Details and historyEdit
The first planet in orbit of the Orion star system, Orion I supported a population with cordial ties to the Federation. This world was the location of the prestigious Institute of Cosmology. Human science prodigy Mortimer Harren had hoped to attend the Institute on Orion I, and to that end he joined the crew of USS Voyager to gain a year of field experience required for admittance. (VOY episode: "Good Shepherd")
ST reference: Star Charts establishes the Orion system mentioned in canon as being Pi-3 Orionis, a non-Federation location. STO video game: Star Trek Online extrapolates on the location shown in Star Charts with sector and sector block naming for the vicinity.
Since Star Charts has specific notation regarding Federation and non-Federation worlds, we can see that the political status of this world is not as a Federation member, but it is entrenched in Federation space, and is an acceptable destination for students from Federation worlds.