At present, the United States of America and its allies have no significant defense against intercontinental ballistic missiles, ICBMs. In this paper, the systems engineering process is applied to the United States' problem with defense against ICBMs. The need for a system that negates this problem is first considered. The need is established. Thus, analysis of the system's feasibility is required. The optimal system chosen to satisfy the need is Global Protection Against Limited Strike~ GPALS. The component of GPALS that will be studied is Brilliant Eyes. Brilliant Eyes is a constellation of satellites that detects and tracks ballistic missiles. The requirements for Brilliant Eyes are set to ensure that the need is achieved. A conceptual design for Brilliant Eyes is performed to analyze trade-offs in satellite configurations. The optimal configuration is obtained. From the conceptual design, a preliminary design is developed. The minimum number of satellites required for the configuration is determined in the preliminary design. In addition, the antenna dimensions and power requirements which provide optimal satellite communications are also obtained in the preliminary design. From the preliminary design, the optimal number of satellites for the Brilliant Eyes constellation is 56. Also from the preliminary design, each ground station supporting the constellation has an antenna diameter of 5.7 m with a transmitting power of 27.8 dBW. Each downlink antenna on the Brilliant Eyes satellite is 0.03 m in diameter with a transmitting power of 20 dBW. The crosslink antennas on the satellites are 0.7 m in diameter with a transmitting power of 0 dBW or 1 W.