2ND-ORDER SOLUTION FOR THE ZONAL PROBLEM OF SATELLITE THEORY

The analytical solution for the perturbations of an artificial satelli te due to the zonal part of the geopotential is presented. The Hamilto nian is fully normalized up to the second order by a single averaging transformation and the generating function is given explicitly. The fo rmulas allow an arbitrarily high degree of geopotential harmonics to b e included. The transformation from mean to osculating variables or vi ce versa is performed by means of a numerical method proposed by the a uthor 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.