How long would it take to get to Alpha Centauri?

1. May 1, 2013

yoyopizza

So Alpha Centauri is about 4.37 lightyears from earth, but that's in earths frame of reference, if you could build a spaceship to go, say 9/10c relative to earth how long would it take to get to alpha centauri, because then space-time would be warped and therefore it would no longer be 4.37 lightyears away relative to the space craft. Also what equation did you use so I can modify it if it takes to long(i'm writing a story, and it needs to be reasonable like 50 years or so if possible)

2. May 1, 2013

PAllen

How long for who, someone on the spaceship or someone on earth? For someone on earth, it would appear the ship took (4.37 / .9) years to arrive. For someone on the spaceship, it would appear to take less time: (4.37/.9) √(1 - (.9)^2)

Plug other numbers in for .9, as you see fit.

3. May 1, 2013

yoyopizza

When you put (4.37/.9) √(1 - (.9)^2), is that (4.37/.9)* √(1 - (.9)^2), or (4.37/.9)/ √(1 - (.9)^2)

4. May 1, 2013

VantagePoint72

The first one.

5. May 1, 2013

VantagePoint72

Also, note that if ~50 years (from the spaceship's) reference frame is what you're after, you only need the ship to travel at around 0.09c. At this speed, relativistic effects are sufficiently small that it's only a couple months longer in the earth's frame.

6. May 1, 2013

ghwellsjr

I don't know what problem you're trying to solve but the one the OP stated requires a speed very, very close to that of light, slightly faster than 0.999934c.

7. May 1, 2013

PAllen

Huh? To get to alpha centauri in 50 years? Even for earth time, it's only 4.37 light years, so 1/10 c would take 43.7 years to get there.

8. May 2, 2013

9. May 2, 2013

VantagePoint72

I think it would be helpful if you explained which problem you are trying to solve. The OP's problem was going to Alpha Centauri in 50 years (according to the rocket's frame) which is what I solved.

10. May 2, 2013

ghwellsjr

You guys are right. For some reason, I was thinking the distance was 4370 light-years, so I was the one that was misrepresenting the OP's problem.

Thanks for the correction and sorry for the mixup.

11. May 2, 2013

Eli Botkin

To yoyopizza:
Travel to a distant star needs to be realistically comfortable for the travelers. That implies that spaceship acceleration (to speeds near light speed) should be about the same as the gravitational acceleration one experiences on Earth, namely 1g (which = 1.0326 ly/y^2).
Accelerating at 1g to the midpoint and then decelerating at 1g from midpoint to Alpha Centauri will result in a trip time of about 3.58 years on the travelers’ clock and 6.00 years on Earth’s clock. At midpoint the speed will be about 0.952 c.

12. May 2, 2013

Eli Botkin

To yoyopizza:
I should have mentioned in the earlier reply that your story need not be limited to traveling to Alpha Centauri. With 1g acceleration/deceleration any galaxy/star in the observable universe (that is, out to about 13.7 BILLION light-years) can be visited with less than about 45 years of traveler's time.

13. May 2, 2013

VantagePoint72

The amount of energy needed to uniformly accelerate a spaceship at 1g for billions of light years is astronomically large. I suspect it would violate yoyopizza's requirement of "reasonable".

14. May 2, 2013

Eli Botkin

To LastOneStanding:
Yes of course, if you have to carry all the needed fuel at take off (old technology).

But what if technology has advanced to the point where the ship can gather its fuel components from intergalactic space (Hydrogen, Helium), manufactures what's needed, and exhausts it at higher velocity?

15. May 2, 2013

yoyopizza

Thanks guys this should be more than enough, when I mentioned 50 years I just meant it had to take less than that. Also, thank you Bandersnatch for the calculators, I plan to use them in the future!