Study of spacecraft orbital motion in the upper atmosphere using averaging.

Abstract

The motion of a spacecraft traveling in the upper atmosphere is studied using the method of averaging. The individual and coupled effects of the two major disturbance forces, Earth oblateness and atmospheric drag, are studied. First and second order approximate solutions for the spacecraft orbital motions are presented. The Earth oblateness effect is found to have a major effect on the eccentricity and to produce an offset in the altitude of the unperturbed motion. For ballistic decay, the approximate solutions provide an accurate prediction of the lifetime of the spacecraft. The investigation in this paper utilizes an arbitrary density function that depends only upon altitude. For the oblateness/drag coupled problem, a novel approach is used to incorporate the effect of Earth oblateness into the drag model. The drag solution is utilized to solve the problem. The averaging approach is simple, effective and gives accurate approximations to the spacecraft orbital motions as verified by numerical simulations. Applications of the solution include estimation of satellite lifetime and the determination of impulsive thrust levels to maintain the altitude of spacecraft.