Relativistic Aberration

 

Astronomers have been aware of a phenomena called aberration for a long time[1]. It occurs when viewing the angular orientation of a distant star and is due to the earth’s motion on it orbit.  It is largest when the velocity of the earth (ve is about 30 km/sec) is perpendicular to the line between the earth and the star.  Thus when an astronomer views a star at midnight that is positioned opposite the sun, he will see the star in a different position in winter than when he views the same star on the horizon in spring.  The angular difference between winter and spring measurements is given by

 

where c is the speed of light.  The ratio ve/c is about 0.0001 so the effect is readily measurable and the angle is about 20 seconds of arc.  It is due to the fact that the wave fronts from the distant star appear tilted when viewed in the moving frame of reference of the earth in orbit.

 

To animate aberration, I chose to use a tilted moving array of detectors angled at  

where v is the linear speed of the detectors along the tilted line. I tilted the wave fronts at this same angle so that they would be optimized to receive the wave fronts.

 

Effectively this is analogous to someone moving with velocity v perpendicular to the light source tilting a single receiver plane by the angle q which is the same angle as the tilt of the wave fronts.  In both cases, the detector receives the entire wave front simultaneously rather than having multiple phases spread across the receiver plane,

 

http://en.wikipedia.org/wiki/Aberration_of_light


[1] http://en.wikipedia.org/wiki/Aberration_of_light