They must have been awfully close to Federation space to be able to get back in only three years without FTL travel.
Assuming that full impulse is 1/4 the speed of light as has been proposed elsewhere, if they maintained that speed the whole time, then they travelled 3/4 of a light year at most. And I think at that speed there would be issues with time dilation.
First off, "full impulse" (as it's called in the
ST Encyclopedia) doesn't mean the maximum
possible impulse speed. That's a common misapprehension. "Full speed" is naval parlance for the maximum
standard speed used in routine situations, which is less than "flank speed," the maximum
possible velocity for emergencies. The
TNG Tech Manual explains in more detail that it's preferred to limit impulse operations to 1/4 lightspeed to avoid time dilation effects, but makes it clear that speeds far closer to the speed of light are well within the realm of possibility for impulse engines.
After all, movement in the vacuum of space isn't like moving over ground or water. There's no friction to cancel thrust (well, hardly any), so it's contradictory to equate a level of engine power with a
constant speed as we do on Earth. In space, you maintain a constant speed by coasting; if you apply forward thrust, you go faster, period. Even if your thrust is tiny, you can accelerate arbitrarily close to the speed of light if you just keep it up long enough. So there are no "speed limits" in space short of the speed of light itself (or the point very close to it where drag from the interstellar medium or from the intense bombardment of blueshifted cosmic background radiation would be sufficient to cancel further acceleration, but that's too small a difference to matter).
Therefore, there's no reason why a ship at impulse couldn't accelerate arbitrarily close to the speed of light, as long as the engines held out and the fuel didn't run dry. If it could accelerate at, say, a steady 100
g, it would take only three and a half days to get to 99% of lightspeed. At 10
g, it'd take 35 days, and so on -- it's pretty linear. (Acceleration equals velocity over time, so time equals velocity over acceleration.)
Any level of impulse power, applied long enough, can take a ship well beyond 1/4 lightspeed. It's just preferred not to do so unless there's a need for it.
Second, as the above discussion implies, the time dilation at 1/4 lightspeed is minimal, only about 3 percent. A shipboard clock would lose about 46 minutes a day compared to a "stationary" clock. You have to go much closer to lightspeed before time dilation really begins kicking in.
I have a pretty bad memory for specifics myself, which is why I rely so much on checking sources.
I have the impression that you are a walking encyclopedia. Appearances are deceptive.
Well, maybe it's more accurate to say that I don't
trust my memory to be reliable. I do know a lot of facts and ideas and stuff, but it's so cluttered that I get details confused sometimes. So I try to be careful about double-checking things rather than just going from memory. (For instance, I have a spreadsheet file that I used for calculating the time dilation and accelerations discussed above.)