This article is from the Stardates in Star Trek FAQ, by Andrew Main zefram@dcs.warwick.ac.uk with numerous contributions by others.
Originally, stardates were used so that Star Trek could be established as
taking place a long way into the future without actually being pinned down to
a particular time. The stardates were arbitrary, chosen without regard to
consistency. The only thing that was consistent was that the stardates
generally increased. However, because episodes got out of order in the
production sequence, and were shown in a different order again, even this
could not be relied upon from week to week.
Furthermore, even ignoring obvious verbal slips, the stardate ranges of
episodes occasionally overlapped, and stardates sometimes even decreased
within the confines of a single episode. When pressed for an explanation,
Gene Roddenberry said:
This time system adjusts for shifts in relative time which
occur due to the vessel's speed and space warp capability.
It has little relationship to Earth's time as we know it.
One hour aboard the U.S.S.Enterprise at different times
may equal as little as three Earth hours. The stardates
specified in the log entry must be computed against the
speed of the vessel, the space warp, and its position
within our galaxy, in order to give a meaningful reading.
Roddenberry went on to explain that stardates would be different in different
parts of the galaxy at any one time. He admitted that he didn't really
understand this, and would rather forget about the whole thing. And that was
when there was only ST:TOS to consider.
Roddenberry's explanation does make some sense. It seems to suggest that
stardates are completely subjective. This will be dealt with in the next
section. Contradicting this, however, is the suggestion that position is
relevant to the calculation. This part of his explanation, at least, must be
discounted on the grounds of absurdity. His explanation is not canonical, so
it may be treated like any other theory.
 
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