<p>In Equation (16) of the paper you link to, <span class="math-container">$z$</span> is the observed redshift. In the first paragraph of section 2.2</p>

<blockquote>
  <p>The heart of the method is to use a measured redshift, z, to infer a velocity, v(z)</p>
</blockquote>

CC BY-SA 4.0
2020-02-20T13:42:25.213Z
2020-02-20T13:42:25.213Z
usernumber
<p>Let us say that we have an object so its total velocity is defined as </p>

<p><span class="math-container">\begin{equation} v_{tot} = v_{pec} + V_{rec} \end{equation}</span> </p>

<p>Where </p>

<p><span class="math-container">\begin{equation} V_{rec} = H_0r \end{equation}</span> </p>

<p>and <span class="math-container">\begin{equation} V(z) = \frac{cz}{1+z}[1+\frac{1}{2}(1-q_0)z - \frac{1}{6}(1-q_0-3q_0^2+j_0)z^2] ~~(4)\end{equation}</span> </p>

<p>for small z.</p>

<p>So my first question is what is the <span class="math-container">$z$</span> value here? Is it the observed redshift or the cosmological redshift? </p>

<p>Also, the relationship between observed and cosmological redshift is given.</p>

<p><span class="math-container">\begin{equation} 1+z_{obs} = (1 + z_{cos})(1 + z_{earth})((1 + z_{sun})(1 + z_{source})(1 + z_{gravity})    \end{equation}</span></p>

<p>If we are using the cosmological redshift then by using above equation we can write, </p>

<p><span class="math-container">\begin{equation} z_{cos} = \frac{1 + z_{obs}} {(1 + z_{earth})((1 + z_{sun})(1 + z_{source})(1 + z_{gravity})}-1    \end{equation}</span></p>

<p>So is this what we put in (4)?</p>

<p>Edit: For the source you can look here <a href="https://arxiv.org/abs/1907.12639" rel="nofollow noreferrer">https://arxiv.org/abs/1907.12639</a> Eqn(16) and (18)</p>

<star><cosmology><redshift>
Redshift and Velocity relation
seVenVo1d
# Redshift and Velocity relation

(Asked by: username_0 on 2019-12-01)

Let us say that we have an object so its total velocity is defined as

\begin{equation} v\_{tot} = v\_{pec} + V\_{rec} \end{equation}

Where

\begin{equation} V\_{rec} = H\_0r \end{equation}

and \begin{equation} V(z) = \frac{cz}{1+z}[1+\frac{1}{2}(1-q\_0)z - \frac{1}{6}(1-q\_0-3q\_0^2+j\_0)z^2] ~~(4)\end{equation}

for small z.

So my first question is what is the $z$ value here? Is it the observed redshift or the cosmological redshift?

Also, the relationship between observed and cosmological redshift is given.

\begin{equation} 1+z\_{obs} = (1 + z\_{cos})(1 + z\_{earth})((1 + z\_{sun})(1 + z\_{source})(1 + z\_{gravity}) \end{equation}

If we are using the cosmological redshift then by using above equation we can write,

\begin{equation} z\_{cos} = \frac{1 + z\_{obs}} {(1 + z\_{earth})((1 + z\_{sun})(1 + z\_{source})(1 + z\_{gravity})}-1 \end{equation}

So is this what we put in (4)?

Edit: For the source you can look here <https://arxiv.org/abs/1907.12639> Eqn(16) and (18)

**Tags:** star, cosmology, redshift

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## 1 answers

### Answer by username_1 on 2020-02-20. Score: 1 | Accepted answer

In Equation (16) of the paper you link to, $z$ is the observed redshift. In the first paragraph of section 2.2

> The heart of the method is to use a measured redshift, z, to infer a velocity, v(z)


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