Relativistic Aberration and Doppler Shift

scaled velocity β

0.7

number of rays

50

show Doppler effect

Suppose a specific number of evenly distributed light rays is incident on an observer at rest. For a moving observer at the given location, with scaled velocity

β=v/c

, these light rays appear to be tilted in the direction of motion (aberration), as indicated by the yellow triangle. As a result of the Doppler effect, light that comes from the direction of motion is blue-shifted, while light from the opposite direction is red-shifted.

Details

A detailed discussion of relativistic aberration can be found in the standard literature of special relativity. Here, we use the aberration formula

cosϕ'=

β+cosϕ

1+βcosϕ

to transform between the stationary reference frame

S

(unprimed coordinates) and the moving reference frame

S'

(primed coordinates). The Doppler factor is defined as

D=γ(1-βcos(ϕ'))=

λ'

λ

, where

λ

is the wavelength of the emitted light from a source at rest with respect to

S

, and

λ'

is the wavelength measured by the moving observer. From the point of view of the moving observer, there will be no Doppler shift,

D=1

, for

cosϕ'=

1

β

1-

1

γ

.

External Links

Doppler Effect (ScienceWorld)

Stellar Aberration (ScienceWorld)

Permanent Citation

Thomas Müller

"Relativistic Aberration and Doppler Shift"
http://demonstrations.wolfram.com/RelativisticAberrationAndDopplerShift/
Wolfram Demonstrations Project
Published: October 13, 2010