Consider a two body system for simplicity: M1 << M2. M1 is in a circular orbit about M2. The tangential speed of M1 is inversely proportional to its distance from the center of M2. However, in order to move to a lower orbit, or to de-orbit completely, M1 must lose tangential speed (in the case of an artificial satellite, the application of reverse thrusters is the most common method), and to go to a higher orbit, M1 must gain tangential speed. So what happens in the case of moving to a lower orbit? M1 briefly slows down, but then immediately gains speed as it falls into a lower orbit?