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The location of Alpha Carinae and Canopus on "The Explored Galaxy" wall chart
The location of Alpha Carinae on the tactical situation monitor
Michael Okuda, who created the wall chart "The Explored Galaxy", believed that Canopus and Alpha Carinae were two distinct stars. So, he created two systems, the Canopus and the Alpha Carinae, and located them in separate regions of space. A large, but indeterminate, number of light years separated these two systems from each other. This conflict with real world facts was understandable because a connection between the two was never established in the canon. A planet may be named Canopus III, or Alpha Carinae III, but never as Canopus III and Alpha Carinae III in the same episode. Another example of this splitting of a system into two systems would be repeated with Pollux (Beta Geminorum) with a different result.
According to Star Trek: Star Charts (pg. 65). Canopus (or Alpha Carinae) was a star located in the Canopus system. This system was located in or near Federation space, in the Beta Quadrant, in the late 24th century. The primary, Canopus, was a F-class star with a magnitude of -1, which was a hundred times brighter than Sol.