A Simple Targeting Procedure For Lunar Trans-Earth Injection

A simple targeting algorithm for trans-Earth injection is developed. The techniques pre-sented in this paper build on techniques developed for the Apollo program and other lunar and interplanetary missions. Presently, more sophisticated algorithms exist for solving this problem, but the simplicity of this particular algorithm makes it well-suited for on-board use during contingency and abort operations. In order to support a return from any lunar orbit with available fuel on the spacecraft the algorithm chooses between one-, two-, or three-burn return scenarios. The one- and two-burn cases are based on existing theory. For the three-burn case however, the existing theory is modified in order to provide a simple solution. Rather than attempting to create fuel-optimal trajectories, the algorithm presented in this paper focuses on computing a trajectory from low lunar orbit to direct atmospheric Earth entry that does not violate a fuel constraint. The algorithm attempts to use a minimal number of impulses to execute trans-earth injection. The algorithm can also be used to quickly generate good initial guesses for other more sophisticated targeting algorithms that can be used to find minimal fuel trajectories or optimize other parame-ters. This algorithm has three principle phases. First, an estimate of the hyperbolic excess velocity at the Lunar sphere of influence is generated. Second, a maneuver is computed that will transfer the craft from a lunar circular orbit to the hyperbolic escape asymptote. Finally, the effects of perturbations are eliminated by using linear state transition matrix targeting. I