I have started reading about relativity and am grappling with the following issue.
If I shine a light beam from a device no matter whether I'm standing still or moving at e.g. 50km/h in the direction of the beam, the light beam will move away from me at the constant speed of light. I understand that the speed of light relative to the observer is always the same no matter the speed of motion of the observer.
However, if I shine a strong enough beam of light towards a planet exactly 1 light year away, it will take that light 1 year to reach the planet. Let's say I then within 10 seconds travel behind the beam at a fraction below the speed of light. If the beam I shone from my device is always moving away from me at the speed of light despite my speed, when do we both reach this planet? That is from the planets perspective, (assuming there are people thereon to observe the approaching beam and me).
Do we not both reach the planet within 10 seconds of each other, yet from my perspective if the light is travelling at a difference being the speed of light ahead of me, it will reach the planet that much quicker than me and not 10 seconds? What would the difference in time be from my perspective and the people on the planet's perspective and why? I'm confused.