This report presents a theory of oblateness perturbations of the orbits of artificial satellites based on Hansen's theory, with modification for adaptation to fast machine computation. The theory permits the easy inclusion of any gravitational terms and is suitable for the deduction of geo-physical and geodetic data from orbit observations on artificial satellites. The computations can be carried out to any desired order compatible with the accuracy of the geodetic parameters.

A comprehensive description of the Hansen theory of satellite orbit calculation, as modified by Musen, is presented. The equations of the theory are developed in sufficient detail to allow the reader to relate them to fundamental laws of celestial mechanics. The physical and mathematical concepts underlying Hansen's coordinate system and auxiliary ellipse are treated. The disturbing potential function and its derivatives are developed in the derivation of equations for the perturbations in the orbit plane, as well as the perturbations of the orbit plane. The method is described for determination of the final position and velocity vectors of the real satellite and determination of the osculating elements. Finally, a brief evaluation of the theory is presented.

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In the 18th century, purely scientific interests as well as the practical necessities of navigation motivated the development of new theories and techniques to accurately describe celestial and lunar motion. "Between Theory and Observations" presents a detailed and accurate account, not to be found elsewhere in the literature, of Tobias Mayer's important contributions to the study of lunar motion—including the creation of his famous set of lunar tables, which were the most accurate of their time.