AN ANALYTICAL STUDY OF THE EFFECTS OF OBLATENESS ON SATELLITE ORBITS,
MARTIN CO DENVER COLO
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This report contains an analytical study of the short term effects of planetary oblateness on the path of a satellite that is under the sole influence of gravitational attraction. Analytical solutions of the equations of the path, valid to the first order in the oblateness parameter J, are determined following the method of Lindstedt. The initial conditions considered in this report require that the satellite be initially at an apse in the equatorial plane, but the inclination and the eccentricity are unrestricted. Subsequent reports will consider 1 initial positions not in the equatorial plane and 2 the escape path from an oblate planet. Both analytical expressions and numerical results are given for the radial position, speed, angular momentum, deviation from the initial plane of motion, rate of nodal regression, and the rate of apsidal advance of a satellite. In addition, the injection speed required for prescribed apses is derived.