Assume that on earth we see something 1 billion light years away

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This is probably an elementary exercise, but my head spins trying to think about it. Assume that on earth we see something 1 billion light years away (i.e. light took 1 billion years to reach us). To simplify, assume no relative proper motion, although the distance will change due to universe expanding. How far apart are the earth and the source now and how far apart were they when the light was emitted ( 1 billion years ago)?

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Redbelly98
Staff Emeritus
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Assuming no relative motion, the object was and still is 1 billion light-years away. Or am I missing something in your question?

cristo
Staff Emeritus
This is probably an elementary exercise, but my head spins trying to think about it. Assume that on earth we see something 1 billion light years away (i.e. light took 1 billion years to reach us). To simplify, assume no relative proper motion, although the distance will change due to universe expanding. How far apart are the earth and the source now and how far apart were they when the light was emitted ( 1 billion years ago)?
You wouldn't do the calculation like this, though. You'd get a redshift of the observed photon, and then relate this to the distance between the observer and the emitter when the photon was emitted.

Assuming no relative motion, the object was and still is 1 billion light-years away. Or am I missing something in your question?
He means that the distance is increasing due to the "universe expanding."

Redbelly98
Staff Emeritus
Homework Helper
He means that the distance is increasing due to the "universe expanding."
Got it. I misread the original post to mean we are ignoring the expansion of the universe.

Thanks for clarifying.

Does anyone know the answer to my original question?

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cristo
Staff Emeritus
Does anyone know the answer to my original question?
I answered your question, didn't I? The point is, how would you know that the light had taken a billion years to travel to you? It's not like a 100m race or something like that, where you can measure it; you need to use the redshift.

Chronos