Doppler redshift of distant galaxies gave first hint that the universe is expanding. I am curious to know how this redshift is actually measured and interpreted from observation. Suppose I observe some visible line say red with wavelength \lambda_1. This is not enough to tell that this line is redshifted, i.e., the original line emitted from that galaxy had a smaller wavelength. How do I know the value of that particular line when it was emitted from that galaxy? It appears that mere observation of a line is not enough. So how do we proceed?
Answer
When we measure a red shift, what we are actually measuring is the absorption spectra of elements in the stars and dust clouds in the target galaxy. These absorption spectra have well known patterns of lines, and when red shifted the entire pattern moves to lower energy/longer wavelength.
So you're correct that you can't measure the red shift from just one line, because you don't know where that line was originally, but you can do it when you measure a known pattern of many lines.
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