"Think of the amount of mass required to generate a gravitational pressure needed to overcome the electromagnetic binding force between molecules inside the mass--the equilibrium occurs, basically, when an object in space becomes spherical. This happens at about 10^20 - 10^21kg. Divided by the mass of a proton implies you need about 10^47 atoms to generate the amount of gravitational pressure to break the electromagnetic strength between atoms." (1)

Richard Feynman would tell you that this immense difference is "what's keeping you from not falling through the floor down to the Earth center." Or why the apple hanging on the "few atoms" of its stalk is not falling from the tree, when the summary gravitation of all atoms of the whole Earth are pulling it down.

Or, again to compare such big numbers, there are "only" 10^86 atoms in the whole Universe observable to us! (2)

1) https://www.physicsforums.com/threads/how-are-the-gravitatio...

2) https://www.universetoday.com/36302/atoms-in-the-universe/

But you do not need to measure it particle by particle. Just because those have mass, there should be a bunch of dark matter particles hanging around with earth. And given that we have quite good idea what earth consists of, there should be a discrepancy in some of the measurements that use earth's mass against the mass we have from our understanding of earth's composition. Unless, of course, the extra mass of earth due to dark matter is calculated in e.g. kilograms. That's why I would like to know the expected density of the dark matter.

Fascinatingly, it is known that the interaction of the dark matter with the Earth is so weak that there would be no "clumping" of it around the Earth at all! No "clumping" even around e.g. Sun can be observed. The "hanging around" is on the level of the whole galaxies, and sometimes the dark matter even remains outside of the whole galaxies, being too slow to follow their gravitational interaction(!) That's the famous example of the "bullet cluster":

https://www.forbes.com/sites/startswithabang/2017/11/09/the-...

That's how weakly the dark matter interacts with anything else. And it obviously doesn't even interact strong enough to "fall" to the center of the galaxy. Otherwise it would be there, but it remains to the outside of even where the "normal" matter is (mostly the stars and black holes, the "supermassive black hole" in the center is only at most 1e-5 of the estimated total mass of our Galaxy).

Or more precise:

https://medium.com/starts-with-a-bang/ask-ethan-if-dark-matt...

There’s “just a little more” of the dark matter in our Solar system but way below the levels it could affect the measurements we can perform.

> Fascinatingly, it is known that the interaction of the dark matter with the Earth is so weak that there would be no "clumping" of it around the Earth at all!

If it interacts so weakly I don't understand why clumps around anything. In fact if it only interacted via gravity I would expect it to start slowly accelerating toward normal matter, spend a short time near it, then speed away as it slowed down again. If the path is an eclipse this would mean it spends most of its time away from the matter rather than near. It would be almost as if gravity caused normal mater to repel dark matter.

> Fascinatingly, it is known that the interaction of the dark matter with the Earth is so weak that there would be no "clumping" of it around the Earth at all!

Would I be right in thinking that also puts severe limits on how much it interacts with itself? Because my intuition would be, if you loose normal matter into a gravity well, it will clump, even if it doesn't interact with the source of the gravity.

Am I inferring correctly?

> Because my intuition would be, if you loose normal matter into a gravity well, it will clump, even if it doesn't interact with the source of the gravity. Am I inferring correctly?

Now I have a little of Newton for you: look at our Solar system: you see the planets, and even more interesting, all the small asteroids circling around the Sun? Can you answer why don't they all fall to the Sun, but move in the orbits?

The way the gravitation works was not "intuitive" before Newton, 300 years ago, and now it's obviously still so for many non-professional readers.

What's actually happening, according to the dark matter model, and the dark matter actually more easily fits much more of our cosmological observations than anything else, is that there is a lot of dark matter but it is simply much more "spread" around the volume of the galaxies. And just like all the visible stuff of the whole galaxy doesn't fall to the galaxy center (like the planets don't fall to the Sun!), the dark matter remains "around" the galaxies, where more of dark matter is "outside" (as in "in the outer regions of it") than in the "inside" of the galaxy (and in the case of the "Bullet Cluster", that I've mentioned in some other comment, dark matter is obviously lagging all the movement of non-dark matter! (1)). That dark matter that is in the inside of the galaxies actually initially "clumped" somewhat, but that "somewhat" is, according to our estimates, significantly below what we are able to measure, when we're interested in the gravitational effect on the Solar system.

1) https://en.wikipedia.org/wiki/Bullet_Cluster#/media/File:Bul... and https://en.wikipedia.org/wiki/Bullet_Cluster#/media/File:1e0...

> Now I have a little of Newton for you

Sweet of you to bring me Newton. Always a welcome gift.

But I think you misunderstand where my question is pitched.

The solar system is rather clumped, you see. A little Aristotle for you. :)

In all seriousness, the more dark matter is around, the less it can have mutual interactions, before it would clump, surely? Assuming such forces exist, there is a nonzero probability that two particles of dark matter will approach close enough that non-gravity forces will be significant, And they will no longer act under an ideal Newtonian gravity. Dust clouds coalesce into suns, given time. Can dark matter have its own dark-only version of the electromagnetic force? Or is that ruled out by the lack of clumping? Or is there just too little of it to make a conclusion on that? My question was entirely consistent with ol' Issac.

> Can dark matter have its own dark-only version of the electromagnetic force? Or is that ruled out by the lack of clumping?

My "feeling" is, it's not "intuitive enough" to "guess" any answer without a lot of computing:

https://www.quantamagazine.org/coder-physicists-are-simulati...

We think we're quite sure in our observations, so that helps, but to be able to claim how the simple laws can exactly produce what we see, we have to do a lot of work. Just like what Newton figured out was not provable before without all the computations:

http://www4.ncsu.edu/~kimler/hi322/halleytale.html

Indeed the mass of dark matter is why we think there is dark matter -- discrepancies such as you mention, but evident from astronomical observations. The problem for characterizing the particles is: Mass and what else? The what else is the thing people are trying to detect.

We don't have that good idea of what the earth consists of. I think much of those theories are based on counting backwards from knowing the mass, and if we have 5% dark mass orbiting Earth, it wouldn't make any material difference.

They are not distributed evenly throughout space. So if you measure more gravity in a region of space that you cannot see (because dark matter doesn’t interact with em), is it dark matter, or an error in your theory of gravity?