Elements release very specific wavelengths of light. This is directly tied to quantum mechanics and is very predictable. Stars have a fingerprint that is defined by the elements they’re made up of and have a distinct pattern. If you’re looking for the line for hydrogen and it’s not there, you know that it’s either being red or blue shifted. Or you’re looking at a star without hydrogen which in of itself would be interesting. Combined with other elements and expected wavelengths of light scientists can figure out pretty easily if it’s being red or blue shifted.
Keep in mind that is not the ONLY way to do it. Scientists usually use multiple methods to confirm and they can involve things like behaviors of certain types of stars.
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