Satellite geodesy: Methods



General Theory. Analytic solutions for the motion of a near-earth satellite are of practical importance for orbit prediction and establishment of reference orbits I (intermediaries) for minimizing perturbations from which the geodetic information is extracted. The best known ones currently in use at various computing laboratories are those of Brouwer and Vinti. Bonavito et al. [1969] favor Vinti's method because of its apparently better speed and accuracy. However, this preference has been questioned by Break- well and Vagners [1970], who claim that it is possible to choose initial conditions for the generation of a Brouwer orbit that keep the errors within acceptable bounds. The Vinti solution has been generalized to hold for triaxially ellipsoidal coordinates [Madden, 1970] so that the equatorial ellipticity can be made part of the reference potential. Deprit and Rom [1970] have refined Brouwer's solution to higher orders of the oblateness by the application of Lie transforms and by the development of requisite literal expansions on a computer. A new intermediary that has received much favorable attention because of its ability to generate higher-order terms in relatively simple fashion is Aksnes' [Garfinkel and Aksnes, 1970].