Optimal, impulsive, direct ascent, time-fixed orbital interception

A method for determining optimal impulsive trajectories is applied to minimum fuel, direct ascent, time-fixed intercept trajectories. The optimal trajectory is obtained by satisfying Lawden's necessary conditions expressed in terms of the primer vector. The vehicle is initially at rest on the surface of a spherical planet and the target is assumed to be in a circular, equatorial orbit around the planet. Results are presented and compared for two planetary models: a non-rotating planet, and one rotating with an angular velocity approximating that of the Earth. Each model is investigated for transfers in which the launch point is in the same plane as the target orbit (coplanar) and in which the launch point is not in the target orbit plane (noncoplanar). Parameters varied during the analysis include transfer time, target radius, initial position of the target in relation to the launch point, and the direction of the transfer trajectory, i.e., posigrade or retrograde. Cost comparisons are made between the various cases, and generalizations indicated.