Groombridge 34
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Groombridge 34 was a star system consisting of binary companion stars, Groombridge 34 A and Groombridge 34 B, located about 11.6 light years from Sol.
On several occasions in 2364, viewscreen readouts aboard the USS Enterprise-D showed the location of the A and B Groombridge 34 stars, in the form of a star chart from the Enterprise-D library computer. The stars names were abbreviated in the chart as GRB 34 A and B. (TNG: "The Naked Now", "The Last Outpost", "Conspiracy")
Background
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The Enterprise computer's star chart was a drawing by Rick Sternbach that had originally been published, years earlier, on page 77 of the non-canon reference book Spaceflight Chronology. This chart showed Earth commercial and exploration routes after the use of warp drive began. Groombridge 34 A and B were not destinations on any of the routes.
Groombridge 34 was a real system in the Andromeda constellation. Modern scientists have determined Groombridge 34's components are spectral class M1.5nV and M3.5nV.
According to the Star Trek: Star Charts, page 44, this star was located in the Alpha Quadrant, in Sector 004.