Optimal invariant spacecraft formation deployment with collision risk management

The analytical solution of the deployment phase of a spacecraft formation is provided. The solution applies to Earth-centered invariant formations. These feature a fixed geometry over one revolution, which renders them useful for numerous purposes, especially radar interferometry and sparse aperture synthesis. First, a formulation useful for formation design is defined in terms of nonsingular elements. This is used as,a basis for solving the deployment phase. The primer vector theory is applied to obtain the minimal fuel consumption. Next, this theory is combined with a geometrical approach to yield the maneuver components of the optimal solution. In addition, the payload separation strategy from the rocket upper stage is also optimized to take into account the collision risk.