The 498th Air Base Group was a military unit located on an unspecified Air Force base near Omaha, Nebraska, United States of America circa 1969 as part of the Air Defense Command. In that year, the USS Enterprise arrived in low Earth orbit above the base following a nearly catastrophic encounter with a black star which had displaced it in time.
Meanwhile, at another unnamed Air Force installation, Technician Webb reported the RADAR contact, and his superior ordered Captain John Christopher, a fighter pilot, to intercept what was then believed to be a UFO. In one version of history, Christopher's aircraft was caught and crushed by the Enterprise's tractor beam. Captain Kirk and Lieutenant Sulu infiltrated the 498th Air Base to retrieve the photographic and audio records of the incident that were recovered from the wreckage of Christopher's aircraft. Later, Spock devised a way to replay history that effectively erased the Enterprise's presence altogether. Its brief appearance was doubtless logged as one more strange aerial incident.
Captain John Christopher had been assigned to the 498th Air Base approximately one year prior to the events of this episode, and was therefore able to provide the Enterprise crew with detailed information on its layout. (TOS: "Tomorrow is Yesterday")