The ability to observe specific orbits is a necessary requirement to perform space surveillance of resident space objects (RSOs). Using the theory of compatible orbits, this paper shows how to design specific repeating trajectories around assigned orbits. This unique orbit is called a "Rock-Around Orbit" (RAO) orbit, that will surround the assigned target orbit allowing the RAO satellite to perform 360 degree surveillance of any RSOs in the target orbit over a given period of time.