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

In summary, the conversation discusses the concept of time dilation and length contraction in the context of traveling between two space stations. The speaker mentions that if they were to travel at a constant velocity of 0.5c, they would only age 17.3 years when arriving at the second station, despite 20 years passing for those on the station. They then ask for an explanation for a scenario where they accelerate and decelerate at 1g for half the distance. An online calculator is referenced, which gives the trip time as 4.85 years and the space station time as 11.78 years. The speaker also mentions calculating the time using the formula t=sqrt(d/a) and getting a different result. They request
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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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http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html
 
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  • #3
jtbell said:
http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html

Excellent! Thanks. :smile:
 
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Question 1:

What is time dilation in Special Relativity (SR)?

Time dilation in SR refers to the phenomenon where time appears to pass at different rates for two observers who are moving relative to each other at high speeds.

Question 2:

How is time dilation related to acceleration in SR?

According to the Theory of Special Relativity, time dilation occurs due to the effects of high velocity or acceleration on the passage of time. As an object's speed increases or it accelerates, time appears to pass slower for that object.

Question 3:

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

The formula for calculating time dilation due to acceleration in SR is t' = t * sqrt(1 - (v^2/c^2)), where t' is the time observed by the moving observer, t is the time observed by the stationary observer, v is the velocity of the moving observer, and c is the speed of light.

Question 4:

What units are used in the equation for time dilation in SR?

The units used in the equation for time dilation are typically seconds (s) for time, meters per second (m/s) for velocity, and meters per second squared (m/s^2) for acceleration.

Question 5:

Does time dilation due to acceleration in SR have any real-life applications?

Yes, time dilation due to acceleration in SR has real-life applications in areas such as space travel and GPS technology. These applications require precise time measurements, and the effects of time dilation must be taken into account in order for them to function accurately.

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