Relativistic aberration

Relativistic aberration is the relativistic version of aberration of light for observers who move with velocities close to the speed of light. It can be described by Einstein's special theory of relativity or other relativistic models such as Newtonian emission theory. The effect is independent of the distance between observer and light source.

Suppose, in the reference frame of the observer, the source is moving with speed $v\,$ at an angle $\theta_s\,$ relative to the vector from the observer to the source at the time when the light is emitted. Then the following formula, which was derived by Einstein in 1905, describes the aberration of the light source, $\theta_o\,$, measured by the observer:

$\cos \theta_o=\frac{\cos \theta_s-\frac{v}{c}}{1-\frac{v}{c} \cos \theta_s} \,$

In this circumstance, the rays of light from the source which reach the observer are tilted towards the direction of the source's motion (relative to the observer). It is as if light emitted by a moving object is concentrated conically, towards its direction of motion; an effect called relativistic beaming. Also, light received by a moving object (e.g. the view from a very fast spacecraft) also appears concentrated towards its direction of motion.

One consequence of this is that a forward observer should normally be expected to intercept a greater proportion of the object's light than a rearward one; this concentration of light in the object's forward direction is referred to as the "searchlight effect" (or headlight effect).