Satellite orbits: Is this what the OP is basically about?
There is one particular speed for a satellite to travel that will cause its orbit to be exactly circular. This will be when the centripetal force is exactly equal to the gravitational force and it is moving at right angles to a radius. If you take a satellite which satisfies these conditions and give it a change in speed (boost or braking), or direction, it will no longer follow a circular orbit but an elliptical one. The gravitational force varies, depending on their orbital distance (inverse square law) and this is the only 'force law' that will lead to a stable, elliptical orbit afaik.
Most (all) orbits of planets, moons, satellites are, in fact, elliptical and not perfect circles. Sometimes they are far away and move slower and at other times they are closer and moving faster. But they do not 'fall out' of orbit nor do they escape because their total energy (Gravitational Potential plus Kinetic) remains the same.