Am I the only one who doesn't quite grok parallax? :( Hydrogen absorption is also a bit shaky, despite my background in chem.
Oniya has a good explanation of Parallax : ) Basically, with a circular orbit there isn't a point in the sky where you can't look at something from 300 million kilometers to the side. Ideally, over the next centuries we'll have telescopes light-years apart to give us much more accurate measurements of such things.
Hydrogen absorption comes from the density of intergalactic gas more than eleven billion years ago. The Universe was a lot smaller then, and the IGM a great deal denser, meaning that we see the spectral lines that hydrogen absorbs get absorbed more in very distant objects.
Also, I thought that if something was, say, 100 million light years away, it's also thought to have occurred in the past. Probably not 100 years on the nose - I think it involves some sort of physics/quantum equation - but if it's reaching us from that far away (let alone billions), it occurred in the been-and-gone as opposed to the here-and-now?
Up to a billion light years away, that applies close enough.
Space is currently expanding at 71 kilometers per second per megaparsec. To put that in perspective, if there were no such thing as gravity, and we were each a billion kilometers apart (roughly), we would slowly accelerate apart at a rate of about 72 meters per second per year. A billion light-years apart, and that becomes several percent of c - enough for relativistic equations to have meaning but most people wouldn't care.
Once you start getting half the Universe away, though, the expansion of space starts to have a huge effect. We see it as being 8.2 billion light-years away, but it was not that far away when the light was sent, and is much, much further away now. This is an important distinction to keep in mind when looking at the size of the Universe.
Perhaps I should do more sciencey articles >_>