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Disclaimer: I'm asking for a friend on Wordbuilding.SE, and since many people there seem to have a great misconception on the matter, it thought it will be helpful for everyone. The full question is this one, but I'll summarize it here. I'll rely on you guys to explain it better than me, on a site that is more suited for this kind of question than on the comment section of Worldbuilding.

Let's say that 2 ships are travelling at 0.8c (originally the asker seems to consider it as an absolute speed in a fixed frame reference, we can consider it's relative to Earth). Both are going in the same direction, so they are immobile relative to each other, only seperated by around 1AU. They want to communicate via a laser beam.

The question is : how their speed will affect the laser beam?

My take on this is that their speed only exists relative to external things (the Earth, their destination and probably some space dust in between), but since they are at rest relative to each other, the laser beam will travel just fine since light travels at $c$ as seen from any point of reference (no redshift, no "aiming formard" needed, and only a small 8 minute delay in communication due to the distance between the two ships).

However, some people seem to think of speed as an absolute thing, and that, for example the laser can't go faster than $0.2c$. While this is wrong, I'm not really good at explaining and I though it would be an interesting question for Physics.SE.

Again, the goal is not to pick the right answer, but to explain it so that everyone can understand (for Science, you know).

Qmechanic
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Keelhaul
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The ships are stationary relative to each other, and so can communicate using lasers as normal. So you are correct that there is an 8 minute delay to the messages sent between the ships from the perspective of their crews, and they do not need to aim ahead.

From the reference frame of the Earth it is indeed true that the component of the velocity of the light that is parallel to the line between the ships will be less than c (3/5 c to be exact) and the light delay becomes $8/(3/5)=40/3\approx13.3$ minutes. But in this reference frame the passengers on the ship have their time dilated by a factor of $\gamma=\frac{1}{\sqrt{1-\left(0.8\right)^2}}=\frac{5}{3}$, and thus don't notice this, since the 13.3 minutes in the Earths frame is then the same as $13.3.../\gamma=\left(\frac{40/3}{5/3}\right)=8$ minutes in the ship frame.

JSorngard
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