Relativistic Aberration for Accelerating Observers

TL;DR

This paper analyzes how a uniformly accelerating observer perceives a luminous object, revealing relativistic aberration effects that influence apparent size, with implications for space-flight scenarios.

Contribution

It provides a detailed analysis of relativistic aberration effects for accelerating observers, highlighting phenomena not present in non-relativistic contexts.

Findings

Initial increase in apparent size of the object

Apparent size approaches a non-zero limit over time

Existence of a critical acceleration affecting size change

Abstract

We investigate the effects of the aberration of light for a uniformly accelerating observer. The observer we consider is initially at rest with respect to a luminous spherical object--a star, say--and then starts to move away with constant acceleration. The main results we derive are the following: (i) The observer always sees an initial increase of the apparent size of the object; (ii) The apparent size of the object approaches a non-zero value as the proper time of the observer goes to infinity. (iii) There exists a critical value of the acceleration such that the apparent size of the object is always increasing when the acceleration is super-critical. We show that, while (i) is a purely non-relativistic effect, (ii) and (iii) are effects of the relativistic aberration of light and are intimately connected with the Lorentzian geometry of Minkowksi spacetime. Finally, the examples we present illustrate that, while more or less negligible in everyday life, the three effects can be significant in the context of space-flight.