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Tethered satellite system end masses do not obey the normal laws of motion developed for determining their orbits. In addition, tethered satellite systems cause unique problems for satellite tracking because there are potentially two or more objects which may be tracked. This thesis provides insight into these issues by developing a method of sorting out observation data of tethered satellite systems into their appropriate end mass and providing an estimate on the center of mass orbit of the tethered satellite system. The method used to accomplish both of these tasks is optimization of an estimated simulated orbit. This orbit estimate is optimized to provide the minimum difference between the end mass position estimates and the observations obtained from one or more tracking sites. This methodology also helps provide a baseline for tracking tethered satellite systems more accurately in the future.