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With relativistic aberration, a sky full of stars gets concentrated in the direction of motion. As a rough measure of the degree of concentration, one could use the radius of a small circle, centered on the direction of motion, which contains the objects which, when you are at rest, are in half the sky (if you take my meaning).

Using the formula for relativistic aberration:

beta=0: half-sky radius=90 deg

beta=0.8: half-sky radius= 36.87 deg (this is just arcos(beta))

When I compare this calculation with diagrams created both by others and myself, there seems to be a difference of a few degrees, and I can't figure out why. I seem to be missing something.

For the case of beta=0.80, I measure the half-sky radius as 39 degrees. The difference is small, but it's large enough that I'm pretty sure it's not a measurement error.

You can measure this for yourself, using this diagram (created by someone else), with the 90 deg lines: http://erkdemon.blogspot.ca/2009/11/relativistic-ellipse.html

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I don't know where you measured 39°. The blue angle is 36.87° (the sides of the red triangle are 3-4-5), as it should be.

enter image description here

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  • $\begingroup$ Yes, that's the same angle, and I still see it as 39 deg. I guess the explanation is that my screen is somehow distorting the image. Weird. $\endgroup$
    – John
    Commented Dec 17, 2013 at 21:24
  • $\begingroup$ @John Yep, it's probably your screen resolution :-) $\endgroup$
    – Pulsar
    Commented Dec 17, 2013 at 21:28
  • $\begingroup$ Yes: if I change my screen to the recommended resolution, it changes to 37 deg. I didn't realize that setting could measurably distort the geometry. Interesting... $\endgroup$
    – John
    Commented Dec 17, 2013 at 21:37

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