Accurate determination of highly eccentric orbits in earth's gravtational field with axial symmetry

In this paper, an algorithm is constructed for the determination of the perturbed motion, in both, the rectangular and the orbital elements of highly eccentric orbits in Earth's gravitational field with axial symmetry whatever the number N of the zonal harmonic coefficients may be. An application of the algorithm for the Explorer 28 satellite (e > 0.94) is given for two geopotential models corresponding to N = 2 and N = 36. In both examples extremely accurate predictions during the satellite life time are obtained.