Multiple-spacecraft orbit transfer problem: Weak-booster and strong-booster cases

Primer vector theory, in combination with a parameter optimization algorith m, is used to compute the optimal transfer of n spacecraft from an initial parking orbit to a final operational orbit with the added constraint that a ll spacecraft an: injected from the parking orbit on one upper-stage booste r and that all are required to be spaced along the final orbit according to some prescribed, but otherwise arbitrary, spacing constraint between indiv idual spacecraft. Two particular cases of the problem, known as the weak- a nd the strong-booster cases, are examined, In the weak-booster case, the bo oster provides the departure maneuver from parking orbit, but because of a booster propellent constraint, its trajectory does not reach the final orbi t, requiring that all spacecraft make at least two maneuvers to complete th e transfer. For the strong-booster case, the booster departure maneuver is unconstrained in magnitude, implying that at least one of the spacecraft ca n complete the transfer with a single maneuver because the transfer traject ory ran reach the final orbit. The solution is formulated for a general for ce field, and examples are given for a three-spacecraft constellation trans fer in the restricted three-body problem force-field model.