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A stardate is a fictional system of time measurement developed for the television and film series Star Trek. In the series, use of this date system is commonly heard at the beginning of a voiceover log entry such as "Captain's log, stardate 41153.7. Our destination is planet Deneb IV..." While the general idea resembles the Julian day currently used by astronomers, writers and producers have selected numbers using different methods over the years, some more arbitrary than others. This makes it impossible to convert all stardates into equivalent calendar dates, especially since stardates were originally intended to disguise the precise era of Star Trek.
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. Pick any combination of four numbers plus a percentage point, use it as your story's stardate. For example, 1313.5 is twelve o'clock noon of one day and 1314.5 would be noon of the next day. Each percentage point is roughly equivalent to one-tenth of one day. The progression of stardates in your script should remain constant but don't worry about whether or not there is a progression from other scripts. Stardates are a mathematical formula which varies depending on location in the galaxy, velocity of travel, and other factors, can vary widely from episode to episode.
(The "percentage point" mentioned was in practice a single decimal.) The official timeline places TOS between the years 2265 and 2269, with the second pilot beginning on stardate 1312.4 and the last-produced episode on stardate 5928.5. Despite the guideline to "pick any combination", the list of episodes shows stardates increasing with time in general, albeit with many instances of a number being lower than in the preceding episode.
Stardates were revised from the above description for Star Trek: The Next Generation and all the subsequent shows and movies set in the same era. They were described as follows in Star Trek: The Next Generation Writer's/Director's Guide of March 23, 1987 (p. 13):
A stardate is a five-digit number followed by a decimal point and one more digit. Example: "41254.7." The first two digits of the stardate are always "41." The 4 stands for 24th century, the 1 indicates first season. The additional three leading digits will progress unevenly during the course of the season from 000 to 999. The digit following the decimal point is generally regarded as a day counter.
Stardates of Star Trek: Deep Space Nine began with 46379.1, corresponding to the sixth season of Star Trek: The Next Generation which was also set in the year 2369. Star Trek: Voyager began with stardate 48315.6 (2371), one season after TNG had finished its seventh and final season. As in TNG, the second digit would increase by one every season, while the initial two digits eventually rolled over from 49 to 50, despite the year 2373 still being in the 24th century. Star Trek: Nemesis was set around stardate 56844.9.
According to Roberto Orci, stardates were revised again for the 2009 film Star Trek so that the first four digits correspond to the year, while the remainder was intended to stand for the day of the year. For example, stardate 2233.04 would be January 4, 2233. Star Trek Into Darkness begins on stardate 2259.55, or February 24, 2259.
In the various TV series, four-digit stardates have been read out in groups of two digits as well as digit-by-digit, whereas only the latter pronunciation has been used with five-digit stardates. For example, stardate 1312.4 can be pronounced "thirteen-twelve point four" as well as "one-three-one-two point four", but stardate 43989.1 is pronounced "four-three-nine-eight-nine point one".