In Star trek TOS, I take the "Five year mission" to mean 5 years aboard the Starship. Do they explain in any of the novels, or anywhere else for that matter, how many years elapsed on Earth during the five years the Enterprise spent exploring space?
Answer
Warp drive seems to defy the general theory of Relativity, in more than one way. Specifically, it seems that the relativistic effects that would normally cause a person to change at a different rate than the outside world seem to not affect anything. The only thing that would cause relativistic effects is the impulse drive. I found a forum on StarTrek.com that seems to indicate that the maximum speed that Impulse drives typically use is .25c. According to the relativity calculator, this would create a dialation of about 3%.
All in all, I'm guessing that a few days would have been gained due to relativistic effects, but nothing significant.
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