How do we calculate the light years between the galaxies?
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1) Generally, the further away stuff is from us, the more redshifted it is. Thus, if you can figure out how redshifted it is, you can make an educated guess as to how far it is from you.
2) There are certain light-emitting events that produce a very consistent and repeatable profile of light no matter where they happen in the universe. Thus, if you see (and can recognize) one of these events, you can almost immediately figure out how far away the event was from you.
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