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Say, for example, I am looking at a distant star. I record the different intensities of light of different wavelengths and observe some spectrum lines. Now, since there are three factors affecting what I see - the temperature of the star, the speed at which the star is receding away from me, and the components of the star - how could I, first of all, tell what components the spectrum lines are of (let's say there are many components of roughly equal abundance) and, consequently, how much each of the two remaining factors contributes to the observed intensities?

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The temperature does not shift the spectral lines, it only makes them broader (it gives them a Gaussian profile). So you can measure the temperature directly from these.

And the Doppler effect scales all of the spectral lines by the same factor.

Now, you can measure the spectral lines of all of the elements in the lab. So all you need to do is scale your observed spectral lines, run the known spectral lines for each element along to see if you get any matches (if so, add to a tally), then scale the observed spectral lines again and repeat. Find the scaling factor that maximises the number of matches. That gives you the scaling factor (and therefore speed).

(This probably isn't how it's done in practice, but it's the same principle)

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  • $\begingroup$ "The temperature does not shift the spectral lines, it only makes them broader": why, then, do we see the Sun as yellow but blue supergiants as blue - even though they are made of roughly the same material? $\endgroup$ – Max Oct 13 '17 at 1:28
  • $\begingroup$ @Max For two very different reasons. The sun appears yellow due entirely to our atmosphere. The relation between temperature and colour of more distant stars (hot=blue, cool=red) is essentially because high-temperature stars give off more high-energy photons (more towards the blue end). See black body radiation. $\endgroup$ – lemon Oct 13 '17 at 9:23
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And you must remember that the red shift (Doppler effect) observed is really the astronomical red shift which includes effects of the expanding universe. So it won't be as straight forward as described by @lemon.

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    $\begingroup$ Why not? The fact that cosmic expansion is part of takes nothing away from @lemon s answer as far as I can see. $\endgroup$ – Thriveth May 29 '17 at 10:32
  • $\begingroup$ The formula from expansion is lightly different function of redshift than for Doppler, for redshifts greater than about 0.5. I can't remember if the fractional wavelength change differs with wavelength for expansion, you can look it up. it might not make any difference, and you could then do what Lemon said. $\endgroup$ – Bob Bee May 30 '17 at 6:14
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    $\begingroup$ There is no observational difference between a doppler shift and a cosmological redshift. All that differs is how the shift is interpreted. $\endgroup$ – Rob Jeffries Jun 4 '17 at 23:26

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