<p>The key assumption is that orbital velocity vectors are distributed randomly. Then the dispersion of velocities along each axis must be the same, e.g. <span class="math-container">$\sigma_x=\sigma_y=\sigma_z$</span> if <span class="math-container">$x$</span>, <span class="math-container">$y$</span>, and <span class="math-container">$z$</span> denote perpendicular axes. But then the total squared velocity dispersion is <span class="math-container">$\sigma^2=\sigma_x^2+\sigma_y^2+\sigma_z^2=3\sigma_x^2$</span>.</p>

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2023-08-06T16:30:19.577Z
2023-08-06T16:30:19.577Z
Sten
<p><a href="https://i.sstatic.net/QwjRH.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/QwjRH.png" alt="enter image description here" /></a></p>
<p>In the above given picture Vi is the velocity of the i-th galaxy in the cluster while Vm is the mean velocity of a galaxy in the cluster. and V i,r is the radial velocity of the i-th galaxy and V m,r is the mean radial velocity. How does converting mean velocity to mean radial velocity introduce a coefficient of 3.</p>
<p>Image source IOAA 2019 question 13.</p>

<gravity><orbital-mechanics><mass>
How to turn find velocity dispersion from radial velocity
Moiz khokhar
# How to turn find velocity dispersion from radial velocity

(Asked by: username_0 on 2023-08-06)

[![enter image description here](https://i.sstatic.net/QwjRH.png)](https://i.sstatic.net/QwjRH.png)

In the above given picture Vi is the velocity of the i-th galaxy in the cluster while Vm is the mean velocity of a galaxy in the cluster. and V i,r is the radial velocity of the i-th galaxy and V m,r is the mean radial velocity. How does converting mean velocity to mean radial velocity introduce a coefficient of 3.

Image source IOAA 2019 question 13.

**Tags:** gravity, orbital-mechanics, mass

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## 1 answers

### Answer by username_1 on 2023-08-06. Score: 5 | Accepted answer

The key assumption is that orbital velocity vectors are distributed randomly. Then the dispersion of velocities along each axis must be the same, e.g. $\sigma\_x=\sigma\_y=\sigma\_z$ if $x$, $y$, and $z$ denote perpendicular axes. But then the total squared velocity dispersion is $\sigma^2=\sigma\_x^2+\sigma\_y^2+\sigma\_z^2=3\sigma\_x^2$.


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