orbit forever

At least twice in the movie, a comment was made that a satellite would orbit forever, at the proper altitude. Later, when a problem happened, they said that the rocket or satellite would stay up a long time, but eventually return. That was because it was at a lower altitude.
Yes, the lower the altitude, the quicker it will come down. But back then, the writers seemed to think that the air was gone past a certain point. Not really.
It peters out slowly (exponentially. Even the ISS drops every day, and supply ships have to boost it up or it would burn up soon.
So even far away, there are atoms and molecules of air. Each one bangs into the orbiting object and slows it up a bit. If you are too far out, the Moon's gravity would mess up an orbit. I believe a small, dense (tungsten), heavy, and round satellite was sent up, with reflectors. Lasers were to be used to check the position. Maybe it was a reference object, or a check on relativity, or the gravity field around the Earth. Or all of the above. But it was very high up, and might stay up for maybe 5 million years. I don't recall the details.
But forever is a really long time.