__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?

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__Answer__:

First, your description of the Doppler effect for cosmic light sources isn't complete.

What you have described (in your "understanding") is a

But one can also observe and measure a

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).

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 shiftedfrom 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

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

The above equation can be used to obtain the

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.**

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The problem pertaining to your example is that the Earth is not a

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.

*light source*, sohas 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:

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.

The photons received would be too diffuse and sparse to conclude anything -

if indeed they could be detected at all.

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