A view of the USS Enterprise-D and Starbase 133.
Starbase 133 is of the same design as the Spacedock orbiting Earth as well as Starbase 74. It is operated by the Federation. Dr. Dalen Quaice worked at Starbase 133 for six years, from 2361 to 2367.
In 2366, the USS Enterprise-D traveled here after its mission to investigate the disappearance of the colony on Delta Rana IV. (TNG: "The Survivors")
In 2367, Starbase 133 was the site of an Enterprise-D crew rotation. The ship also picked up Dr. Quaice in order to take him back to his home on Kenda II. While docked at the starbase, an experiment conducted by Wesley Crusher trapped Dr. Beverly Crusher in an alternate universe, contained within a warp bubble. One day later, the Enterprise was returned to its exact position within the starbase during the accident in order to create a gateway for Dr. Crusher to return. (TNG: "Remember Me")
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Background
Starbase 133 was a reuse of footage of Starbase 74 from "11001001", which in turn was reuse of footage of Spacedock from Star Trek III: The Search for Spock. However, Starbase 133 appears to be much bigger than Spacedock, based on the relative size of the Enterprise-D compared with Starbase 133 and of the original Enterprise compared with Spacedock: the Enterprise-D is a much bigger ship than the original Enterprise, while both roughly fill the respective base's starship entrance.