The control problems of two different configurations of tethered satellite systems forNASA’s Submillimeter Probe of the Evolution of Cosmic Structure (SPECS) mission are studied and their control performances are compared. The configuration of main focus is the TetraStar model composed of three controlled spacecraft and three uncontrolled counterweights. This system is compared with a triangular tethered satellite system consisting of three controlled spacecraft. The equations ofmotion are derived usingLagrange’s equations. Severalmission scenarios for the SPECS mission considering the operation of an infrared telescope are introduced and asymptotic tracking laws based on Lyapunov control are developed.