Background information Edit
According to production sources concerning Star Trek: The Motion Picture, and as published in Star Trek: The Magazine Volume 2, Issue 9, the Betelgeuse star system, which was located within Federation space during the 23rd century, was the home to the Betelgeusians, an alien species that appears in the aforementioned film. The Betelgeusians' homeworld was, according to the production sources, the planet Betelgeuse II. (Starlog #33, April 1980, p. 51; The Making of Star Trek: The Motion Picture, p. 130; Star Trek: The Magazine Volume 2, Issue 9, January 2002, "Who is that Alien?")
According to Star Trek: Star Charts ("United Federation of Planets I", "United Federation of Planets II"), the Betelgeuse (Alpha Orionis) system was located in the Beta Quadrant. The system's primary was a M-class star. The star lent its name to an inhabited planet in the system – Betelgeuse – which was by 2378 a member of the Federation.