I think your understanding might be incomplete. To "stop" in space, relative to a viewer on the ground, means going into geostationary orbit. Or, I suppose, t

I think your understanding might be incomplete. To "stop" in space, relative to a viewer on the ground, means going into geostationary orbit. Or, I suppose, to a Lagrange point. To borrow an XKCD-ism, space isn't high so much as it's fast. You have to go very very fast to stay in orbit, and if you were to attempt to slow down and stop whilst orbiting, you'd essentially be executing a de-orbit burn and would find yourself re-entering the atmosphere.