The recent discovery of HD85512b only 36 light years from Earth has promising attributes to harbor life. Assuming we want to travel there, we cannot instantaneously jump to light speed, (StarTrek euphemisms aside), we'll have to accelerate the conventional way by building momentum.
Now, how long would it take to first reach the speed of light at a rate of acceleration that wouldn't kill the occupants of the spacecraft ? (We can't continuously accelerate at 4g's for prolonged periods because it would eventually kill you from physical stress.) Secondly, then given the time to accelerate to the speed of light, how long would it then take to travel the remaining distance and reach our new utopia ?
Answer
At constant 1 g acceleration half-way through, then constant 1 g deceleration the remaining half, it takes 7 years in rocket time, 38 years in Earth time:
http://www.cthreepo.com/lab/math1.shtml
Scroll down to Long Relativistic Journeys and enter your data.
To the Andromeda Galaxy (2.5 mil ly) it's 29 years in rocket time! :)
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