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I've wondered about this since I was a kid. I've been told the speed of light is a constant ($c$), which would mean that light always travels at the same velocity. Now, here's what interests me: if I'm the source of light for a given observer, light would travel away from me and towards the observer at the speed of light when measured from our absolute positions at that time. Because of this, my velocity at the time of "emission" seems to be irrelevant to the absolute velocity of the light I'm sending.
However, for the calculation of time it takes for the light to reach the observer, its velocity seems in fact to be relevant, because its velocity determines when the light would reach the observer. I hope I still make sense.
Say me and the observer are a light-minute apart and the observer is travelling towards my absolute position at the time of emission at a speed of $c/2$. Would I be correct to assume that the light would reach the observer (or the other way around) in 40 seconds?
My absolute position would be quite hard to calculate. However, my position relative to the observer is relatively easy to calculate during the experiment, so let's say I'm also travelling at $c/2$ in the exact same direction as the observer. The observer would still meet my light after 40 seconds, even though from where I'm standing it looks like the observer is not moving at all. Am I still correct so far?
Let's say I turn around and move towards the observer at a speed of $c/2$. The observer would still meet the light I emitted after 40 seconds, but our relative speed towards each other would be exactly the speed of light. So, relative to another moving object, I can move at the speed of light or even approximate a speed of $2c$. Does that make sense?
Why I'm asking this
In space travel, distances are often measured in light years. Because one would not be able to travel at the speed of light, travelling at almost the speed of light would mean that you would need just over 30 years to reach another star system that is located 30 light-years from Earth. But as our galaxy is expanding, it could be that all these star systems are moving away from the center at a certain speed (say $c/2$). Assume that the center of our galaxy does not have an absolute velocity. Moving to a star system that is located between Earth and the center of our galaxy at almost the speed of light would mean that I'm moving away from Earth and towards the other star system at a speed of almost $1.5c$, meaning I would reach the other star system in approximately 18 years, even though it's 30 light-years away.