Consider an observer B is moving with speed $0.8c$ relative to another observer A in standard-configuration (I think it is called that in english: that the system B is only moving along the $x$-axis of system A).
- At what speed will A observe the light leave the system B in the direction in which B travels away from A? Is it just $0.2c$ or would you have to use the velocity-addition formula to calculate it?
- And what about the light leaving system B in the opposite direction (towards A) seen from A relative to B? B would observe the speed as being the same in every direction (c) relative to itself, but would A see the light moving with the same speed relative to B in every directions?
- If that is actually true, then the speed of light is not the same observed by A relative to A, so I guess they would observe different happenings? So how would one calculate the speed of light emitted by B relative to B as observed by A in different directions?
Remember I do not ask about the speed relative to any of the systems themselves observed inside the system as that would always be $c$. I hope you understand the question. I gladly accept mathematical explanations.