A semi-analytic theory for satellite orbit prediction

A semianalytical theory for satellite orbit prediction was developed. The conservative perturbation affecting the satellite is handled analytically using the Lie-Hori approach, and a numerical version of the method of averaging is used to average the nonconservative perturbation over one revolution of the satellite. The generalized Lie-Hori method and the averaging method are compared. In the comparison the equivalence of the two methods to the second order in the small parameter is shown. However, the approach used can be extended to demonstrate the equivalence for higher orders. To illustrate the equivalance, Duffing's equation, the van der Pol equation, the oscillator with quadratic damping problem, and the oscillator with linear damping problem are solved using each method. The equivalence is used to develop a semi-analytical theory for satellite orbit prediction. The mean element rates are numerically integrated, and the osculating elements are recovered by transforming to the osculating element space. The semianalytical method developed is compared with numerical integration.