NP, since you couldn't answer the star distance question I will you provide you with a few links to your favorite source so you can speak intelligently on the topic. There are several different ways scientists determine the distance to stars and as you can see, they are all based on theories, some with many variables...
Cepheid variable - Wikipedia, the free encyclopedia
Extragalactic observations
The most distant objects exhibit larger redshifts corresponding to the Hubble flow of the universe. The largest observed redshift, corresponding to the greatest distance and furthest back in time, is that of the cosmic microwave background radiation; the numerical value of its redshift is about z = 1089 (z = 0 corresponds to present time), and it shows the state of the Universe about 13.7 billion years ago, and 379,000 years after the initial moments of the Big Bang.[59]
Redshift - Wikipedia, the free encyclopedia
Spectroscopic parallax - Wikipedia, the free encyclopedia
I know about the concepts of redshift and parallax shift as it applies to making these measurements, but I do not know the actual methodology of how they use these concepts to obtain such measurements, mathematically, although I seem to remember it involving trigonometry and parallax view, but I could be wrong. I don't see how any of this important, and I don't know why I follow you on these wild goose chases. I am truly a sucker. Are you saying that because I don't understand the methodology behind these measurements, that I am not able to use them?
If you consider the methodology in determining these distances to be flawed, then just say so. If you don't, then you have no basis for needing to know whether or not I understand how these measurements were obtained. It is irrelevant to my using them, unless you think they are questionable, in which case, we can have a discussion about that, and I will do the proper research to learn how these measurements were garnered. I must say that, this just seems like an ego-trip for you, and I don't understand what it has to do with my purposes here.
At bottom, you seem to be implying that a star that has been measured at 13 billion light years away, is not actually 13 billion light years away, and therefore I should not cite this measurement. Is this the case?