Thready reminder to those who don't understand orbital mechanics, like OP: if an object in orbit fires and object into a lower orbit the object fired will INCREASE the speed at which it orbits because you've shortened the orbital distance which is inversely proportional to it's velocity.
For clarity: anything "shot down" from something in orbit will orbit faster than what fired it and launch out of earths orbit into outer space–it's the same orbital mechanics used for the gravitational slingshot maneuver.
It isn't.