Okay, stars are made of different elements depending on their size and age. Each element of the periodic table emits, and absorbs light differently. (It has to do with the electron orbits, but that’s a bit complicated and not necessary to know for this question. )
Anyway, because each element absorbs light differently, they leave unique patterns. It’s like a barcode in the light spectrum. Each barcode pattern is located at precise points on the electromagnetic spectrum. I’m talking with nanometer precision.
Okay, so we know the exact pattern for every element, and we know the exact location in the spectrum for every element. Remember this.
Now, the shifting occurs when the universe itself is expanding. It’s pretty much all redshifted. An object would have to be traveling immensely fast towards us to blue shift.
As the universe expands it stretches the Lightwave out with it. So, the part that was orange is now red, yellow has become orange, etc.
BTW, this is oversimplified, the shifting is much more subtle, but the idea it conveys is correct.
Anyway, say we find the pattern for oxygen, which is green, in the yellow. How far into the yellow can tell us how far the star is. We know the light has shifted because the oxygen barcode is in the wrong place.
These barcodes are also how we know what elements are in stars and nebulae and such.
I think I got all the relevant information in here, ask about anything confusing, I’ll do me best.
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