How do I calculate time dilation due to acceleration in SR please?

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The discussion revolves around calculating time dilation due to acceleration in special relativity (SR) for a journey between two space stations 10 light years apart. The user describes traveling at a constant velocity of 0.5c, noting that while 20 years would pass for those on the stations, they would age only 17.3 years due to length contraction. They then consider a scenario involving constant acceleration at 1g for half the distance, leading to calculations that yield a trip time of 4.85 years for the traveler and 11.78 years for the space stations. The user seeks clarification on the calculations and expresses difficulty with the notation. The discussion emphasizes the complexities of relativistic travel and the effects of acceleration on perceived time.
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2 space stations are separated by a distance of 10 light years and are at rest wrt each other. I set off from A to B at a constant velocity of 0.5c.

As I understand it, 20 years would pass for people on the space station but when I arrived at the second station I would have only aged about 17.3 years and only traveled about 8.6 light years due to length contraction.

So imagine a similar situation, but this time I constantly accelerate at 1g for half the distance and then decelerate at 1g or the other half of the distance.

I found an online calculator that gave me the answer as below but it did not show me the math.
My trip time = 4.85 years
Space Station time = 11.78 years

Can anyone show me how this was calculated and how to work out what distance I have traveled please. (I am not very good at the understanding notation so would appreciate it if you could add a comment or two please!)

EDIT: When I work out the time just using t=sqrt(d/a) I get 4.4 years in the space station FoR. (I.e. 2.2 years to travel 5 light years at constant acceleration of 1g + same again for deceleration.)
 
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Physics news on Phys.org
http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html
 
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jtbell said:
http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html

Excellent! Thanks. :smile:
 
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