Man I wish I had come up with this idea in time for Star Trek's 50th anniversary in 2016.
Anyway, my idea is for a real life Starfleet. The Enterprise - well all ships named Enterprise on Star Trek - serves an organization known as Starfleet. It is the diplomatic, exploratory, scientific and defense service of the galactic power know as the United Federation of Planets. Starfleet is not considered a military organization, but the service itself is built along military lines with a naval tradition.
Now a real life Starfleet - which wouldn't be a mere fan organization - would basically be a private organization dedicated to scientific & technological research & development in addition to exploration. From what I've casually observed with what's going on in space these days is there is a trend towards privatizing space. Who says government has to do all the work to send people and probes into space?
Perhaps this Starfleet could be the organization that is able to send people to the "red planet". Perhaps they also send people back to the moon. In both cases establish settlements or at the very least actual bases for scientific purposes. Of course this Starfleet could send astronauts around the solar system all the while developing better technologies - such as warp drive - to get our people exploring in shorter periods of time.
Of course to bring this back full circle, what about building the real starship Enterprise? Well the proposal I've heard involves using the design of a Constitution class starship - not clear if it's either the original series version or the movie refit version or even the one redesigned in 2009 - with nuclear reactors to power the ship, an ion engine for propulsion, & a gravity wheel in the saucer section. This proposed ship would get astronauts to the moon in three days - the same amount of time as the Apollo astronauts - and astronauts to Mars in 90 days. Mars in 90 days? OK worth a shot!
Of course using the Constitution class design seems like over kill. I always though a more practical design for today's spacecraft engineers is to use a design similar to the USS Defiant from Star Trek: Deep Space Nine or the NX-01 Enterprise from Star Trek Enterprise. While I recognize conventional wisdom is no need to built a space crusier - hence no Constitution based design - I think a practical design for a real live spacecraft based on a design from Star Trek should start with the compact or submarine based designs of the Defiant & Enterprise.
In my mine Enterprise would be what I wish we could start building for that mission to Mars. I'm not an engineer, however, this design could incorporate that gravity wheel. As far as the nuclear reactors or ion propulsion the real engineers of the world can figure this out.
So here's the NX-01 Enterprise as portrayed in the prequel eponymous Star Trek series in action. [VIDEO]
BTW, this has got to be the geekiest post written here!