Can We See Distant Galaxies at Multiple Points in Time?

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Okay last one for today. promise.

When we look back at distant galaxies, we are looking back into time. If the galaxy is 2 billion light years away, we are looking 2 billion years back in time. But hold on a second. 2 billion years ago it was at that point. But present day it's somewhere else. Most galaxies are spreading apart, but some are headed for collision.

If another galaxy was coming closer to us (not headed directly towards), couldn't we point our telescopes to where it was 2 billion years ago and also to where it was 5 years ago and see it in both places? Why don't we see a blur of the path the galaxies have traveled? If we can look back into time, shouldn't we be able to see that galaxy at every point in time as long as it is within 13.7 billion light years?

This raises another question. Assume the universe is a sphere (I really don't know if it is). If the radius is 13.7 billion light years (the age of the universe), then shouldn't we be able to see further than 13.7 billion light years, since we are not at the center? But how in could we see further than 13.7 billion years ago back into time? Thanks :D.

Since this is all relative it won't really help anyone with anything. I'm just curious.
 
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zewpals said:
If another galaxy was coming closer to us (not headed directly towards), couldn't we point our telescopes to where it was 2 billion years ago and also to where it was 5 years ago and see it in both places?
The galaxy would have to be moving faster than the speed of light for this to happen.
 
I don't understand why, though.
 
zewpals said:
I don't understand why, though.
Well, think about it. Let's take an object that, ten minutes ago, was ten light minutes away. So we would just now be seeing this object and the light it emitted ten minutes ago.

If we also see the light that it emitted 11 minutes ago, then that would mean 11 minutes ago it was 11 light minutes away, meaning it would have been traveling one light minute per minute, i.e. the speed of light.

For an object traveling slower than the speed of light, it would have been 11 light minutes away before 11 minutes ago, and so the light would have already passed us by.
 
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