"I'm guessing the building a separate "rocket that nudges dead satellites out of earths orbit" is extremely expensive?" Yes, at least as expensive as launching

"I'm guessing the building a separate "rocket that nudges dead satellites out of earths orbit" is extremely expensive?" Yes, at least as expensive as launching the original satellite, if not more (because it has to have the ability to intercept). Also, just adding a little nudge doesn't really help. It changes the orbit slightly, but it isn't like an additional 44 meters per second (which is what 100 mph is) of velocity is going to make the derelict spacecraft achieve escape velocity. You'll just change the shape of the orbit some. You need to add an additional ~ 3300 m/sec (7400 mph!) in velocity to get to escape velocity. Decreasing the velocity, such that the derelict eventually de-orbits and burns up in the atmosphere is typically much less expensive. A few hundred m/sec would probably do it, but it depends a lot on what orbit the derelict starts in.