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

1. Aug 24, 2011

### rede96

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. Aug 24, 2011

### Staff: Mentor

http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html [Broken]

Last edited by a moderator: May 5, 2017
3. Aug 24, 2011

### rede96

Excellent! Thanks.

Last edited by a moderator: May 5, 2017