The large amount of space debris currently in Earth orbit raises particular concerns regarding the current and, above all, future safety of space activities. Some future forecasts suggest that, even if we immediately stopped creating debris, this would not be enough to prevent a series of uncontrolled collisions. This situation is certainly not helped by the ever-increasing intensity of space traffic in recent years. Therefore, in addition to managing the end-of-life of active satellites and developing advanced collision avoidance systems, it is necessary to actively remove the most potentially dangerous objects and maintain the most critical Earth orbits. This thesis addresses the problem of Active Debris Removal, studying the optimal trajectories and mission profile of a cleaner satellite that focuses on debris trapped in orbits around 800 km.