<p>From eq. 10 in <a href="http://adsabs.harvard.edu/cgi-bin/bib_query?arXiv:astro-ph/9905116" rel="nofollow">Hogg's classic paper</a>, assuming that the peculiar velocity $v_\mathrm{pec} \ll c$:
$$v_\mathrm{pec} = c \frac{z_\mathrm{obs} - z_\mathrm{cos}}{1 + z_\mathrm{cos}},$$
where $z_\mathrm{obs}$ is the observed redshift, and $z_\mathrm{cos}$ is the redshift from cosmological expansion only.</p>

<p>Let me invert that and wrap it up in Python for ya:</p>

<pre><code>def zobs(vpec,zcos):
  c = 3e5
  return (1+zcos) * vpec/c + zcos
</code></pre>

CC BY-SA 3.0
2015-05-18T18:36:31.550Z
Thanks for the ref and the very complete answer!
(and I corrected my typo thanks to you).
cbienpourtoi
CC BY-SA 3.0
2015-05-18T20:39:45.560Z
You very welcome @cbienpourtoi. I'll remove my first comment, then.
pela
CC BY-SA 3.0
2015-05-18T13:17:31.977Z
2015-05-18T20:40:17.127Z
2015-05-18T20:40:17.127Z
pela
<p>I have a galaxy 'A', say at redshift 1. Let's suppose this galaxy has no peculiar velocity. What would be the redshift of another galaxy 'B', that has a radial velocity of 500 km/s, relative to A?</p>

<p>All this in the standard (Planck) model.</p>

<p>Any tools to do get this easily (an python code, astropy?)</p>

<galaxy><cosmology><python><astropy>
Difference in redshift between 2 interacting galaxies
cbienpourtoi
# Difference in redshift between 2 interacting galaxies

(Asked by: username_0 on 2015-05-15)

I have a galaxy 'A', say at redshift 1. Let's suppose this galaxy has no peculiar velocity. What would be the redshift of another galaxy 'B', that has a radial velocity of 500 km/s, relative to A?

All this in the standard (Planck) model.

Any tools to do get this easily (an python code, astropy?)

**Tags:** galaxy, cosmology, python, astropy

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## 1 answers

### Answer by username_1 on 2015-05-18. Score: 3 | Accepted answer

From eq. 10 in Hogg's classic paper, assuming that the peculiar velocity $v_\mathrm{pec} \ll c$:
$$v_\mathrm{pec} = c \frac{z_\mathrm{obs} - z_\mathrm{cos}}{1 + z_\mathrm{cos}},$$
where $z_\mathrm{obs}$ is the observed redshift, and $z_\mathrm{cos}$ is the redshift from cosmological expansion only.
Let me invert that and wrap it up in Python for ya:
def zobs(vpec,zcos):
  c = 3e5
  return (1+zcos) * vpec/c + zcos

> **Comments:**
> **username_0**: Thanks for the ref and the very complete answer! (and I corrected my typo thanks to you).  
> **username_1**: You very welcome @cbienpourtoi. I'll remove my first comment, then.  

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