# MOND: Explaining the “Missing Mass” Problem in Galaxies

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• exmarine
In summary, MOND adds one parameter to the equations - can't get much simpler than that. It uses the simplest equation that matches the data. It does well on galactic scales, but does not do well at larger scales. Our solar system is on the flat part of our own galaxy's rotation curve, and we are rotating "too fast" about the galaxy center. There is suspected to be dark matter in our galaxy and within our solar system, and its density is estimated to be around 1013 kg per AU3.

#### exmarine

I’ve been reading various things on the internet about how Modified Newtonian Dynamics attempts to solve (or just model?) the “missing mass” problem in galaxies. It sounds more reasonable to me than hypothesizing conveniently undetectable dark matter. But I am wondering why they are using what seems like more complicated expressions than necessary. Isn’t it a simple curve fit for the universal gravitation “constant”? I am assuming there must be good reasons why it is not that “simple”. Any help in understanding this is appreciated.

MOND adds one parameter to the equations - can't get much simpler than that. It uses the simplest equation that matches the data.

Note that while MOND does well on galactic scales, it does not do well at larger scales.

vanhees71
I see. So that makes it difficult or impossible to correct by adjusting a universal “constant” and making it a function of distance.

Are we – our solar system – on the flat part of our own galaxy’s rotation curve? Are we rotating “too fast” about the galaxy center?

Is our solar system then permeated with Dark Matter? If so, wouldn’t that require reformulation of Newton dynamics / Kepler’s laws?

What distribution of DM is suspected in our galaxy, and within our solar system?

exmarine said:
Are we – our solar system – on the flat part of our own galaxy’s rotation curve? Are we rotating “too fast” about the galaxy center?
Here are example graphs with plotted approximated mass distribution and its contribution to rotation curves in the MW (precision is exaggerated):

The sun is at approx. 8 kpc from the centre. As you can see, it's a roughly flat curve at that distance.
exmarine said:
Is our solar system then permeated with Dark Matter? If so, wouldn’t that require reformulation of Newton dynamics / Kepler’s laws?
The graph on the right shows that there's approx. 25% more dark matter than baryonic (i.e. Disc+Bulge) matter enclosed within the radius of the orbit of the Sun. However, unlike baryonic matter DM does not clump, so its density in any given region of space is extremely low - so low that any effect it might have on the dynamics within the solar system is negligible.
The graph to the right allows you to make a rough calculation of the density of DM in the solar system using simple algebra - the result being about 1013 kg per AU3. That is, according to this estimate, at any given time there's about 100 000 supertankers' worth of DM spread around in a sphere inside Earth's orbit, or ~10-22g/cm3, which is not far from estimates done using other, more precise methods (such as here or here).

These values are too low to have a noticeable effect, unless you look extremely carefully - the first of the two papers quoted above actually attempts just that. As such, they could not affect formulation of Kepler's, Newton's and other laws or experiments with insufficient precision.

exmarine said:
What distribution of DM is suspected in our galaxy, and within our solar system?
The distribution in its simplest form is shown on the graph above (right). Linear growth of enclosed mass translates to a spherically symmetric cloud whose density is falling with the square of the distance.
Unless it turns out DM can sufficiently interact with matter (e.g. weak force), it will be freely streaming through the solar system with density corresponding to the density in the galactic DM profile at this distance from its centre.

exmarine
Thanks for the info and the papers! Fascinating subject.

## What is MOND and how does it explain the "Missing Mass" Problem in Galaxies?

MOND (Modified Newtonian Dynamics) is a theory that proposes a modification to the laws of gravity in order to explain the discrepancy between the observed mass in galaxies and the amount of mass predicted by current theories. It suggests that instead of dark matter, the laws of gravity should be modified at low accelerations, which can account for the "Missing Mass" problem.

## How does MOND differ from the theory of dark matter?

Unlike the theory of dark matter, which proposes the existence of invisible and undetectable matter, MOND suggests that the laws of gravity should be modified at low accelerations. This means that MOND does not require the existence of any new type of matter, making it a more conservative and simpler explanation for the "Missing Mass" problem.

## What evidence supports the MOND theory?

One of the main pieces of evidence for MOND is the observed rotation curves of galaxies, which show that the velocity of stars and gas in the outer regions of the galaxy do not decrease as expected according to Newton's laws. MOND can accurately predict these observed rotation curves without the need for dark matter. Additionally, MOND can also explain other phenomena, such as the Tully-Fisher relation, the mass discrepancy in galaxy clusters, and the distribution of matter in the universe.

## What are the criticisms of the MOND theory?

One of the main criticisms of MOND is that it does not provide a complete explanation for all observations related to the "Missing Mass" problem. While it can explain the observed rotation curves of galaxies, it struggles to explain other phenomena, such as gravitational lensing and the cosmic microwave background. Additionally, MOND requires modifications to the laws of gravity, which goes against the well-established principles of general relativity.

## How does MOND impact our understanding of the universe?

MOND challenges our current understanding of the universe and the laws of gravity. If it is proven to be a valid explanation for the "Missing Mass" problem, it could potentially revolutionize our understanding of gravity and the structure of the universe. It could also have implications for other areas of physics, such as cosmology and the study of dark energy.