If stars moving away/towards Earth appear blue/red shifted, how do we know their colours are red/blue because they are moving, and not just that they are a red/blue coloured star that’s relatively stationary?

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I copied the wording from a Quora post because all the answers were ELIhave a PHD in astrophysics.

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You know how a prism splits up white light into a rainbow of individual colors? [This](https://www.shutterstock.com/image-vector/emission-spectrum-sodium-element-2025986870) is what it looks like when you take a pure element, sodium in this case (salt if you want to try it at home), and split up the light it gives off when really hot – it forms bands that make up a distinct pattern. Each element forms a distinct pattern. This is what the pattern for [hydrogen](https://en.wikipedia.org/wiki/Hydrogen_spectral_series#/media/File:Hydrogen_spectrum.svg) looks like.

Stars have a lot of hydrogen, so when you split up the light using in a spectrograph, you can look for that distinctive pattern (distinctive to astronomers, at any rate) in the spectrum of light from the star. If the pattern is shifted to the red then you know the star is going away. Shifted towards the blue and it’s coming at you. How much shift tells you how fast.

This technique can tell you more! When a star is spinning, one side may be going away and the other side coming towards you, and if your equipment is super sensitive, you can tell how fast the star is spinning!

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