The Corbomite Maneuver - S1-E11
Other mistake: When Kirk is in sickbay with McCoy he uses sickbay's desktop monitor to contact Spock on the bridge, then when Kirk is in his quarters he uses his own desktop monitor to contact Spock again. Both have the same paint dings and smudges around the console screens, revealing the same one was used during filming. (00:04:30 - 00:06:30)
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