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I want to calculate the distance between two quasars of which I know the angular position and the red shift. Let $Q_1=(\alpha_1,\delta_1, z_1)$ and $Q_2=(\alpha 2,\delta 2, z_2)$ and suppose $z_2 > z_1$.

I know how to find the angular separation $\theta$ between them by means of the angular coordinates. But how to find the comoving distance (at epoch $z=0$) from them ? I know how to find the comoving distance from the Earth of the two quasars, can we find the distance between them using these two distances?

A related question is to find the redshift of $Q_2$ as seen by $Q_1$ at the epoch when $Q_1$ received the light emitted from $Q_2$ .

There is some standard method to solve this problem ?

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Edit: I found you a very relevant paper!

http://arxiv.org/pdf/astro-ph/0007341v1.pdf seems to be solving exactly your problems for sources with arbitrary angular separation $\alpha$. Equations (12) and (14) will give you the comoving distance $\chi_2'$ and redshift $z_2'$ between them at the epoch when $Q_1$ received light from $Q_2$. You will have to solve these equations numerically to find the solutions, which will be more complicated depending on the cosmological model you use.

Have a read of these notes http://arxiv.org/abs/astro-ph/9905116. They are my go-to when trying to work out cosmological distances.

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  • $\begingroup$ This is what we consider a link-only answer. While it may be helpful, a summary of the information found there is a good idea to include. $\endgroup$
    – SE - stop firing the good guys
    Apr 27, 2016 at 8:20
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    $\begingroup$ Thanks, I've edited with more information about another source $\endgroup$
    – cnosam
    Apr 27, 2016 at 18:04
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    $\begingroup$ That is better. Welcome to Astronomy SE! $\endgroup$
    – SE - stop firing the good guys
    Apr 27, 2016 at 18:26

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