Perturbation treatment of the restricted three-body problem

Abstract: The motion of an artificial Earth satellite is continually under varying perturbations caused by the Earth’s oblateness and the Moon’s gravitational pulls, as well as other disturbances. The present work studies the J2 and third-body perturbations in the restricted three-body problem of the Earth-Luna-satellite model. This is achieved by using the variation of parameters method to derive and apply the Lagrange equations of planetary motion, and by determining the long-term disturbing potentials using the averaging method. The Runge-Kutta-Fehlberg 7(8) method is employed to determine the time evolutions of the orbital elements, and hence the way the satellite orbit is changed by the presence of J2 and third-body perturbations. Comparisons are then drawn between the two perturbation effects on the satellite, for low Earth orbits and for high altitude orbits.M.Sc. (Applied Mathematics