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

[mathman]

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)?

 

[Redbelly98]

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

 

[cristo]

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]

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.

 

[mathman]

Does anyone know the answer to my original question?

 

[cristo]

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]

By the redshift distance, is the short answer. See Ned Wrights cosmic calculator for the details.

 

[mathman]

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.

Using the redshift and Hubble's constant I can get the fact the light has traveled one billion years since it was emitted. What I don't know is how far away from the receiver is the source now and what was the source to receiver distance one billion years ago. Basically how does one factor in the universe expansion to calculate these distances?