Satellite formation flight is a much-anticipated technology for future space-science missions, such as high-resolution space-based telescopes. A potentially enabling technology under development allows clusters of spacecraft to maneuver without the use of propellant, instead using electromagnetic control of the relative degrees of freedom within the cluster. This electromagnetic formation-flight technology offers potentially limitless mission life, in exchange for a highly coupled, nonlinear control problem. Several methods have been explored to address this problem, and some have achieved considerable success at its optimal, or at least locally optimal, solution. This paper does not produce optimal trajectories for unconstrained maneuvers, but instead provides a method for determining all of the feasible control solutions that will produce a specified maneuver. An example is provided for the case of three spacecraft rotating in a planar, equilateral triangle configuration, while the plane of rotation is simultaneously changing direction, as might be encountered while retargeting a separated spacecraft interferometer. The approach may be used on its own to find feasible, albeit suboptimal, solutions, or in conjunction with an optimal-control solution, to probe its optimality, find alternative solutions, or plan for contingencies. The current research deals solely with free-space translational solutions, without consideration of torques that are developed or the resulting buildup or removal of angular momentum. Extension of the current approach to address these issues is the subject of a follow-on paper.