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I have a question about relativistic speed and the math behind it.

I was wondering: If I were traveling at 10% the speed of light (about 18,600mps by my estimates) exactly how long would it take to reach our nearest star at Proxima Centuri.

I figured around 42 years, but I would love to know the exact equation that would be used in this instance.

I don't know if anyone here would know, but its just a bit of fun for me to try and figure these kinds of things out.

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Yes - if you do the simple maths, this is right.

velocity = distance/time, so time = distance/velocity, time = 4.3 LY / 0.1 LY/year = 43 years

However - you are now travelling at a fair percentage of the speed of light, so special relativity applies. However 10% doesn't make a lot of difference, it affects things by ~1.005 times. So this comes out at about 42.78 years on board I think if I've got my equations right.

(4.3LY / (gamma * 0.1)

gamma = 1/sqrt(1-v2/c2)

It's more interesting if you consider acceleration, the equations get a bit more complicated, but there is a useful website here that does it for you.


So if you accelerate/decelerate at 1g, its just 3 1/2 years on board, but you are peaking at 0.95c

The savings get better for further away stars.

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