# B Object A is moving relative to O , what does it mean?

1. Mar 20, 2017

### diazdaiz

since i am new at learning special relativity, i still miss the concept about how thing move in special relativity. In highschool, i am doing several problem about velocity addition, and that word always appear. for example:
A is moving with velocity vAO relative to O, and B is moving with velocity vBO relative to O, what is A velocity relative to B?
and then i am using formula
VAB=(VAO+VOB)/(1+VAO.VOB/c2)
and then you get the answer
but i can't really understand it. So i try to draw it
(in this image, i just draw object O and A (without B), so i can understand what VAO really mean)
(let say that A is travelling 0.5c from our viewpoint)

so, VAO will be 1/3 c because O see A only travel 1.5x108m after 1.5 second (or 3x108m after 3 second), is this what we say A is moving relative to O?

2. Mar 20, 2017

### Vitro

No, A moving relative to O means that the position of A as measured by O (in O's coordinate system) changes over time. The relative speed $V_{OA}$ is the change in A's position $\Delta x$ over the interval of time $\Delta t$ (as measured in O's coordinates), and in your diagram it's just 0.5c. Nothing to do with what O sees (i.e. light from A reaching O).

3. Mar 20, 2017

### diazdaiz

thank you very much, that's the keyword, its measured from O's coordinate

4. Mar 20, 2017

### Vitro

The fact that A and O are moving relative to each other is invariant, you could use any inertial frame to make that determination. But if you want to measure their relative velocity then you need to use either A's or O's coordinates. Using a different frame of reference will give you what's called a closing or separation velocity which is not the same thing as their relative velocity.