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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.

Relativistic aberration is the change of an incoming ray's apparent direction between relatively moving inertial frames. It follows by applying a Lorentz transformation to a photon's four-momentum, so the effect changes angles even when the source and receiver are observing the same ray.

If a photon propagates at angle $\theta$ to the positive $x$ axis in frame $S$, and $S^{\prime }$ moves at velocity $v=\beta c$ along that axis, thenThese are propagation-direction angles; the sky position from which the light appears to arrive points in the opposite direction. That distinction avoids sign errors when applying the formula to stellar observations. The annual stellar aberration amplitude uses Earth's changing orbital velocity, whereas stellar parallax uses a changing viewing position and depends on the source's distance.