Well I'm kind of disapointed by what I see there. I don't remember where I read that, but I once read that when travelling at a relativistic speed, stars in the sky gather in a narrow angle in front of the traveler, just in the motion axis. This is due to the fact that waves coming from asides or even behind seem to be coming from the front (I once managed to understand why, but I forgot later. It's not easy to understand).
In
this video for instance it doesn't seem to be so.
Apart from the doppler effect, doesn't the sky look different at near light speed?
PS. I remember now.
Say a traveler travels at v in the x direction. A star very far away in the y direction emits a plane wave exp j(ky - t) [c=1]
In the reference frame of the traveler, we have y' = y, t' = gamma*(t - vx), so the plane wave becomes:
exp j(ky' - (t'/gamma + vx')) = exp j( (ky' + vx' ) - t'/gamma )
and it's clear that the propagation vector of the wave is now slightly pointing towards the x' direction. (Also, the angle seems to depend on the wave length of the light, which is weird)
PS#2. Ok found a simulation including it:
http://apod.nasa.gov/apod/ap111018.html It's called angular compression.
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