I can't believe I'd never encountered Gene Roddenberry's original pitch for Star Trek, dated March 11, 1964. [pdf via Hacker News] He did it by wedding a (if not the) Drake equation with the "wagon train" concept.
Star Trek offers and almost infinite number of exciting Science Fiction stories, thoroughly practical for television. How? Astronomers express it this way:
Fr2 (MgE) – C1R11 x M = L/So
A wild pitch by modern expectations, but in 1964 it blew minds! Be sure to meet the original character conceptions–Uhura as a dominating XO and "Mr Spook" in blatantly satanic form–evidently a little too progressive for executives already mercilessly tenderized by Roddenberry's cosmic numbers.