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Influence of thermal distortion of booms on attitude of gravity stabilized satellites.
It was reported that the long-period (80-day) variations in the eccentricity of the orbit of Satellite 1958 beta2 (Vanguard) can be explained by a north-south asymmetry in the gravitational potential of the earth. That is, the axial symmetry of the field is retained, but the third harmonic in latitude is added. The first part of this paper is a mathematical analysis of this problem.
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.