formula for the eccentricity function  is not 
numerically stable when values of this function are calculated for high 
values of indices l, p, q  and for a high value of the eccentricity e.
     The paper presents the efficient method for calculation of the 
Hansen's coefficients, which is numerically stable for high eccentricities: 
e ~ 0.6 - 0.8 and for high indices l, p, q corresponding to maximum orders 
and degrees of contemporary gravity models (e.g. 70x70 for the Earth 
and 50x50 for the Mars). The method is based on some modification 
of the classical formula of the Hansen's coefficients. The summation 
of an appropriate number of terms in this formula enables the determination 
of the eccentricity function with a requested precision.