# A question of mathematics.

## Recommended Posts

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.

##### Share on other sites

http://www.fourmilab.ch/cship/timedial.html

This provides good indication of the effect of velocity on time dilation.

At 10% the speed of light the effect is very small and is calculated using the time dilation formula at the top of the article.

##### Share on other sites

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.

http://mysite.verizon.net/res148h4j/javascript/script_starship.html

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.

## Create an account or sign in to comment

You need to be a member in order to leave a comment

## Create an account

Sign up for a new account in our community. It's easy!

Register a new account