A new first order solution to the relative motion problem with applications to intercept and rendezvous

Abstract

An improved first order linearized solution, describing the relative motion between an interceptor vehicle and a target vehicle in a circular orbit, has been developed by means of a transformation of the variables which occur in the differential equations of relative motion. The results of this analysis are compared with other first order solutions and with complete solutions obtained by numerically integrating the exact, nonlinear differential equations of motion. It was found that this improved first order method is considerably more accurate than the previously developed first order solutions, especially for large initial separation distances between the target and the interceptor. In order to fully utilize these results they have been applied to both the intercept and the rendezvous problem. In addition to the basic analysis, a method was developed to determine the time at which a velocity impulse should be applied to the interceptor in order that the total velocity impulse would be a minimum for both the intercept and rendezvous situations.