I am trying to wrap my head around some of the implications of relativity. Hopefully somebody can help enlighten me with a specific example I am wondering about:
We have 2 objects, A and B, that are traveling away from each other and emitting light towards each other. We also have a "stationary" object, C, that will be one of our observers stationed between A and B.
According to C, A is traveling at 0.6c in one direction and B is traveling at 0.6c in the opposite direction. From C's perspective there is 1.2c relative motion between the objects.
I am trying to figure out the perceived behavior of the light from the reference frame of the 3 different objects. I believe A and B will see the same thing so are equivalent, this leaves 2 different reference frames.
My assumption is C will see 1.2c relative motion between the two objects, but since all light is traveling at 1c from C's reference, the light from A will eventually reach B. From C's point of view, is there a 0.4c relative motion between A's light and B? My thinking is that C sees A's light going 1c towards B but B is receding at 0.6c so there is 0.4c difference. I am not confident in these assumptions. Does the time-dilation effect of the relative motion between these objects alter this?
The situation from A's point of view is harder for me to think about. B cannot seem to be moving faster than c from A's (or anybody's) point of view. How fast DOES B appear to be moving away from A (in A's point of view)? How does this affect A's perception of light from B (or vice versa)?
Finally, if an object leaves A heading towards B at 0.61c (relative to A), will it ever reach B? From C's perspective I don't think it does (C will see the object approaching at 0.1c, clearly not fast enough to approach B). If not, what speed would an object need to have, relative to A, to reach B? Does whether or not this object appears to reach B depend on your reference frame?
I apologize in advance if this is too many questions at once, or otherwise inappropriate. I have attempted to solve this for myself by searching this site and google but haven't found anything that clicks with me yet. If there is already a question/answer on this sight that could help me better understand this type of thing I would love to learn about it. I would really like to gain an intuitive understanding of how these things work, so analogies and metaphors are appreciated. That said, as an engineer I am not afraid of mathematical explanations, just understand that if I ever studied this stuff it was many decades ago and long forgotten...so baby steps.