| Abstract
| - Points on the surface of a sphere can be mapped by stereographic projection to points on the plane of complex numbers. If the points on the sphere are identified with the directions of incoming light rays, then the effect of a Lorentz transformation, a rotation plus a boost, is represented by a bilinear or Möbius transformation applied to points on the complex plane. This procedure allows the effects of the aberration of light, precession and nutation, required for computing the mean and apparent positions of celestial objects, to be accounted for in a common framework and yields expressions that are readily evaluated in practice. The general form of the bilinear transformation representing a pure Lorentz boost is derived. Explicit expressions are given for the bilinear transformations representing aberration, precession and nutation as well as frame bias and transformations to the Celestial Intermediate Reference System. The approach described simplifies, and is an alternative to, the standard matrix methods commonly used to perform coordinate system rotations.
|
