 Solution

Let $\theta$ describe the direction towards the star, measured from the Earth's positive direction of motion. The arriving photon propagates in the opposite direction, so in the stellar frame its four-momentum hasA Lorentz transformation into the Earth's frame, moving at $\beta c$ along $x$, givesThe observed stellar bearing is opposite to the transformed photon momentum. Since a photon satisfies $|{\mathbf{p}}^{\prime }|=E_{\gamma }^{\prime }/c$,This is relativistic aberration. For small $\beta$, ${\theta }^{\prime }=\theta -\beta \sin \theta +O({\beta }^2)$: stellar directions shift towards the direction of the observer's motion. Keeping the distinction between stellar bearing and photon propagation direction explains the plus signs.