You know what I've always loved about the inclusion of the Space Shuttle in that display? The fact that then-President Gerald Ford stated that the Space Shuttle test-bed vehicle name came from the ship on the TV show -- not any previous real-life ships.
So Star Trek including the shuttle Enterprise in a list of ships named Enterprise was self-referential. It was (in a way) "breaking the fourth wall".
I hate to douse this idea with a bucket of cold water, but I don't believe this is actually the case; myths about
Star Trek's influence on history tend to be exaggerated.
It's clear enough that the letter-writing campaign from
Star Trek fans was the primary motivation for renaming the shuttle to
Enterprise, but there's no record of Ford publicly citing this is the reason for the renaming.
Two PDFs of White House memos on the renaming are available online. One is
http://static.history.state.gov/frus/frus1969-76ve03/pdf/d133.pdf at
https://io9.gizmodo.com/declassified-memos-reveal-debate-over-naming-the-shuttl-1603073259. The other is
https://www.enotrans.org/wp-content/uploads/Ford-Decision-to-Name-Orbiter-Enterprise.pdf at
https://www.enotrans.org/etl-materi...aming-first-space-shuttle-orbiter-enterprise/. I don't doubt that there are others.
William F. Gorog's memo that Ford initialed to approve the name change cites millions of
Star Trek fans, the letter-writing campaign, and public relations as the motivating reasons for the name change. So, it's completely clear that
Star Trek fans were the prime movers and that both Ford and his staff at the White House understood this.
However, there was a debate among Ford and his advisers behind the scenes about whether using
Star Trek as the rationale was beneath the dignity of the situation. Jack Marsh said:
"I have no objection to this selection of a name, however, I am not enthusiastic about the rationale for the selection. "Enterprise" is a famous name for vessels since the early days of the Republic. I think that is a far better reason than appealing to a T.V. fad."
Jim Cannon on the other hand appreciated the PR angle that was at stake, saying:
"It seems to me "Enterprise" is an excellent name for the space shuttle.
It would be personally gratifying to several million followers of the television show "Star Trek", one of the most dedicated constituencies in the country."
But Ford seems to have been swayed by Marsh's side of the argument. Rather than mentioning the letter-writing campaign, in his public remarks Ford said he was partial to the name "Enterprise" and had served on a ship that operated with USS
Enterprise (CV-6) in WWII [
https://news.google.com/newspapers?id=JGIgAAAAIBAJ&sjid=2GUFAAAAIBAJ&pg=2595,1284578].
(I Googled up the reference to the Eno Center for Transportation's PDF of memos. The remaining references were culled from the Wikipedia page
https://en.wikipedia.org/wiki/Space_Shuttle_Enterprise.)