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If I look at a galaxy 13 billion light years away, how much closer was it when it first emitted its light?

Galaxy MACS0647-JD is about 13.3 billion light years from Earth, and it apparently formed about 420 million years after the Big Bang.

Light can travel around 5,878,499,817,000 miles in a year. (Yep, someone paced it out πŸ™‚ We think that star and galaxy formation occurred in the 300 to 500 billion years post-Big Bang time frame, so MACS0647-JD would be one of the younger galaxies in the universe.

So how much closer β€” and closer to what? β€” would that proposed galaxy in the question be? Our own galaxy, the Milky Way, is around 13.6 billion years old (How Did the Milky Way Form? – Universe Today). Since the universe is estimated to be around 13.7 billion years old (measured from the Big Bang, of course), the two galaxies β€” the one in the question and our Milky Way β€” would have come into existence about 0.1 billion years post-Big Bang (Milky Way) and 0.6 billion years post-Big Bang (the galaxy in the question).

That’s a difference of 0.5 billion years. Say the sources of the two galaxies were moving directly away from each other. When the galaxy in the question came into existence it would have appeared 0.6 billion years in one direction, and the Milky way would have appeared at 0.1 billion years in the opposite direction, and then would have traveled an additional 0.5 billion years before the galaxy in the question formed. So their distance would have been the amount they had moved β€” or rather, the amount the universe had expanded β€” during 0.5 + 0.1 + 0.6 billion years, or during the first 1.2 billion years of the universe.

If the galaxies were moving in the same general direction β€” carried so to speak by the expansion of the universe β€” they would be less farther apart. Going in opposite direction would give you their maximum original distance.

So what is the maximum distance between the two galaxies? It would be the amount of expansion of the universe in its first 1.2 billion years.

(Source of image: Farthest Known Galaxy in the Universe Discovered)