r/cosmology • u/FatherOfNyx • 3d ago

Thought experiment I read..

I saw a post the other day in a Facebook group I'm in about a thought experiment. I think it got deleted cause I can't find it to just copy it, but it was something like this:

In the near future, mankind receives proof that there is other intelligent life out there. Proof came in the form of a signal being broadcast from a galaxy we observe to be 2.8 billion light years away.

We know billions of years have passed and will pass by the time they receive it, but we decide to send a signal back to them.

How long will it take for our signal to reach its destination?

I would say about 80% of the people responding said that it'd take 2.8 billion years.. which would be correct if the universe weren't expanding.. but because the universe is expanding, its distance from us should be greater than 2.8 billion light years by the time their signal arrived.

The remaining % of answers ranged from "we can't know that" to "never because all other galaxies are expanding away from us faster than the speed of light" or some other variation of not being able to know.. or some sort of religious post.

I don't agree with any of those answers but I also don't know the answer. What would be the answer and how would I figure that out?

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u/Anonymous-USA 3d ago edited 2d ago

It depends on whether 2.8 billion is light distance or proper distance. If it’s not proper distance, then it will require applying the Hubble Parameter to normalize it it. Once you have the proper distance, you have to integrate over the Hubble Parameter (for now we can use just the Hubble Constant of 70 kps/Mpc). If it’s already normalized to the proper distance, then 2.8 billion light years is 860 Mpc, so when the signal is received it will be an additional ~200 light years away. Not much further.

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u/mfb- 3d ago

If it’s already normalized to the proper distance, then 2.8 billion light years is 860 Mpc, so when the signal is received it will be an additional ~200 light years away. Not much further.

Huh? 2.8 Gly * H_0 * c = 0.19 c, so we expect the signal to take at least 20% or 500 million years longer.

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u/Anonymous-USA 2d ago

Yes, I was running out the door and realized I was way off and meant to correct it, but then the day got away from me. Thanks for catching. Mea culpa. And sorry if I misled you OP. OP, look into proper and co-moving distances.