I have a few questions here, I hope you can help me get answer or reasonable solution. From the earth I see a star which is estimated to be 10 billion light-years away. Questions: 1) Since light takes time to travel from that star to my eyes, the star "right now" must be more than 10 billion light-years away from me, right? Because what I am seeing now is the "history" of that star. So what could be the Actual Distance between me and the star right now? 2) While light is continuously emitting from the star to my direction, and simultaneously the star is flying away from me, the "relative distance" between me and the star is not constant, and the "relative velocity" between the star and me is not zero, right? In this case, 10 billion year later, what is the distance between me and the star? 20 billion light-years or more? If we roll back the clock, 10 billion years ago, what is the distance between me and the star?
You cannot see a star that is 10 billion light years away. You can see galaxies that far away but not stars. Correct. This is a little hard to understand. If the light has been traveling for 10 billion years, then the galaxy was about a couple of billion ly away when the light was emitted. The galaxy is now about 20-25 billion ly away. correct
You are seeing that galaxy as it was 10 billion light years ago... the information is coming to you. Where is it right now? Anywhere from 15 billion light years to 20 away. Also keep in mind that considering we are A and that galaxy is B and both were together 14 billion years ago and have dually been expanding from each other that it is possible the speed A and B are retreating from each other may be relativistic, keeping the expansion of the universe in mind. I laid this out in detail in the physics sub-forum months ago but looking now I see it was archived.
Back to the first information of "the galaxy is 10 billion years away", when the astronomer says that, how did he measure or estimate this distance from his telescope? Redshift?
Does Redshift disprove Big Bang? Does Redshift disprove Big Bang? I read something about this but it is not clear. Seems that the BB supporters can introduce something to do correction to their BB theory.
There are several different methods of estimating distances, forming a ladder, as distances increase. For fairly close interstellar distances, parallax can be used, using the diameter of earths orbit as the baseline. Cephid variables are stars which regularly brighten and dim. These stars always have the same intrinsic brightness, and so distances can be gauged by the apparent brightness. On galactic distances, Type 1 supernova can be seen across the universe, and they also always have the same intrinsic brightness. These methods give us the baseline to calibrate redshift.
Type 1a supernova light curves, which is used for calculating the greatest distances has an error range of 5%. Here, read it yourself. http://en.wikipedia.org/wiki/Cosmic_distance_ladder