In cosmology, we have a couple of different length measures. Among them, comoving and proper distnlances seem to be good fit to real world use cases in astronomy.

So my quesion is which length measure are we using in astronomy? For instance, when we say a certain galaxy is # light yrs distant from the Earth, what does it actually mean?


  • $\begingroup$ In astronomy it seems to me that we intend proper distances. When the objects are too far the only sensible value is z. The rest comes from the model and parameters used. $\endgroup$ – Alchimista Aug 31 at 10:38

comoving distance is not something that we can measure. We are actually measuring either luminosity distance or angular diameter distance. And they are related to the comoving and proper distances.

By making observations we can determine the luminosity distance of an object $d_L$. And the $d_L$ is related to the transvverse comoving distance $r$ via $$d_L = r(1+z)$$ For flat universe $$r = c\int_0^z dz/H(z)$$

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  • $\begingroup$ I think this answer is too thin given that it is apparent that the OP is touching upon these issues for the first time. For example, how is the comoving distance related to angular diameter distance? One has to assume that we somehow know the diameter of the object, but if we do we can understand that distance. Comoving distance is more abstract. All this needs to be addressed. $\endgroup$ – garyp Oct 22 at 11:39
  • $\begingroup$ @garyp We mostly use angular diameter distance for CMB and BAO measurements. We can know their angular seperation on the sky (physics allows us to calculate it) and by measuring the angle we can refer to an angular diameter distance. In general of course we dont know the diameter of the furthest galaxies. $\endgroup$ – Layla Oct 22 at 13:36

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