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In a previous thread https://www.physicsforums.com/showthread.php?t=240886 we concluded that an observer moving away from a luminous object would see the luminosity as reduced by a factor of 1/(1+z)^n where n is 3 or 4 and z is defined as :

[tex]z= \frac{\sqrt{1+v/c}}{\sqrt{1-v/c}} -1[/tex]

The question in this thread is how would the apparent angular size of an object be calculated?

For example if a observer was passing the Earth at a relative velocity of v/c moving away from the sun, would the angle subtended by the disk of the Sun appear to larger or smaller (and correspondingly nearer or further) than the angle measured by an observer that stationary with respect to the Earth?

First guess would be be that distances tangential to the relative motion are Lorentz transformed so that there would be no change in angular size. Further thought suggests that the moving observer would see the the Earth-Sun distance as length contracted and so she should see the Sun as subtending a larger angle so as to maintain the aspect ratio. In other words the moving observer considers himself to be nearer the Sun than the stationary observer and so she should see the Sun as a larger disk.

Relativistic aberration also suggests that an observer would see objects behind him as subtending a larger angle than when she is at rest with those same objects at the same distance.

Please ignore the effects of gravity to keep thing (relatively) simple :)

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# Angular distance in SR

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