Final answer:
According to special relativity, all observers measure the speed of light as constant ('c'), regardless of relative motion. Hence, regardless of how two spaceships approach each other, each will measure the light from the other at the same speed. Length contraction and constant light speed are key concepts in understanding these relativistic scenarios.
Step-by-step explanation:
Understanding the Speed of Light in Special Relativity
When discussing spaceships moving at speeds close to the speed of light, the principles of Einstein's theory of special relativity come into play. According to special relativity, the speed of light in a vacuum, denoted as 'c', is always measured to be the same by all observers, regardless of their relative motion. This means that even if two spaceships are approaching each other at high speeds, each will measure the speed of light from the other as 'c'.
In the scenario where a spaceship moves towards the Earth at half the speed of light and sends a light signal, we would still measure the speed of that light as 'c', due to the invariance of the speed of light. This concept is counterintuitive, as our classical intuition might suggest that speeds should simply add up.
However, relativistic velocity addition shows us that this is not the case when dealing with relativistic speeds. Moreover, if we observe a spacecraft traveling at 95% the speed of light, its length contraction would be apparent, another fascinating consequence of special relativity.