Coulomb propulsion has been proposed for spacecraft cluster applications with separation distances on the order of dozens of meters. This thesis presents an investigation of analytic charge solutions for a planar and three dimensional four satellite formations. The solutions are formulated in terms of the formation geometry. In contrast to the two and three spacecraft Coulomb formations, a four spacecraft formation has additional constraints that need to be satisfied for the individual charges on the spacecraft to be unique and real. A spacecraft must not only satisfy the previously developed inequality constraints to yield a real charge solution, but it must also satisfy three additional equality constraints to ensure the spacecraft charge is unique. Further, a method is presented to reduce the number of equality constraints arising due the dynamics of a four spacecraft formation. Formation geometries are explored to determine the feasibility of orienting a square formation arbitrarily in any given plane. The unique and real spacecraft charges are determined as functions of the orientation of the square formation in a given principal orbit plane. For a three-dimensional tetrahedron formation, the charge products obtained are a unique set of solution. The full three-dimensional rotation of a tetrahedron is reduced to a two angle rotation for simpler analysis. The number of equality constraints for unique spacecraft charges can not be reduced for a three-dimensional formation. The two angle rotation results are presented for different values of the third angle. The thesis also presents the set up for a co-linear four-craft problem. The solution for the co-linear formation is not developed. The discussion of co-linear formations serves as an open question on how to determine analytic solutions for system with null-space dimension greater than 1. The thesis also presents a numerical tool for determining potential shapes of a static Coulomb formation as a support to the analytical solutions. The numerical strategy presented here uses a distributed Genetic Algorithm (GA) as an optimization tool. The GA offers several advantages over traditional gradient based optimization methods. Distributing the work of the GA over several processors reduces the computation time to arrive at a solution. The thesis discusses the implementation of a distributed GA used in the analysis of a static Coulomb formation. The thesis also addresses the challenges of implementation of a distributed GA on a computing cluster and presents candidate solutions. / Master of Science