
Revealing mistake: When the Russian pod is launched, a wide shot shows the Monolith at top/right with Jupiter in the background and both the Leonov and Discovery at bottom/right with the pod nearby. Just before this shot ends, all three spacecraft vanish, leaving only Jupiter and the Monolith for a very short but obvious moment. (01:04:35)
Answer: If they didn't, any further manoeuvring would require much more fuel. They would be moving the mass of two ships.