# Calculating distance to High Redshift Galaxies based on observations

I am aware that we need to account for the expansion of the universe, changing $$H$$, the relativistic redshift eqn: $$1+z=\sqrt{\frac{c+v}{c-v}}$$ and so on, but can we accurately calculate velocity using just redshift from observations of very high redshift galaxies? I'm thinking redshifts of $$z>7$$. I'd expect the light from these distant objects to be extremely redshifted, faint, and small, near point sources. What kind of assumptions/methods do astronomers use to calculate light-travel distance of these difficult to resolve objects? For instance, how would we know that an object being observed is a QSO at $$z=7.64$$ versus a Galaxy at $$z=7.66$$?

• NB You question isn't clear. Distance can be "calculated" from redshift and a cosmological model. Distance could also be "measured" in various way to help constrain cosmological models, but that would be a very broad question. Dec 31, 2021 at 14:26
• @ProfRob Edited. I wasn't asking if z=7 is nearby, I know it isn't even close, just clarifying what I meant when saying "high redshift" was the most distant and faintest objects. Hopefully, the edits add clarity. Dec 31, 2021 at 14:41 There are various calculators on the internet you can use to do these calculations - for example this calculator tells me that for a flat universe with $$\Omega_M=0.3$$, then $$z=7$$ corresponds to a light travel distance of 12.79 billion light years or a comoving distance of 28.3 billion light years.