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

  1. Aug 24, 2011 #1

    rede96

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    Gold Member

    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 travelled 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 travelled 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.)
     
    Last edited: Aug 24, 2011
  2. jcsd
  3. Aug 24, 2011 #2

    jtbell

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    Staff: Mentor

    http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html [Broken]
     
    Last edited by a moderator: May 5, 2017
  4. Aug 24, 2011 #3

    rede96

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    Excellent! Thanks. :smile:
     
    Last edited by a moderator: May 5, 2017
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