A SEMI-ANALYTIC THEORY FOR SATELLITE ORBIT PREDICTION (PERTURBATION METHODS, EQUIVALENCE PERTURBATION METHODS, GEOPOTENTIAL HAMILTONIAN, POINCARE ELEMENTS, DENSITY MODELS)

This dissertation develops a semi-analytical theory for satellite orbit prediction. 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 non-conservative perturbation over one revolution of the satellite. A comparison is made of the generalized Lie-Hori Method and the method of averaging. In the comparison presented here, 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 equivalence, 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. This equivalence is used to develop a semi-analytical theory for satellite orbit prediction. The equations of motion of a satellite perturbed by the J(,2) and J(,3) coefficients in the Earth's geopotential and either atmospheric drag or solar radiation pressure, depending on the satellite's altitude, are developed in nearly Hamiltonian form in the non-singular canonical set of Poincare. For the Hamiltonian part, i.e., J(,2) and J(,3) terms, elimination of short periodic functions is carried out analytically using the original Lie-Hori method. For the non-Hamiltonian part, i.e., drag or solar radiation pressure, the elimination is carried out using a numerical averaging technique. The mean element rates are numerically integrated, and the osculating elements are recovered by transforming to the osculating element space. The semi-analytical method developed in this dissertation is compared with numerical integration.