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Originally Posted by gwiz
One g for one year gets you near to light speed, so a reasonable time for a journey with hypothetical drive which would provide this acceleration is light travel time plus the best part of two years, eg six years from Alpha Centauri.
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Don't forget relativity. Well before you get to lightspeed, you'll need to increase your thrust in order maintain 1 G of acceleration. The force you need to go faster will increase exponentially as you pass 77% of lightspeed.