I think the relevant equations are here:
but I have no idea of how to apply them.
I just finished a rather good Science Fiction book, "Red Thunder" by John Varley. In it, a device is invented that draws unlimited mass and energy from elsewhere and it is used as the propulsion of a spacecraft. Using it, the protagonist is able to get to Mars in about three days.
In an off-hand remark at the close of the book, the narrator indicates that he'll be leading a colony ship to a star that is 30 light years away, and says that it will take about 1 year ship's time, and that he could actually pick from a number of stars, e.g., one that is 60 LY distant and it would take about one year ship's time to get to any of them.
The idea is that (I ASSUME) once you reach any large fraction of the speed of light, you travel vast distances in virtually no (shipboard) time... that, for instance, if you stay at that velocity for a few more (shipboard) days you'll have gone 30 LYs further than if you had started decelerating a few days earlier.
In the Mars trip, they accelerate at a constant 1G, and I ASSUME that the same would be used for longer trips.
"Hard SF" authors are usually very good at getting such details correct (else they get raked over the coals in reviews). But in a couple of wikipedia sources, I've seen that one could only reach about 77% light speed in one year of constant 1G acceleration, and Math & Science Genius ozo has stated:
>> At a 1G constant acceleration, it would take almost 2 years ship time to go a light year...
That is clearly in opposition for what I ASSUMED that the author declared.
My question(s) is (are):
For a spaceship accelerating at 1G, with turn-around at midpoint and constant 1G deceleration for the rest of the trip, how much time would elapse on the ship for a journey of
1) 30 light Years (at 1G constant acceleration)
2) 60 light years (at 1G constant acceleration)
3) 120 light years (at 1G constant acceleration)
What if they decided they were in a hurry and traveled:
4) 30 light Years (at 1.5 G constant acceleration)
5) 60 light years (at 1.5 G constant acceleration)
6) 120 light years (at 1.5 G constant acceleration)
And, the actual "core" question:
7) What rate(s) would need to be true in order to travel
"30 or 60 light years in about 1 year" shipboard time?
This time-dilation concept is rather counterintuitive, so this may sound stupid, but: Would it make any difference if they went 1.0 G for a longer distance -- somewhere beyond the halfway mark -- then decelerated at 1.5G until they reached their destination? They would be traveling at max speed longer, so would they go further in the same amount of shipboard time?
Thanks for looking into this!