Stellar Aberration and Retarded Position
1. Stellar Aberration … the View from Frame K.
Fig. 1_1 depicts a point source of light at rest in inertial frame K. The telescope is at rest in frame K’, which moves in the positive x-direction of K at speed v. Owing to its motion relative to the light source, the scope must be tilted slightly in order for photons to propagate from the scope entrance to the eyepiece without being absorbed by the scope walls.
Moving Scope, Tilted to View the Resting Light Source
The requirement that the scope be tilted is well known in astronomy. As the Earth orbits the Sun (presumed to be at rest with the other "fixed stars"), the tilt of Earth-bound telescopes must be adjusted slightly throughout the year in order to keep a given star in view. The effect is referred to as stellar aberration. The tilt angle is the same for all stars, near and far.
2. Retarded Position … the View from K’.
We should be able to explain the required tilt from the perspective of frame K’, relative to which the scope is at rest and the light source moves to the left at speed v. And as discussed in another article, from the resting scope’s perspective the apparent location of the light source is the same as its retarded position. Fig. 2_1 illustrates.
Scope Pointed Toward the Moving Source’s Retarded Position
As previously derived, xr’ is proportional to yS:
Thus the tilt angle, q’, is the same for all sources, near and far.
Now cos(q) and cos(q’) are not quite equal (owing to length contraction). But the transformation is straightforward. For present purposes suffice it to say that one frame’s stellar aberration model is another frame’s retarded position model. Although both K and K’ agree that the scope must be tilted, each has its own explanation of why this must be done … a type of disagreement often encountered in Special Relativity.