Optimal two-impulse rendezvous using multiple-revolution lambert solutions

Abstract

The minimum-A V, fixed-time, two-impulse rendezvous between two spacecraft orbiting along two coplanar unidirectional circular orbits (moving-target rendezvous) is studied. To reach this goal, the minimum-A V. fixed-time, two-impulse transfer problem between two fixed points on two circular orbits is first solved. This fixed-endpoint transfer is related to the moving-target rendezvous problem by a simple transformation. The fixed-endpoint transfer problem is solved using the solution to the multiple-revolution Lambert problem. A solution procedure is proposed based on the study of an auxiliary transfer problem. When this procedure is used, the minimum A V of the moving-target rendezvous problem without initial and terminal coasting periods is obtained for a range of separation angles and times of flight. Thus, a contour plot of the cost vs separation angle and transfer time is obtained. This contour plot, along with a sliding rule, facilitates the task of finding the optimal initial and terminal coasting periods and, hence, obtaining the globally optimal solution for the moving-target rendezvous problem. Numerical examples demonstrate the application of the methodology to multiple rendezvous of satellite constellations on circular orbits.