<p>It is miniscule. General Relativity is not required to understand the dynamics of galaxies. Motions are non-relativistic, a few 100 km/s at most, so the kinetic energy of objects is always much smaller than their rest mass energy.</p>
<p>Another way of seeing this is to calculate <span class="math-container">$GM/Rc^2$</span>, a ratio which tells you the relative size of errors you will get in ignoring GR in any calculation.</p>
<p>For our Galaxy, we might say there is about <span class="math-container">$M\sim 10^{11} M_{\odot}$</span> within <span class="math-container">$R\sim 15$</span> kpc, and the ratio is then <span class="math-container">$3\times 10^{-7}$</span>, which indicates Newtonian gravity is fine for most purposes.</p>
<p>Note that gravitational potential energy is <em>negative</em> and is somewhat larger in magnitude  than the kinetic energy for an object in a bound orbit. This means that adopting a General Relativistic approach would mean that the &quot;effective gravitational mass&quot; is actually <em>less</em> than adding up the masses of all the Galaxy's components. But as I said above, the effect is negligibly small.</p>
<p>Note also that the distribution of the inferred dark matter extends <em>way</em> beyond the location of most of the visible matter. Thus the distribution of kinetic energy density of the things we can see <em>does not</em> meet the requirements.</p>

CC BY-SA 4.0
2020-08-01T09:33:47.790Z
2021-08-06T06:30:39.617Z
2021-08-06T06:30:39.617Z
ProfRob
<p>The higher than expected rotational velocity of stars and gas clouds in the outskirts of galaxies is explained today by invoking dark matter that supplies not only the additional gravitational mass explaining the increased rotational speed in the arms, but explains the amount of gravitational lensing of more distant galaxies.</p>
<p>Furthermore, dark matter distribution about spiral galaxies places it on the outside of galaxies and not so much on the inside.</p>
<p>Certainly the higher than expected velocity on the outside of galaxies also translates into higher than expected kinetic energy. Should the extra kinetic energy also increase the gravitational stress energy tensor in that region of space.</p>
<p>If so, do our models already factor in kinetic energy and it's gravitational stress energy tensor,  overlook it, or the effect is just too minuscule to be of any importance?</p>
<p>I don't expect the extra kinetic energy to be a replacement for dark matter, and suspect the effect may be too small to be of much importance, but the kinetic energy distribution around a galaxy, intuitively on the surface, appears to have the right distribution, so I'm asking generically, do astrophysics factor this in their models, or not, and if not, should it?</p>

CC BY-SA 4.0
2021-08-06T00:07:17.850Z
Do you feel the current answer is sufficient? I've been going through my old questions and [looking for answers I'd forgotten to accept](https://astronomy.meta.stackexchange.com/a/776/7982) and I ran across this post by accident.
uhoh
CC BY-SA 4.0
2021-08-06T01:14:24.410Z
@uhoh I'm not entirely sure. I was kind of hoping that maybe some kind of explainable energy warped spacetime enough to explain the kinds of gravitational lensing and anomalous velocities of stars around galaxies. In other words, explain dark matter with what's already known. I did mention kenetic, but maybe I should have included gravitational potential energy in my question. Is it appropriate to change or clarify my question so late? I think gravitational potential energy between black holes warps spacetime with some of it lost to gravitational waves.
Keith Reynolds
CC BY-SA 4.0
2021-08-06T01:15:45.660Z
I noticed that you haven't left a comment under the current answer, so the answer's author is not yet aware of your concern.
uhoh
CC BY-SA 4.0
2021-08-06T01:25:57.460Z
@uhoh Thank you. But is it appropriate  to change the question so late?  As is, the author's answer to my question looking at just kenetic energy seems appropriate in scale though I'm not well qualified to judge it.
Keith Reynolds
CC BY-SA 4.0
2021-08-06T01:34:36.690Z
We generally don't substantially change a question once an answer is posted, but ProfRob is an active and responsive question-answerer and I think would be receptive to adding some elaboration if queried. But another strategy is to adjust this question to *better fit* the existing answer and then go ahead and ask a new and different question. In it you'd link back here and mention what's different which avoids anyone from thinking it might be a duplicate. That's what I normally do and I like it because new answers happen this way.
uhoh
<galaxy><gravity><rotation><general-relativity><dark-matter>
Kinetic energy and galaxy arm rotation rate
Keith Reynolds
# Kinetic energy and galaxy arm rotation rate

(Asked by: username_0 on 2020-07-31)

The higher than expected rotational velocity of stars and gas clouds in the outskirts of galaxies is explained today by invoking dark matter that supplies not only the additional gravitational mass explaining the increased rotational speed in the arms, but explains the amount of gravitational lensing of more distant galaxies.

Furthermore, dark matter distribution about spiral galaxies places it on the outside of galaxies and not so much on the inside.

Certainly the higher than expected velocity on the outside of galaxies also translates into higher than expected kinetic energy. Should the extra kinetic energy also increase the gravitational stress energy tensor in that region of space.

If so, do our models already factor in kinetic energy and it's gravitational stress energy tensor, overlook it, or the effect is just too minuscule to be of any importance?

I don't expect the extra kinetic energy to be a replacement for dark matter, and suspect the effect may be too small to be of much importance, but the kinetic energy distribution around a galaxy, intuitively on the surface, appears to have the right distribution, so I'm asking generically, do astrophysics factor this in their models, or not, and if not, should it?

**Tags:** galaxy, gravity, rotation, general-relativity, dark-matter
> **Comments:**
> **username_1**: Do you feel the current answer is sufficient? I've been going through my old questions and [looking for answers I'd forgotten to accept](https://astronomy.meta.stackexchange.com/a/776/7982) and I ran across this post by accident.  
> **username_0**: @uhoh I'm not entirely sure. I was kind of hoping that maybe some kind of explainable energy warped spacetime enough to explain the kinds of gravitational lensing and anomalous velocities of stars around galaxies. In other words, explain dark matter with what's already known. I did mention kenetic, but maybe I should have included gravitational potential energy in my question. Is it appropriate to change or clarify my question so late? I think gravitational potential energy between black holes warps spacetime with some of it lost to gravitational waves.  
> **username_1**: I noticed that you haven't left a comment under the current answer, so the answer's author is not yet aware of your concern.  
> **username_0**: @uhoh Thank you. But is it appropriate  to change the question so late?  As is, the author's answer to my question looking at just kenetic energy seems appropriate in scale though I'm not well qualified to judge it.  
> **username_1**: We generally don't substantially change a question once an answer is posted, but ProfRob is an active and responsive question-answerer and I think would be receptive to adding some elaboration if queried. But another strategy is to adjust this question to *better fit* the existing answer and then go ahead and ask a new and different question. In it you'd link back here and mention what's different which avoids anyone from thinking it might be a duplicate. That's what I normally do and I like it because new answers happen this way.  

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## 1 answers

### Answer by username_2 on 2020-08-01. Score: 4 | Accepted answer

It is miniscule. General Relativity is not required to understand the dynamics of galaxies. Motions are non-relativistic, a few 100 km/s at most, so the kinetic energy of objects is always much smaller than their rest mass energy.

Another way of seeing this is to calculate $GM/Rc^2$, a ratio which tells you the relative size of errors you will get in ignoring GR in any calculation.

For our Galaxy, we might say there is about $M\sim 10^{11} M\_{\odot}$ within $R\sim 15$ kpc, and the ratio is then $3\times 10^{-7}$, which indicates Newtonian gravity is fine for most purposes.

Note that gravitational potential energy is *negative* and is somewhat larger in magnitude than the kinetic energy for an object in a bound orbit. This means that adopting a General Relativistic approach would mean that the "effective gravitational mass" is actually *less* than adding up the masses of all the Galaxy's components. But as I said above, the effect is negligibly small.

Note also that the distribution of the inferred dark matter extends *way* beyond the location of most of the visible matter. Thus the distribution of kinetic energy density of the things we can see *does not* meet the requirements.


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