Okay, lets say you have frame S which is a spaceship who is travelling with speed v = c/3 relative to S' which is some planet Y. In the spaceship two photons are shot in opposite direction, to the right and the left. What would the velocity of both photons be in the S' frame. I think the one to the right, which let's say is positive would have +c photon, so relatively its travelling with 2c/3. But how fast does the other go, as it can't go faster than the light speed. I'm really stuck with this so any help is much appreciated!!
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A photon in a vacuum is always traveling with $v=c$. The relative speed of the two photons to each other is $2c$, in both the system of the spaceship and the planet.
On the planet, the photon going in forward direction has relative speed to the spaceship of $2/3c$, and the backwards travelling photon $4/3c$.
In the spaceship, the forwards backwards moving photon both have a relative speed of $c$, w.r.t. to the ship.
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