Galilean and relativistic Doppler/aberration effects deduced from spherical and ellipsoidal wavefronts respectively

TL;DR

This paper reveals that electromagnetic Doppler and aberration effects are better represented by ellipsoidal wavefronts rather than spherical ones, leading to more accurate analysis within special relativity.

Contribution

It introduces a geometric analysis of ellipsoidal wavefronts for Doppler and aberration effects, correcting traditional spherical assumptions and deriving exact relativistic results.

Findings

Ellipsoidal wavefronts better model electromagnetic effects.

Traditional spherical models lead to errors in light Doppler analysis.

Revised aberration formulas align with relativistic predictions.

Abstract

The diagram showing off-center nested spheres which is traditionally used to illustrate the Doppler effect, is misleading and its trigonometric analysis leads to errors concerning light, because electromagnetic Doppler and aberration effects conform to a wavefront surface that is not a sphere but an ellipsoid stretched along the trajectory of the source. The Cartesian and polar equations of the spherical and ellipsoidal wavefronts are compared here and related to their respective angular Doppler functions. As wavefront surfaces directly link inter-frame coordinate transformations to the aberrations they generate, the simple analysis of their geometry is sufficient to find exact results of special relativity and incidentally to revise the classical aberration formula.