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.  favor Vinti's method because of its apparently better speed and accuracy. However, this preference has been questioned by Break- well and Vagners , 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  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].