alexis wrote:Actually, all light from stars would be infinitely redshifted in the light-speed limit!
I think you might be wrong, there. Time dilation of course has an effect, but it is eventually overpowered by first-order Doppler effects. So as your spacecraft approaches light-speed, although the
proportion of the sky that is red-shifted tends asymptotically towards 100%, the
number of stars it contains goes asymptotically to
zero - all the stars in the sky are eventually wrenched around by aberration and incorporated into the tiny blue-shifted spot ahead of you.
There's a simple relationship between the angular radius of the blue-shifted patch you see ahead in the moving reference frame, and the radius of the patch of sky it represents, as it would be seen by an observer at rest at your location:
blue-shifted radius (moving) = 180 degrees - blue-shifted radius (rest)
So as velocity increases, the moving-frame and rest-frame radii go like this:
Code: Select all
velocity blue-shifted blue-shifted
radius radius
(v/c) (moving) (equiv. in rest frame)
0.9 51.2 deg 128.8 deg
0.99 29.8 deg 150.2 deg
0.999 17.0 deg 163.0 deg
0.9999 9.6 deg 170.4 deg
0.99999 5.4 deg 174.6 deg
0.999999 3.0 deg 177.0 deg
and so on. That blue spot, although it's shrinking, is gobbling more and more of the sky.
Grant
PS: Sorry, the originally posted table was unreadable - I've converted it to "code" to get the columns to behave!