Serial mid-course corrections direct any spacecraft to approximate a pre-computed cruise trajectory. An iterative series of corrective rocket thrusts hone in on a desired trajectory. In the case of a moon-lander, a quality cruise trajectory is essential for precise orbit insertion. Although an ideal trajectory can be pre-computed, the corrections must be planned and implemented during flight. There are two primary errors for each correction. One error is the imperfection in estimation the spacecraft’s location. It is possible to approximate how close that the spacecraft is to its intended trajectory. It is not possible to know the spacecraft’s trajectory error precisely. Each correction is planned using the estimate of position, so each correction plan is imperfect. The second primary error is imperfection in the correction maneuver. Each correction impulse varies a little based on thrust transients and attitude controls. So, plans are imperfect and thrusts are imperfect, but iterative corrections converge on a quality trajectory.
It is important to simulate and analyze the cruise correction process to (1) insure correction for imperfect injection, (2) insure stability and convergence, and (3) insure propellant margin for any eventualiity. The method employed here is to (1) pre-compute viable earth-moon trajectories, (2) simulate trajectory errors, (3) plan corrections, (4) simulate correction errors, and (5) compute statistics, since this is a probabilistic process. Position/velocity coordinates created by each source of error are modeled as a normal distribution. The first distribution is the set of actual position/velocity coordinates possible due to the error of the thrusters. The distribution is centered on the desired trajectory. The second distribution is the set of estimated position/velocity coordinates. These coordinates are centered about the actual position/velocity computed during the cruise simulation.