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I'm racking my brain over what should be a simple problem in special relativity. Consider the angle $f$ between two stars, as measured by a an observer at rest: enter image description here

The observed angle should be the same whether the observer is moving towards the stars, or the stars are moving towards the observer. In the first case, we have the classic formula for stellar aberration: $\cos f' = \frac{v/c + \cos f}{1+v/c \cos f}$ enter image description here

But in the latter case, it seems to me that the star can simply emit light at the angle $f''$ with $\cos f''=\frac{\cos f - v/c}{1-v/c \cos f}$ and still reach the observer: enter image description here

So in the first case, the observer measures the stars to be $f'$ apart, but in the second case, they appear to be $f$ apart. What am I missing??

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  • $\begingroup$ Well that is correct. Now we may ask how is principle of relativity not violated. Are we asking that? $\endgroup$
    – stuffu
    Jul 20, 2017 at 3:15

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