Prediction of satellite motions in the Earth's gravitational field with axial symmetry by the KS regularized theory

In this paper, economical and stable recurrence formulas for the earth's zonal potential and its gradient for the KS regularized theory will be established for any number N of the zonal harmonic coefficient. A general recursive computational algorithm based on these formulas is also established for the initial value problem of the KS theory for the prediction of artificial satellites in the earth's gravitational field with axial symmetry. Applications of the algorithm for the problem of the final state prediction are illustrated by numerical examples of three test orbits each for two geopotential models corresponding to N = 2 and N = 36. A final state of any desired accuracy is obtained for each case study, a result which shows the flexibility of the algorithm. (Author)