An alternative derivation of Einstein's Doppler shift and aberration formulae

TL;DR

This paper presents a purely kinematical derivation of Einstein's Doppler and aberration formulas, applicable to any periodic signals traveling at light speed, providing new insights into their foundational principles.

Contribution

It introduces an alternative, purely kinematical derivation of Einstein's Doppler and aberration formulas, expanding the theoretical understanding of these phenomena.

Findings

Derivation valid for signals of any shape propagating at light speed

Provides an asymptotic form based on relative distance variation

Offers an alternative proof of Einstein's aberration formulas

Abstract

I propose an alternative, purely kinematical, derivation of Einstein's Doppler formula. It is valid for periodic signals of any shape that propagate with the velocity of light. The formula is asymptotic in a parameter proportional to the relative variation of the distance source-receiver during one period. As a by-product, I also derive an alternative proof of Einstein's aberration formulae.