<p>I read somewhere that the galaxy is spinning too fast (in places). Therefore, there must be dark matter.  What are the equations that explain how fast the galaxy should be moving, and how are they violated?  What are the speeds and masses involved?</p>

CC BY-SA 4.0
2021-01-14T09:47:24.293Z
Could you explain what's missing from the already abundant explanations of this on the internet. e.g. https://en.wikipedia.org/wiki/Galaxy_rotation_curve  which has the relevant equations and typical numbers.
ProfRob
CC BY-SA 4.0
2021-01-14T23:02:23.493Z
I understand your confusion.  I am not asking for abundant explanation.  Just simple answers.  What is the equation that relates gravity to galactic spin?  What are the observed masses and speeds?  With the modern obsession with complexity, I find it difficult to get help with the simple questions.
Hoytman
CC BY-SA 4.0
2021-01-14T23:16:44.543Z
Newton's second law and Newton's universal gravitational law. The mass of the Galaxy is about $10^{12} M_\odot$ and typical rotation speeds at the radius of the Sun and beyond are 240 km/s, which is of order two times bigger than can be explained with visible mass.
ProfRob
CC BY-SA 4.0
2021-01-18T18:39:57.207Z
Where would the dark matter be situated?  In an around the individual suns and planets, making them heavier?  Where does the extra mass need to be added?
Hoytman
CC BY-SA 4.0
2021-01-18T19:22:55.853Z
The density of the required dark matter scales as $r^{-1}$ for small Galactocentric radii, smoothly changing to $r^{-3}$ at large radii. There is not expected to be any significant clumping around stars or planets. See https://en.wikipedia.org/wiki/Navarro%E2%80%93Frenk%E2%80%93White_profile It is thought to be roughly spherically symmetric, in contrast to the visible matter. The vast majority of the dark matter mass is outside the orbit of the Sun.
ProfRob
<galaxy><orbital-mechanics><dark-matter>
Why is dark matter required?
Hoytman
# Why is dark matter required?

(Asked by: username_0 on 2021-01-14)

I read somewhere that the galaxy is spinning too fast (in places). Therefore, there must be dark matter. What are the equations that explain how fast the galaxy should be moving, and how are they violated? What are the speeds and masses involved?

**Tags:** galaxy, orbital-mechanics, dark-matter
> **Comments:**
> **username_1**: Could you explain what's missing from the already abundant explanations of this on the internet. e.g. https://en.wikipedia.org/wiki/Galaxy_rotation_curve  which has the relevant equations and typical numbers.  
> **username_0**: I understand your confusion.  I am not asking for abundant explanation.  Just simple answers.  What is the equation that relates gravity to galactic spin?  What are the observed masses and speeds?  With the modern obsession with complexity, I find it difficult to get help with the simple questions.  
> **username_1**: Newton's second law and Newton's universal gravitational law. The mass of the Galaxy is about $10^{12} M_\odot$ and typical rotation speeds at the radius of the Sun and beyond are 240 km/s, which is of order two times bigger than can be explained with visible mass.  
> **username_0**: Where would the dark matter be situated?  In an around the individual suns and planets, making them heavier?  Where does the extra mass need to be added?  
> **username_1**: The density of the required dark matter scales as $r^{-1}$ for small Galactocentric radii, smoothly changing to $r^{-3}$ at large radii. There is not expected to be any significant clumping around stars or planets. See https://en.wikipedia.org/wiki/Navarro%E2%80%93Frenk%E2%80%93White_profile It is thought to be roughly spherically symmetric, in contrast to the visible matter. The vast majority of the dark matter mass is outside the orbit of the Sun.  

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