An Automatic Terminal Guidance System for Rendezvous with a Satellite

This study includes a consideration of the design philosophy for an automatic terminal guidance system, a derivation of guidance equations required, and an outline of the general type of instrumentation necessary to provide the essential information. A control system for a sample vehicle is analyzed. A representative case, rendezvous with a satellite in circular orbit at 400 nautical miles, was examined. Terminal-stage nominal burning times of 200 and 400 seconds were used. For the 200-second case, initial errors in circumferential displacement of +/- 25,000 feet, in radial displacement of 7,000 to -9,000 feet, and in lateral displacement of +/- 20,000 feet were within the capabilities of the system. Velocity errors of 300 to -400 ft/sec in the circumferential direction, 180 to -200 ft/sec in the radial direction, and velocity offsets of at least 20 (+/- 800 ft/sec) in the lateral direction could also be handled. The 400-second case was capable of correcting larger errors, but limits were not determined. The dependence of required characteristic velocity on initial errors was determined and it was found that increases over the nominal terminal-stage characteristic velocity of the order of 15 percent covered most of the previously mentioned in-plane errors. The requirements were more severe for cases with lateral velocity offsets. A simplified set of guidance equations was tested and produced only slight variations in performance. Overall velocity requirements and mass ratios were determined for terminal-stage burning times of 100, 200, 300, and 400 seconds and for a range of transfer angles by using exact calculations for the terminal stage and an impulsive launching velocity. These results indicated that the shortest burning time consistent with the launch guidance errors expected gave the best mass ratio.