<p>The relationship between <a href="https://en.wikipedia.org/wiki/Distance_measure#Proper_distance" rel="nofollow noreferrer">proper distance</a> and the rate of change of proper distance is Hubble's law. So
<span class="math-container">$$ v(r_0) = H_0 r_0 \ .$$</span>
Note that <span class="math-container">$H_0$</span> is the Hubble parameter at the present epoch. The Hubble parameter changes with time.</p>
<p>There are however different ways to define velocity and distance... <a href="https://en.wikipedia.org/wiki/Distance_measure" rel="nofollow noreferrer">https://en.wikipedia.org/wiki/Distance_measure</a> and these will have more complex relationships between them that depend on other cosmological parameters.</p>

CC BY-SA 4.0
2023-11-13T08:29:42.047Z
2023-11-13T12:50:57.400Z
2023-11-13T12:50:57.400Z
ProfRob
<p>How does the distance <span class="math-container">$r$</span> scale with the expansion of the universe?For example if <span class="math-container">$r_{o}$</span> is the distance between us and a galaxy and <span class="math-container">$V(r_{o})$</span> is the rate of expansion of the universe at that distance , what is <span class="math-container">$V(r_{0})$</span> equal to?</p>

CC BY-SA 4.0
2023-11-13T08:24:34.177Z
Define "distance". https://en.wikipedia.org/wiki/Distance_measure
ProfRob
CC BY-SA 4.0
2023-11-13T08:24:53.580Z
The coordinate distance , not the proper distance
Root
CC BY-SA 4.0
2023-11-13T08:30:59.477Z
"coordinate distance" isn't a term I recognise, can you define it?
ProfRob
<observational-astronomy><observable-universe><dark-energy>
Formula for rate of expansion of the universe vs distance?
Root
# Formula for rate of expansion of the universe vs distance?

(Asked by: username_0 on 2023-11-13)

How does the distance $r$ scale with the expansion of the universe?For example if $r\_{o}$ is the distance between us and a galaxy and $V(r\_{o})$ is the rate of expansion of the universe at that distance , what is $V(r\_{0})$ equal to?

**Tags:** observational-astronomy, observable-universe, dark-energy

> **Comments:**
> **username_1**: Define "distance". https://en.wikipedia.org/wiki/Distance_measure  
> **username_0**: The coordinate distance , not the proper distance  
> **username_1**: "coordinate distance" isn't a term I recognise, can you define it?  

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## 1 answers

### Answer by username_1 on 2023-11-13. Score: 2

The relationship between [proper distance](https://en.wikipedia.org/wiki/Distance_measure#Proper_distance) and the rate of change of proper distance is Hubble's law. So
$$ v(r\_0) = H\_0 r\_0 \ .$$
Note that $H\_0$ is the Hubble parameter at the present epoch. The Hubble parameter changes with time.

There are however different ways to define velocity and distance... <https://en.wikipedia.org/wiki/Distance_measure> and these will have more complex relationships between them that depend on other cosmological parameters.


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