Satellite formations or distributed satellite systems provide advantages not feasible with single satellites. Efficient operation of this platform requires the use of optimal control of the entire satellite formation. While the optimal control theory is well established, only a very simple dynamical system affords an analytical solution. Any practical optimal control problem solve the resulting two-point boundary value (TPBV) problem numerically. In this research, the optimization of satellite formation control is solved analytically. The relative satellite dynamics using Hill's coordinate system and approximations made by Clohessy and Wiltshire, combined with body-fixed thruster control, result in a linearized dynamic system. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.