ANALYTICAL AND NUMERICAL STUDIES OF THREEDIMENSIONAL TRAJECTORIES TO THE MOON,
TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF
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The purpose of this paper is to present theoretical calculations of lunar trajectories from the point of view of the guidance problem. Section 1 contains the conventional two-dimensional analysis with the usual decomposition of the actual N-body problem, the earth, moon, vehicle, sun, etc., into the more tractable succession of two-body pro blems. The analytic statement of the required accuracy to impact on the moons surface is then determined and compared with the actual accuracy needed. Section 2 examines the effect on the necessary guidance accuracy of launching out of the plane of the moon. This three-dimensional analysis indicates that the velocity accuracy requirements increase sharply as the plane of the trajectory is inclined with respect to the plane of the moon, and also that the accuracy requirements vary greatly for different launch times, both for given times of the day and given days of the month. Methods for analytically determining appropriate launch times and azimuths are also given. Section 3 is a brief application of the ideas presented above to some of the special problems posed by attempting to establish a lunar satellite.