The Astral V Annex was a historical museum, noted for its interest in ancient space-going vessels.

In 2366, upon the discovery of Promellian battle cruiser Cleponji by the USS Enterprise-D, Captain Jean-Luc Picard requested that the Annex be contacted so that the ship could be catalogued and scheduled for retrieval. However, the vessel never reached the museum – the Enterprise was disabled by a field of Aceton assimilators which had doomed the Cleponji a millennium before, and after escaping just minutes before the crew would have succumbed to radiation created by the assimilators, Picard ordered the Promellian ship, and an asteroid field around it, destroyed so that no other ship would fall prey to the trap. (TNG: "Booby Trap")

According to the Star Trek Encyclopedia (4th ed., vol. 1, p. 49), "An early draft script for "Booby Trap" suggested the Astral V annex was part of the Smithsonian Institution." In the revised final draft script, the Astral V annex was identified as being of the Smithsonian Institution.. [1]
According to Star Trek: Star Charts ("United Federation of Planets I"), in 2378, Astral V was listed as a Federation member.
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