Low Earth Orbit is over-cluttered with rogue objects that threaten existing technological assets and interfere with allocating new ones. Traditional satellite missions are not efficient enough to collect an appreciable amount of debris due to the high cost of orbit transfers. Many alternate proposals are politically controversial, costly, or dependent on undeveloped technology. This dissertation attempts to solve the problem by introducing a new mission architecture, Space Sweeper, and bespoke hardware, Sling-Sat, that sequentially captures and ejects debris plastically. Resulting momentum exchanges are exploited to aid in subsequent orbit transfers, thus saving fuel. Sling-Sat is a spinning satellite that captures debris at the ends of adjustable-length arms. Arm length controls the angular rate to achieve a desired tangential ejection speed. Timing the release exacts the ejection angle. This process redirects debris to burn up in the atmosphere, or reduce its lifetime, by lowering its perigee. This dissertation establishes feasibility of principles fundamental to the proposed concept. Hardware is conceptualized to accommodate Space Sweeper ’s specialized needs. Mathematical models are built for the purpose of analysis and simulation. A kinematic analysis investigates system demands and long-term behavior resulting from repeated debris interaction. A successful approach to enforce debris capture is established through optimal control techniques. A study of orbital parameters and their response to debris interactions builds an intuition for missions of this nature. Finally, a J2-compliant technique for path optimization is demonstrated. The results strongly support feasibility of the proposed mission.