Analytical Evaluation of a Method of Midcourse Guidance for Rendezvous with Earth Satellites

A digital-computer simulation was made of the midcourse or ascent phase of a rendezvous between a ferry vehicle and a space station. The simulation involved a closed-loop guidance system in which both the relative position and relative velocity between ferry and station are measured (by simulated radar) and the relative-velocity corrections required to null the miss distance are computed and applied. The results are used to study the effectiveness of a particular set of guidance equations and to study the effects of errors in the launch conditions and errors in the navigation data. A number of trajectories were investigated over a variety of initial conditions for cases in which the space station was in a circular orbit and also in an elliptic orbit. Trajectories are described in terms of a rotating coordinate system fixed in the station. As a result of this study the following conclusions are drawn. Successful rendezvous can be achieved even with launch conditions which are substantially less accurate than those obtained with present-day techniques. The average total-velocity correction required during the midcourse phase is directly proportional to the radar accuracy but the miss distance is not. Errors in the time of booster burnout or in the position of the ferry at booster burnout are less important than errors in the ferry velocity at booster burnout. The use of dead bands to account for errors in the navigational (radar) equipment appears to depend upon a compromise between the magnitude of the velocity corrections to be made and the allowable miss distance at the termination of the midcourse phase of the rendezvous. When approximate guidance equations are used, there are limits on their accuracy which are dependent on the angular distance about the earth to the expected point of rendezvous.