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I have a question dealing with distances of, lets say galaxies. I researched a little and saw that there are plenty of coordinates. Mostly used are spherical (celestial) ones, RA α and DEC δ. To have a three dimensional distance measure, one uses the redshift and from there the line of sight distance.

According to Hoog arXiv:astro-ph/9905116v4, this computes like:

[tex] D_C = D_H \int_0^z \frac {dz'}{E(z')} [/tex]

where D_H is a constant and E(z) is

[tex] E(z)=\sqrt{\Omega_M (1 + z)^3 +\Omega_k (1 + z)^2 +\Omega_M } [/tex].

So if I got it correctly I some up little line elements along dz, depending on the cosmology i consider ([tex] \Omega_k=0 [/tex]). But this is just the line of sight distance right? What about the position on the skymap α and δ? How can I compute the distances of objects that differ in redshift z and in celestial coordinates? Does it even make sense as the universe expanded in between?

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# Distance Measures

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