Star Trek was a TV show that ran from 1966 to 1969, and has spawned ongoing TV series, movies, books, toys, graphic novels, games, etc, set in its universe. Even a Barbie. The show's 60th anniversary was a few weeks ago. The model was for the NCC-1701 Enterprise - not to be confused with NGC 1701, a galaxy numbered for the show's ship.

The show crafted several versions to use for filming, from a small 100mm model to a large 3.4m version. The large model could only be filmed from one side, due to lighting cables entering from the other. The film stock was reversed to simulate the other side of the ship.

The original 3.4m studio model is a "living cultural object", and was itself a character in the show, voiced by Majel Barrett. The artifact was donated to the Smithsonian National Air and Space Museum, who has an online exhibit detailing what their world class conservationists did to restore and preserve it. Here is the display of the restored late 60's studio model.

In the 1970s, a write-in campaign from Trek fans convinced NASA to name the first Space Shuttle test vehicle after the show's ship. It was not capable of space flight, but it was used for 5 atmospheric flight tests. Many NASA engineers and scientists developed an interest in real life space exploration from watching the TV show as children. This is most of the show's cast in front of NASA's Enterprise in 1976.

Almost every online version has been remastered, but this TV intro looks original (youtube). This is what the studio model looked like in the show.

Lastly, here is a modern symphony orchestra in Prague (youtube) doing the famous Star Trek theme.

I saw it in the museum in the early 1980s, just hanging from the ceiling in a corner with a little wall tag. It's the only thing in the museum I took a picture of with my Kodak Disc camera. I could not get anyone in my family to be excited about it at all.

I had one of these.

Lights and all.

Fun times.. 1969?

Were they into the show?

Early 80s was a long time after ST:TOS ended, but still before ST:TNG, so that might've been a low point for the number of fans who would appreciate the model.

Not only didn't they watch it, they made me stop watching it if dinner had been served.

Fun fact: The Shuttle Enterprise was intended to fly in space but by the time they got around to retrofitting it too many design changes had been made. Columbia, the first Shuttle to fly to space and the one that was lost in 2003, was started from the same design as Enterprise and was too heavy to easily fly to the ISS as a result of being an earlier design so it never did.