Selected Questions- Answers From All Experts Astronomy Forum (Doppler effect on traveling lightwave)

Question:  I have heard of the Doppler effect, mostly as it applies to lightwaves which arrive at the earth after traveling from a distant star. As I understand it, the wavelength of light shifts from the visible to the  red or infrared.  Does the same apply to a lightwave traveling away from the earth?

For example, how would you calculate the wavelength of a Doppler-shifted  lightbeam that left the earth 10 years ago and is just reaching, say, the nearest galaxy?



Answer:

First, your description of the Doppler effect for cosmic light sources isn't complete.
What you have described (in your "understanding") is a red shift of the light source.

But one can also observe and measure a blue shift, where the source is
approaching - i.e. its frequency is increasing - and the spectral lines are shifted
from the red toward the blue or ultraviolet (e.g. higher energy)band of the EM spectrum.

In either the red or blue shift case, one would need to  obtain a spectrum 
(e.g. spectrogram)  of the receding  (or approaching)  light source. Then
compare it to the standard positions (wavelengths) of known spectral lines 
(e.g. for hydrogen).

Say the standard spectral line of interest is at L1 measured in nm
(nanometers). Say the red shifted line is at L1' such that: L1' >  L1.  Then
the Doppler shift would be computed according to:

(L1' - L1)/ L1  = v/c

where v is the recession velocity, and c the speed of light.

The above equation can be used to obtain the red shift of the light beam from

a light source, if you know the other quantities (v, c and L1).

If, however, the spectral line observed is blue-shifted, e.g.

L1 > L1'

Then the Doppler (blue) shift would be computed according to:

(L1 -  L1')/ L1  = v/c

where v is the velocity of approach of the light source.

The problem pertaining to your example is that the Earth is not a light source, so
has no ability to emit a source light spectrum of its own to be measured (say in a
defined spectrogram) as any shift  from a distant destination. 

In reality, what your example is all about isn’t the Doppler shift per se, but rather the

distance travelled by the light beam leaving Earth. Hence, if said light beam left our

planet ten years ago – say from a powerful Excimer laser – then the photons would
now be at a distance of:

D  = (300,000 km/s)  x  (86,400 s/d) x 365.25 d   x 10 

D =  9.4 x 10 ¹³ km

But as a matter of practicality no outside observer would be able to detect a red

or blue shift of this feeble artificial light source - say from a distance of ten light years- far less from a nearby galaxy (thousands of light years distant). 

The photons received would be too diffuse and sparse to conclude anything -
if indeed they  could be detected at all.