I understand that at smaller scales the strong, weak, and nuclear forces, and chemical bonds have more influence on the formation of objects than gravity. At what amount of mass does gravity become the dominant force that holds together the matter that will become planetesimals, asteroids, or comets?
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It depends on the charge on the particles and distances involved. – bemjanim Dec 21 '19 at 21:21
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It depends on what the dust is made of, specifically how many coulombs it has (a surplus or deficit of electrons). As mass can be measured in energy, electronvolts/speed-of-light2, and eV is the energy of 1 electron subject to 1 joule of electric potential difference (or one volt [force exerted over distance behind a coulomb's worth of electrons] with the coulombs canceling out, I think), if you know the number of missing or extra electrons and the distance and masses of the dust particles, you can multiply the masses by the gravitational constant and divide by the distance to get the gravitational energy which can be compared to the product of the two electron surpluses/deficits and the electrostatic constant in a vacuum divided by distance for the electric field energy. It's no coincidence that these two look the same, both gravity and electricity are fields described in classical field theory.
Essex
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The original question was edited, and the answer is now in the comments.
Gravity is the weakest of all forces at the small scale as you say. Now you are asking what amount of mass (in reality stress-energy) do I need to make gravity dominate over all the other forces?
Now imagine you hold two magnets (same pole to repel) close to each other (above each other) at the surface of the Earth. Gravity might appear as strong, since it holds you to the ground, but the magnets can easily repel each other, and make the upper magnet appear as if it was levitating (and even at the smallest scalethe EM and the strong force being stronger then gravity makes objects made of molecules have volume too).
So Earth is not enough, it does not have enough stress energy.
And all matter is a mixture of positive protons and negative electrons which are attracting and repelling with this great force. So perfect is the balance however, that when you stand near someone else you don't feel any force at all. If there were even a little bit of unbalance you would know it. If you were standing at arm's length from someone and each of you had one percent more electrons than protons, the repelling force would be incredible. How great? Enough to lift the Empire State building? No! To lift Mount Everest? No! The repulsion would be enough to lift a "weight" equal to that of the entire earth!
What does it mean to say "Gravity is the weakest of the forces"?
The only object in the universe, that we know of, that has enough stress energy to dominate over all the other forces even on the smallest scale (even molecules could get spaghettified) is the black hole (though, please note that this is due to tidal forces too caused by gravity). Though, please note for example neutron stars have a lot of stress energy too.
Anything above elementary particles should in theory be ripped apart, yes. Talking about elementary particles themselves or even just the separation of hadrons or baryons is a whole different story. Because we lack an understanding of black holes at a quantum mechanical level it is surprisingly difficult to actually examine spaghettification at these fundamental levels.
Árpád Szendrei
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I was hoping to learn at what point in the formation of a solar system does electrostatic interactions no longer dominate the formation of the material that will form protoplanets, comets, and asteroids. – Bob516 Dec 21 '19 at 22:59
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Granted, the Earth does not have enough gravitational force to prevent two magnets of the same pole from repelling. Is the fact that the Earth is a dipole a result of gravity or some other force. – Bob516 Dec 21 '19 at 23:06
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1@Bob516 the Earth is a dipole because of its magnetic field, which originates from molten iron currents that create electric currents in the outer core. https://en.wikipedia.org/wiki/Earth%27s_magnetic_field – Árpád Szendrei Dec 22 '19 at 00:59
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1@Bob516 EM interactions dominate inside the molecules of dust, but after that, dust is dominated by gravity (in space) and gravity pulls dust particles together to form all objects. – Árpád Szendrei Dec 22 '19 at 01:02
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