## Time dilation problem

The distance to Alpha Centauri is 4,3 light years. How fast would a space ship have to travel to get there in 10 years, according to the crew?

The answer *should* be 0,395c. So far I've gotten all sorts of answers but not much close, so I seem to be approaching the problem the wrong way.
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 The first part of the assignment asks for the time required when traveling at 30% of light speed. Given a gamma factor of 1,048 I get ~13,7 years, which is correct (so the gamma factor must be correct as well). velocity = distance / time But... for t = 10 and d = 4,3 v = 4,3 / 10 v = 0,43, which is wrong taking length contraction into account gives 4,3/1,048 = 4,1 v = 4,1 / 10 v = 0,41, which is still wrong

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## Time dilation problem

 Quote by spXq Edit: velocity = distance / time
Good. Keep going.

From Earth's viewpoint, you have the distance. What's the time?

 Quote by Doc Al Good. Keep going. From Earth's viewpoint, you have the distance. What's the time?
Hmm... i don't know. :/

The distance is 4,3 ly but I don't know the speed, so how do I find the time?
 Hang on... the time for the crew is 10 years so the time for the observer is t/gamma 10/1,048 = 9,54 years Edit: no that's not right....... I have no idea what I'm doing Edit2: the time from earths viewpoint is d * gamma = 4,3 * 1,048 = 10,48 years, while the time is 10 years for the crew

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 Quote by spXq Hang on... the time for the crew is 10 years so the time for the observer is t/gamma
You have that reversed. If the ship time is 10 years, then to earth observers it will be longer: t*gamma, not t/gamma.

 10/1,048 = 9,54 years
In addition to what I already pointed out, do not use the gamma from the previous part of the question.

So continue with that velocity equation, v = d/tearth.