= 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,
$$
v=\frac{2\pi(1.5\times10^{11}\,\mathrm m)}{365.25(86400\,\mathrm s)}=2.99\times10^4\,\mathrm{m\,s^{-1}},
\qquad
\boxed{\delta\simeq9.96\times10^{-5}\,\mathrm{rad}=20.5\text{ arcseconds}.}
$$
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.
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