Distance of Stars / Size of the Universe calculation

[I0sens]

TL;DR Summary

How far in the past do we see stars

Hi, I am a new user,
This question is bothering me for a long time and now with all the Webb telescope hype I need to ask:

It sounds very logical to think that a star that is a billion light years away is seen as it was a billion years ago because the light
took 1 billion years to get here. Very easy to understand... if everything is static.

My problem though is that 1 billion years ago the star was not 1 billion light years away but - due to the expansion
of space - at a shorter distance

To take it to the extreme and take the Webb Telescope now, where they are looking 13 billion years into the past... supposedly.
But 13 billion years ago the universe was MUCH smaller.
I could not find how big actually, but let's say (for discussion sake) 2 billion light years: (pick your number).
One of these earliest Galaxies sent out a light beam into the direction where the Earth will be in 9 billion years...
It should only take 2 billion years at the most...(the end of the universe back then).
But the universe keeps expanding and the target is moving away... so it will take longer, until it actually reaches Earth 13 billion years later.
(Amazing!)

BUT THAT SHOULD NOT HAVE TAKEN 13 BILLION YEARS. or alternatively, if it took 13 billion years the distance should be larger.

Bottom line: It will take longer than if the distance hat stayed the same (2 billion years) but shorter
than if the distance would have been 13 billion light years (constant) in the first place.

(I should put this into Excel...)

It probably has all to do with Einstein and that the light beam also is taken with the expanding space and all nulls out, but it is hard to wrap
your head around it...

ThanksAnd by the way, how do we know in the first place how long the light was on the way until it reaches us? (or how far a faint start is away.)
I know that for supernovas there is a intensity measurement to get a distance, but how about your run-of-the-mill star?

 

[Janus]

When they give the distance measure, it is the "observed" distance. So when they say an object "is" 13B ly away, they mean that is how long it took the light to reach us. During that time, the universe has expanded, so, at this present moment, it is much further away.
As far as distance measures go: https://en.wikipedia.org/wiki/Cosmic_distance_ladder

 

[timmdeeg]

My problem though is that 1 billion years ago the star was not 1 billion light years away but - due to the expansion
of space - at a shorter distance

That is correct. To come to a better understanding this article of Tamara Davis might be helpful:
https://arxiv.org/pdf/astro-ph/0310808.pdf
together with the spacetime diagram, showing the distances then and now depending on the redshift of a particular object (galaxy) we observe now:
https://i.stack.imgur.com/JdoRt.png

 

[I0sens]

Thanks a lot.. I love forums!
I will look at your sources.
I have a question for Janus though. If the "observed distance for the furthest objects is now somewhere around 12-13 billion light years and it took the light that long to get to us, space also has that long to expand...
So observed distance plus looong expansion... The the universe should be much bigger than 13 billion light years.. but that's what I hear.

 

[phinds]

So observed distance plus looong expansion... The the universe should be much bigger than 13 billion light years.. but that's what I hear.

Uh ... Google is your friend

 

[Bandersnatch]

So observed distance plus looong expansion... The the universe should be much bigger than 13 billion light years.. but that's what I hear.

Re: the distances reported - the sources you may find out there are not always terribly clear on what distance they mean. Sometimes they mean the 'light travel time' distance Janus mentioned, sometimes the distance the objects are at now (as the figure for the size of the observable universe in the post above).
Oddly enough, nobody ever seems to report the distance at emission.

For example, this Wiki article:
https://en.wikipedia.org/wiki/MACS0647-JD
on one of the farthest galaxies mentions light travel distance of 13.26 billion ly in the text. That's what Janus was talking about - it's just the time it took for the light to get here (i.e. how old an image it is) times the speed of light. Doesn't actually, really, represent any physically meaningful distance.
In the info box to the right, you can see this distance listed alongside another, the 'comoving distance' of approx 32 billion ly. That's where the galaxy is now, when its early light has finally managed to reach us.

Once you know the distinction, it's easier to spot the intended meaning.

Btw, if you ever need to find the distance at emission, and your source lists both the comoving distance and the redshift, then you can just divide the former by the latter+1. For that galaxy, it's 32 billion ly and redshift z=10.7. So the distance at emission is 32/(10.7+1)= approx. 2.7 billion light years. I.e. that's how far it was when the light of the image we see now started its journey.

 

[I0sens]

A lot to digest.. Thanks!