On the determination of near-body orbits using mass concentration models

The observations of a near-body satellite are used in the determination of certain constants appearing in a mathematical representation of the gravitational field of the central body. This representation is based on the assumption that the mass of the central body can be closely modeled by several concentrated masses located near its geometric center. The determination method employs a perturbation technique, numerical integration of linear and nonlinear differential equations, least-squares fitting criteria, and matrix inversion to determine estimates for the parameters involved. Several models for the representation of central body gravitational fields are discussed and the numerical techniques for evaluation of the parameters involved are briefly reviewed. The computations performed indicate that the parameters of such models can be estimated numerically. Some of the obstacles associated with using the method described herein to solve typical trajectory problems are discussed and some actual results are presented. Finally, suggestions for additional study of the theory and its applications are proposed.Mechanical Engineering, Department o