Tenth-Order Expansion Formulae for the Orbital Eccentricity Function K (sub lpq)(e) Obtained Using a Symbolic Algebraic Manipulation System

摘要

The development of symbolic algebraic manipulation systems for use on digital computers is a fairly recent technical innovation that has not even begun to be fully exploited. The potential for application of these systems to the nonnumeric resolution of complex problems seems boundless. The purpose of this report is to provide the results obtained from the utilization of one such state of the art system, MACSYMA, to provide high-order expansion formulae for the classical orbital eccentricity function found in celestial mechanics theory. These formulae are generally applicable to low eccentricity orbits, and the relative ease with which they were generated demonstrates MACSYMA's analytical process.