Limitations of the standard method for the midcourse correction of lunar trajectories

Abstract

A method for computation of the midcourse correction velocity for lunar impact trajectories is analyzed. Only the magnitude of the impact miss, but not the impact time, is considered for correction. The method introduced in 1959 by W. Kizner utilizes the impact parameter as the measure of the target miss. It is shown that this method has certain limitations. When applied for correction of trajectories intended to impact a material point in space, or for correction of lunar fly-by trajectories, this method performs flawlessly. It also performs reasonably well when applied on standard trajectories. However, it may become inadequate for a general type of impact trajectory. The reasons for that are found to be inherent in the nature of the method. Two kinds of deficiencies are determined due to the method: the possible incorrect magnitude of the computed midcourse correction velocity, and the nonuniqueness in relation between the target miss and the injection errors or midcourse correction velocity. A partial improvement of the method is proposed. Also another measure of the target miss which does not cause drawbacks and which is also used presently, however less frequently, is picked up and recommended.