Once something is in orbit, it's pretty much going to stay there a good long time. In fact, lacking any other influences, an object would theoretically stay up forever. A couple of things can perturb orbits. Other objects (particularly the moon) influence orbits by their own gravity. The atmosphere doesn't just end at the top, it thins out, and very slight amounts of air can be found even a few hundred miles up, and the drag eventually affects lower-orbit objects.scribble said:
But yes, any object in orbit has a considerable amount of kinetic energy. Unfortunately, to transfer that energy from booster to satellite would require an enormous impulse between the two, because it would occur while they are in contact, over a very short period of time. The forces would be huge, you'd blow the satellite apart. Rockets and satellites already have to be very carefully designed to withstand the g forces of a launch.