Return to Glory by Jack McDevitt

Return to Glory by Jack McDevitt (Asimov’s SF, November/December 2020) is set on Earth two hundred years from now. It is a better place than now, but one that has abandoned its Mars colony and dreams of space exploration.
The story opens with the narrator getting a call from a call from a school friend to say he’s found a copy of a long lost show called Star Trek at a site he’s developing, and the narrator’s wife agrees to screen the show (the library she works at has the tech to read the recording’s ancient format). The three of them then meet the next morning to watch it—only to find the disc contains a fan production. The friend shrugs off his disappointment, and agrees to let the wife copy the disc for the museum.
That night the narrator and his wife watch the show at home:

The storyline wasn’t great, but it was okay. It wasn’t the narrative that caught our attention. It was entering the ring system at the gas giant. And watching stars pass steadily through the windows of the Republic. And looking down on other planets. The special effects took us for a serious ride.
“I think the magic,” said Sara, “is knowing it was put together by people who believed it was coming.”   p. 164

The show becomes a hit at the museum, and then the series is remade, which in turn provides stimulus for new research in space/warp flight.
If you are in the mood for a mawkish, boosterish tale about how Star Trek will inspire future generations to travel into space, and one that includes a three page synopsis of a fan show, then this will be right up your street. It wasn’t up mine, and reads like something that was pulled out of Analog’s slush pile.
– (Poor). 4,000 words.