# Aerospace The theoretical max. speed in deep space

1. Nov 3, 2012

### Faux Carnival

Hello,

Isn't the theoretical max. speed in deep space unlimited? There is no friction. Therefore, any energy we add to the spacecraft will increase its speed. So can't the speed of light be reached?

Thanks.

2. Nov 3, 2012

### tiny-tim

Hello Faux Carnival!
(hmm … i thought pf had an faq on this, but i can't find it )

first, we add momentum, not energy (force times time = change in momentum)

second, yes we can keep adding momentum, and the speed will keep increasing , but it will never quite reach c

(momentum = mv/√(1 - v2/c2) -> ∞ as v -> c)

3. Nov 3, 2012

### Faux Carnival

Thanks for your reply. I was thinking of kinetic energy. They seem to be the same thing anyway.

But my thinking is not flawed, right? In space, accelerating from 30,000 to 31,000 km/h is the same thing as accelerating from 50,000 to 51,000 km/h?

4. Nov 3, 2012

### tiny-tim

Nope!

The latter involves slightly more change in momentum … mv/√(1 - v2/c2) … than the former.

And so the latter takes slightly more force (technically, impulse) than the former.

And the closer you get to the speed of light, the greater the difference!