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We can detect the presence of an element in, say, a star because of the frequency of light that it absorbs which produces a line on an absorption spectrum. And we can detect relative motion towards or away from Earth because of a Doppler shift. But how do we know that we are seeing a shifted spectral line of one element and not the unshifted or differently shifted spectral line of another element?

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This is because the different spectral lines of an element form a characteristic pattern and you would usually see the Doppler shift also in other known lines of the characteristic spectrum of an element.

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The key is the difference in the wavelength of the spectral lines of a certain element. Since the wavelengths of light all traveled the same distance, they would be red shifted equally, thus retaining the difference in their respective wavelengths.

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