1
$\begingroup$

Let's first have a look at the observed speed within galaxies (source): measure of speed within galaxy

On the left side we can see the speed of celestial bodies within galaxies derived by gravity only (gravity is usually created by a black hole at the center of a galaxy), on the right side we can see the observed speed of celestial bodies, both in respect of the distance from the galactic center.

As a result, the strength of dark matter (or "space force") could be calculated as:

$F$dark matter = $m$galaxy $\cdot$ $v$celestial body within galaxy $\frac{d}{dt}$ - $g$black hole, center of galaxy

Is this a viable calculation? And if so, are there any a graphs online which show this strength of dark matter (or "space force") in respect of the distance from the galactic center?

(Note: In this formula, a galaxy would be assigned a mass $m$galaxy much higher than the mass of its black hole. However, mathematically speaking one could also just decrease $dt$, so with a celestial body wandering from the center to the outskirts of the galaxy, $dt$ would decrease, hence the speed of time would increase. I doubt this is true because it would change the basic definition of speed $v$celestial body within galaxy as well and introduce all kinds of illogical contradictions, but in math everything is possible as we know from theory of relativity...)

Addendum:

  • $m$galaxy $\cdot$ $v$celestial body within galaxy $\frac{d}{dt}$ $[kg·\frac{m}{s^2}]$ = observable force (shown in picture on the right)
  • $g$black hole, center of galaxy $[kg·\frac{m}{s^2}]$, the force caused by gravity of a black hole (shown in picture on the left)
  • $F$dark matter $[kg·\frac{m}{s^2}]$, the force of dark matter up until a point in space
$\endgroup$
5
  • $\begingroup$ Please explain your notation. What do $F_{\text{dark_matter}}$, $dt$ and $G_{\text{black hole}}$ mean ? Without knowing what your terms mean, it is not even clear that your formula is dimensionally correct. $\endgroup$
    – gandalf61
    Oct 6, 2020 at 13:39
  • $\begingroup$ $mvd/dt$ is the force that is supposed to be caused by dark matter up until a point within the galaxy (shown in the right picture). $G_{black−hole}$ is the force that is caused by the black hole's gravity (shown in the left picture). $F_{dark-matter}$ is the difference... $\endgroup$
    – Marcus
    Oct 6, 2020 at 14:19
  • $\begingroup$ Hope that addendum will clarify things... $\endgroup$
    – Marcus
    Oct 6, 2020 at 14:29
  • 1
    $\begingroup$ "Note that the gravity usually comes from a black hole at the center of a galaxy)". No it doesn't. $\endgroup$
    – ProfRob
    Oct 6, 2020 at 19:27
  • $\begingroup$ @Rob: Changed some notations, I think it's pretty clear now. $\endgroup$
    – Marcus
    Oct 7, 2020 at 7:50

1 Answer 1

1
$\begingroup$

Your equation seems to be trying to express the gravitational contribution of dark matter as the difference between the observed gravitational force on a star at a given distance from the centre of a galaxy and the theoretical gravitational force based on the stars that can be seen in the galaxy.

This is pretty much what the velocity/distance curves show. The difference between observed and theoretical gravitational force can be worked out from the rotational velocity at a given distance because the centripetal force required to keep a star in a galactic orbit with speed $v$ and radius $r$ is proportional to $\frac {v^2}{r}$.

The super-massive black hole which lies, we believe, at the centre of most galaxies makes only a very small contribution to the gravitational attraction of the galaxy as whole. The typical mass of such a black hole is around $1 \%$ of mass of the stars in the galaxy, or around $0.1 \%$ of the total galactic mass including dark matter.

$\endgroup$
1

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.