Abstract
This paper presents an approximate analytic solution of the drag-free equations of motion of a particle in the equatorial plane of an oblate spheroid subject only to the gravitational attraction of the spheroid. The solution, correct to second order in the planetary ellipticity e, is obtained using the Poincare-Lighthill-Kuo perturbation method. Additional results pertaining to the speed, flight-path angle, time, and the escape path are given as functions of angular displacement from an apse. Results are obtained as power series in the oblateness parameters J and D, and are valid for all eccentricities, i.e., no restriction is placed on \r)J. The results agree with similar results given by Tisserand and DeMoraes and offer excellent agreement with numerical data.
Published Version
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