 Relativistic aberration

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.

Relativistic aberration is a phenomenon predicted by the theory of relativity that describes how the observed direction of light from an object changes depending on the relative motion between the observer and the source of the light at relativistic speeds (that is, speeds comparable to the speed of light).