Space Seed - S1-E23
Plot hole: It is stated during the episode that Khan was, at one time, the ruler of over 1/4th the Earth's population, during a very key moment in the planet's history (The "Eugenics" Wars). Such a personage undoubtedly would be very well known to 23rd century Earth people, at a level of infamy approximating Julius Caeser or Adolf Hitler. Yet it is only 2/3rds the way through the episode, thanks to a computer search by Spock, that the crew divines his identity. Lt. McGivers at the very least should have almost instantly recognized him.
Chosen answer: If they're in orbit, they're being pulled along by the planet's gravity well, therefore, impulse engines would only be used for minor corrections and would be "on standby" while in orbit, but not active. (Like keeping your car idling without revving the engine and creating plumes of exhaust).
Captain Defenestrator
Thank you for the info.
Movie Nut