Booyakasha!

Imagine an interstellar human trip to Barnard's Star, onboard a futuristic starship, using some as-yet-unknown propulsion system. This drive is capable of accelerating the starship at a constant 1 G for years at a time, making the crew quite comfortable on board.

The stats (some numbers rounded):
Of course, the crew won't be parachuting out of the starship at 0.97% speed of light as it screams past Barnard's, so halfway through the trip, we need to spin the craft around and spend the second half of the voyage decelerating.

Can anyone do the math on that? In other words, start accelerating at a constant 1g from our system, then build up speed until about the halfway point, then start decelerating all the way until coming to a dead stop in the Barnard's Star system. How long would the whole trip, one-way, take?

This calculator HERE seems to show that the trip would take about 4 years for the crew, and about 7.7 years back on earth, due to relativistic time dilation. Is that right?

Jesse

Check out The Relativistic Rocket, which gives formulas for exactly this problem of a rocket undergoing constant acceleration. Note that the time as measured by observers at rest relative to the earth/Barnard's star is different from the onboard "proper time" measured by the astronauts. Also, the formulas are just for constant acceleration, so if you want the crew to start decelerating at the halfway point, then you want to calculate the time to get halfway to the destination using these formulas, then just double it.

Styrofoam

Are you just giving this to us a little problem to do? I saw times there, both for the crew and on earth before you edited them out.

Booyakasha!

Styrofoam, sorry, I wasn't sure if they were correct.

Booyakasha!

Ah, cool. So a trip to Vega, 27 light years away, would take 6.6 years for the crew, while back on Earth, about 29 years will have passed, one way.

Styrofoam

Oh, okay. No offense intended.