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:
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: $\cos f' = \frac{v/c + \cos f}{1+v/c \cos f}$
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:
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??
