Abstract
The analytical solution for the perturbations of an artificial satellite due to the zonal part of the geopotential is presented. The Hamiltonian is fully normalized up to the second order by a single averaging transformation and the generating function is given explicitly. The formulas allow an arbitrarily high degree of geopotential harmonics to be included. The transformation from mean to osculating variables or vice versa is performed by means of a numerical method proposed by the author in a previous paper (Breiter,1997): periodic perturbations are computed by means of a Runge-Kutta method of order 2 instead of being explicitly derived from a generator.
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