Reative Position Change in Spacecraft Formation by Two Impulses

2nd Report, the Case when Formation Size is Reduced

Abstract

This paper proposes a basic method for constructing a formation flight based on Hill's equations of motion. It proposes a trajectory design of minimum fuel consumption for spacecraft relative position change by two impulses. We have already considered the case where the formation size is enlarged. Focusing on the case of reducing the formation size, we consider here a problem to obtain the time and the phase of the second impulse when the phase of the first impulse is given. As is different from the preceding case, the optimality condition becomes more complicated in this case. The procedure to obtain the optimal solution is given, and the results show that the optimality condition in the preceding report covers the large part of the simulation cases, while the new optimality condition is valid in some cases.