<p>Edit: I found you a very relevant paper!</p>

<p><a href="http://arxiv.org/pdf/astro-ph/0007341v1.pdf">http://arxiv.org/pdf/astro-ph/0007341v1.pdf</a> 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.</p>

<hr>

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

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2016-04-27T08:20:20.093Z
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.
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2016-04-27T18:04:08.610Z
Thanks, I've edited with more information about another source
cnosam
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2016-04-27T18:26:52.603Z
That is better. Welcome to Astronomy SE!
SE - stop firing the good guys
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2016-04-27T07:15:39.397Z
2016-04-27T18:03:47.627Z
2016-04-27T18:03:47.627Z
cnosam
<p>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 $z_2 &gt; z_1$.</p>

<p>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?</p>

<p>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 $Q_2$ .</p>

<p>There is some standard method to solve this problem ?</p>

<cosmology><distances><quasars>
How to find the distance between two quasars
Emilio Novati
# How to find the distance between two quasars

(Asked by: username_0 on 2015-07-22)

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 ?

**Tags:** cosmology, distances, quasars

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## 1 answers

### Answer by username_1 on 2016-04-27. Score: 6

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.

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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.

> **Comments:**
> **username_2**: 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.  
> **username_1**: Thanks, I've edited with more information about another source  
> **username_2**: That is better. Welcome to Astronomy SE!  

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