 Solution

During the time light crosses a telescope of length $L$, Earth moves sideways by approximately $vL/c$. The telescope must tilt towards Earth's motion so that both ends intercept the ray. Thus the annual stellar aberration amplitude at a transverse sightline is $\delta \simeq v/c$.

Taking one orbital year as $365.25$ days and treating the orbit as circular,This is the instantaneous shift relative to a stationary heliocentric observer, not the doubled peak-to-peak annual excursion. The exact Lorentz transformation for a ray transverse in that frame gives $\sin \delta =v/c$, with the same first-order result.