The original date of composition and the author are unclear, but the sample stardates are consistent with the range from the second pilot.
We invented "Stardate" to avoid continually mentioning Star Trek's century (actually, about two hundred years from now), and getting into arguments about whether this or that would have developed by then.
'We thought this was hilarious, because everyone would say, "How come this date is before that date when this show is after that show?
" The answer was because you were in a different sector of the universe.'  The following instructions to writers were copied from the series bible Star Trek Guide; they are quoted at Star Trek Fact Check.
The term was used during the Federation-Klingon War of that timeline.
( In addition, Star Trek Fact Check shows a scripted narration from the same draft containing "star date 1312.6".
So I checked that, yes, the astronomers had a way of dating called a Julian day system, in which, based on the calculations of a 16th century French mathematician/philosopher that felt that because he devised this calendar with a thousands and thousands of year cycle and each day was numbered, and astronomers have used that since, because it, you don't have to bother with years and leap years and AD and BC.They concluded that the 'time continuum' would therefore vary from place to place, and that earth time may actually be lost in travel.'So the stardate on Earth would be one thing, but the stardate on Alpha Centauri would be different,' Peeples says.He called (Sam) Peeples (whom Roddenberry had contacted early on for help in learning about science fiction, a subject he knew nothing about; it was Peeples who wrote "Where No Man Has Gone Before," the pilot that sold ST).The two men had a few drinks while brainstorming, and soon began chuckling over their imaginative 'stardate' computations.According to Kellam de Forest: The original script for the pilot of Star Trek was titled "Menagerie" (sic) and we in the research department, De Forest Research, didn't see it until it was in script form and came to us to review just like any other Desilu script, or any other script from any other client.