Relativistic aberration for accelerating observers

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.

Optics in a field of gravity

“…We shall now show that the angle is equal to the corresponding angle ' in IF which Beig and Heintzle (1) found by using the aberration formula. The angle in eq.…”

“…The path of a photon in R is found most simply from the transformation (1). In IF the path is a straight line.…”

“…The observer, P, is at a height 1 xx . The centre of the sphere is at a distance b vertically beneath P. The radius of the sphere is r. Figure 2 A geometrical consideration shows that the radius of the circular arc is where 1 1/ ax is the acceleration of gravity at the position of the observer. Hence, as observed from above the sphere appears enlarged.…”

“…The even (2) is found by transforming to IF and then backwards to R. In IF the light moves along a straight path tangent to the sphere which is at rest. In IF the event (1) is given by 1 1…”

Relativistic satellite astrometry atμarcsec precision and the measurement of the stellar aberration

“…As is well known, in the context of special relativity the aberration formula can be obtained from Lorentz-transforming the coordinate components of the velocity of light, and expressing these components in terms of the angles measured by two different observers between the line of sight of the star and the apex of their motion. The case of uniformly accelerated observers has been recently dealt with in Beig & Heinzle (2008). In the context of general relativity, a covariant formula for the stellar aberration can be directly derived from the general-Relativistic Astrometric MODel (RAMOD) 1 , which was conceived and developed in de Felice et al (1998de Felice et al ( , 2001), , , de Felice et al (2004, de Felice & Preti (2006, Crosta & Vecchiato (2010), to reconstruct the trajectory of a light ray from the event of observation back to the star position in terms of the observational data represented by the direction cosines of the incoming light ray with respect to a given spatial frame.…”