Planar Motions About an Oblate Planet

Abstract

Two cases of plane motion (equatorial and polar) of a vehicle about an oblate planet are discussed. Further, the results of these drag free plane motion studies may be applied to the determination of radial position, speed, and angular momentum for a motion whose initial velocity vector is inclined at an arbitrary angle to the equatorial plane. Approximate analytic results are found by expanding the solution of the system of nonlinear differential equations of the path in powers of the oblateness parameter /. Although only the first power is retained in this solution, no restriction is placed on eccentricity. Thus, for example, the results for an eccentricity of 0.5 may be found from the analy­ sis. In fact, results for speeds in excess of escape speed (e.g., e = 1.1) may be found. Comparison with results obtained by numerically integrating the equations of motion indicates excellent agree­ ment with the analysis.