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Time dilation problem 
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#1
Nov1312, 05:34 AM

P: 4

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. 


#2
Nov1312, 06:13 AM

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P: 41,454

Show what you've done so far.
Hints: What's the basic idea of time dilation? What's the definition of velocity? 


#3
Nov1312, 06:20 AM

P: 4

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 


#4
Nov1312, 06:22 AM

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P: 41,454

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


#5
Nov1312, 06:26 AM

P: 4

The distance is 4,3 ly but I don't know the speed, so how do I find the time? 


#6
Nov1312, 06:29 AM

P: 4

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 


#7
Nov1312, 07:21 AM

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P: 41,454

So continue with that velocity equation, v = d/t_{earth}. 


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