Detection of eccentric objects near the geosynchronous region is a very important issue. However, the extremely narrow fields-of-view of optical telescopes hinders us from identifying eccentric objects. An observation strategy to systematically detect these objects and determine their orbits precisely with one telescope is outlined in this presentation. Basically, one specific geosynchronous location (not one specific celestial position) is observed on two nights. Objects which pass through that location in the first night must pass through that location again in the second night. By identifying the same objects from two nights of data, rough orbits for those objects are determined. A third night is needed for precise orbital determination. An application of this strategy to the observation for Titan fragments is also discussed.