Computerized Algebraic Utilities for the Construction of Nonsingular Satellite Theories

Abstract

This thesis investigates the possibilities offered to celestial mechanics by a general purpose algebraic language, MACSYMA. A computerized algebraic utility has been implemented for the construction of a first-order nonsingular semianalytic satellite theory. This package can generate the special functions which appear in the expansion of the gravitational potential in terms of equinoctial variables, the averaged potential and equations of motion and short-periodics due to an arbitrary harmonic. The MACSYMA satellite theory package is used to build an analytical tool to handle the critical inclination problem for small eccentricity orbits. The eccentricity variations due to the zonal harmonics computed theoretically are in agreement with actual observation data. The dramatic importance of the high degree odd zonal harmonics in the vicinity of the critical inclination is illustrated.

Semianalytic Satellite Theory

“…The J 2 -squared auto-coupling mean element rates A i11 , correct to first power of the eccentricity and with (α, β, γ) replaced by the explicit formulas (2.1.9-3) in p and q. These terms were constructed with the MACSYMA algebraic utilities of [Zeis, 1978] and [Bobick, 1981].…”