I know this question, or similar ones have likely been asked before, but I have tried reading several, and they just don't properly explain what I'm trying to understand.
The quick version of the question is, if 3 bodies, each relative to the previous are moving at a speed where their combined velocity would be greater than the speed of light, what would be the final velocity of the 3rd body during the fastest time.
For this I'll be using 3 bodies, A Galaxy, Solar System & Planet.
To make the numbers simple, I'm going to round c to 3 million m/s
If the galaxy was moving at 1.5m m/s (0.5 c)
A solar system in that galaxy was moving around the galaxy at 1.2m m/s (0.4 c)
And a planet was moving around that sun at 600k m/s (0.2 c)
Relative to a static observer, during the ideal time, when the planet is moving away from the observer and the solar system is moving away from the observer, the combined velocities of the 3 would be (1.5 + 1.2 + 0.6 = 3.3m (1.2 c ) which is impossible according to general relativity.
Now, I know that some of the math here will move into special relativity, which I'm not quite as familiar with, but as they are all traveling at a relatively slow velocity (relative to their frame of reference), how would the planet be affected as it moves into the part of its rotation where to the static observer it would be moving faster than the speed of light?
I guess what really confuses me is, I know that c is a constant, and that relative speeds are not the same. I also have a limited knowledge of special relativity which may be what is hampering my understanding in this case.
What if someone tried to launch a space ship off the planet while its going 3.3m m/s (from the static reference frame)