# Relativity Question: Two spaceships following each other near C

1. Aug 13, 2004

### relativitydude

Howdy,

What equations do I use to calculate how frame A observes frame B's velocity and vice versa if two spacecraft are following each other?

is it:

v = ux + v / ( 1 + (Ux*v)/(c^2))

I have a feeling it isnt since if both craft are travelling say, 2.5*10^8 m/s, then the observed speed from another frame is .98c off the top of my head. I know this is relativity and all, but shouldnt frame A perceive frame B as simply going 0 m/s?

2. Aug 13, 2004

### Integral

Staff Emeritus
That is correct, if the 2 ships would have the same velocity then you do not need to use the equations of SR. Note that there must be some reference frame from which they measure a velocity of .95c. That is the frame which must use relativity calculate the ships speed and distance traveled.

3. Aug 13, 2004

### relativitydude

Thanks.

Now lets say ship A is traveling .6c and ship B is traveling .8c, a would view b speed as...

v = ux - v / ( 1-(ux*v)/(c^2))

or

v = (.8c - .6c) / ( 1- (.6c*.8c)/(c^2) = .34c

so ship A view ships B as travelling .34c faster?

4. Aug 13, 2004

### Staff: Mentor

Assuming you mean that A travels at 0.6c and B travels a 0.8c with respect to some common frame.
Right.
Closer to 0.38c
Ship A sees ship B moving at a speed of 0.38c with respect to ship A. And vice versa.

5. Aug 13, 2004

use:
$$u' = \frac {u+v}{1- \frac{uv}{c^2}}$$

6. Aug 13, 2004

### relativitydude

Thanks Everyone :)