For normal nuclei it does, but when you get up into a solar mass sized blob of them, gravity exceeds it. That's because the repulsion is going in all directions and nets out against itself but all the gravity points inwards cumulatively.

(Edit because we got a little confused in the replies: If it were all protons, they would repel and overcome gravity. But real matter isn't that, it's always protons and neutrons and electrons with close to no net repulsion so gravity wins.)

Similarly, radioactive nuclei (alpha emitters and spontaneous fission) happen because the electromagnetic repulsion exceeds the strong force, which has a very short range and doesn't reach across those large nuclei.

> That's because the repulsion is going in all directions and nets out against itself but all the gravity points inwards cumulatively.

Is that true? All of the protons repel all other protons with the electric force and attract with the gravitational force, and it seems like gravity is just much weaker at all distances...

I haven't thought about this very hard though.

Think of three protons in a line, A-B-C. Proton B is repelled in both directions so experiences no net force.

Now think of 10^50 protons in a line. They're all experiencing net gravity towards the middle.

A is repelled outward, B is not repelled, C is repelled outward.

With gravity, A is attracted inward, B is not attracted, C is attracted inward.

Your idea doesn't generalize. With A-B-C-D-E, only C experiences no net forces along the horizontal axis, while all the others (A, B, D, E) are repelled outward. Therefore the electromagnetic force is not cancelled as you seem to imply.

Of course, in practice, we don't know what the inside of a black hole is like, as quantum gravity is very much unsolved.

Okay, but A and B are both repelled outward and it explodes.

So the conclusion is any proton star would just explode? That's what I already thought.

We like to say gravity is "weak", however it seems to operate on many orders of magnitude larger distances.

Even if you make the argument that the energy complicit in the strong/weak forces is cumutavily much greater than the energy due to gravity, I'm still not sure "weak" is the right word for the job...

Gravity onstensibly runs at infinite speed over infinite area (the effect of gravity waves non-withstanding).

I think that gravity starts winning once it becomes strong enough to encourage the positive charges to evacuate, leaving neutrons where there once were protons, like the juice leaving a squeezed orange.

Don't forget electron capture and positron emission converting some of those protons into neutrons.

Gravity is strictly accumulative. All other forces are paired with positive and negative carriers (electromagnetic, weak nuclear, strong nuclear).

Protons can generate neutrons through beta decay. I suspect something like this happens in neutron stars, which don't spontaneously fly apart into a proton cloud, so far as we've observed.

This SE comment explains why neutron stars don't contain (many) protons:

<https://physics.stackexchange.com/a/149656>

(The ratio seems to be ~100:1 neutron:proton.)

protons can generate neutrons and neutrons can generate protons . why are there no nuclea with only neutrons ? — these could be as big as you want because there is no electric repulsion . the answer is that only neutron nucleus would have — by pauli exclusion principle — very large kinetic energy . so nucleus turns couple of its neutrons into protons to lower the kinetic energy of neutrons . same reason for small fraction of protons in neutron stars

There are nuclei with only neutrons. We call those "neutron stars".

They're ... both big (by atomic scales) and massive (atomic and astronomical).

and they _always_ have few percent of protons and electrons — every single one of them .

and they _always_ have few percent of protons and electrons — every single neutron star .

Does that mean that in some ridiculous sense, a neutron star is a unique element?

I've seen similar suggestions, but it's ... probably not an especially useful conceptualisation.

The conceptualisation of elements is useful to us because physical characteristics of atoms are (mostly) stable over time, with atoms having distinctive masses, atomic numbers, and most importantly, electron shells. The latter account for most of what we consider to be "chemistry", along with some other effects, most notably the van der Waals force.

Neutron stars ... lack most of this. They're in constant flux, they (probably) don't have stable masses (if only due to constant accretion) or atomic numbers, they probably don't have anything resembling an electron shell, and in interactions with other objects any electromagnetic forces would probably be overwhelmed by gravity or, say, spin-induced magnetism. If a measure of a concept or model's usefulness is how much it explains behaviours, "neutron-star-as-element" doesn't buy you much.

Though there's possibly some truth or conceptual validity to it.

So in a single sentence - you can't do chemistry with a neutron star, so don't bother asking the question...? Not OP but I'm buying it.

Questions are almost always worth asking, and there's at least some philosophical interest in this case. But from a practical perspective as a chemical phenomenon, not much use.

I subscribe strongly to a pragmatic approach to knowledge and understanding. That is, knowledge isn't so much true as it is useful, in that it provides a useful mental model of the world. There are cases where multiple truths are possible, as with wave-particle duality, or mass-energy. Either classification may be useful, that is, provide predictive, understanding, or manipulative power, depending on contexts and circumstances. Some of the classic philosophical paradoxes (Sorites, Ship of Thesus, falling tree in a forest) resolve at least somewhat under this view. What is often called "truth" I think of as "useful mental models". The distinction is that whilst both are grounded in observation and empiricism, "truth" is an absolute, whilst "usefulness" is a bit like evolutionary fitness: changing over time, dependent on circumstance, not entirely arbitrary, but also not perpetually fixed.

So, is a neutron star a gigantic nucleus? Yes, in a sense, in that it's primarily made of what we'd otherwise consider nuclear material. Does this give us useful insights on neutron star behavior above and beyond those given by gravitational, thermodynamic, and electromagnetic descriptions? No, not really, because the attendant characteristics and properties of much smaller nuclei (from atomic number 1 to the low 100s or so) simply don't apply. There's not much behaviour that is explained, predicted, or controlled by applying that knowledge.

How do we know this? That seems difficult to observe from a couple of light years away.

A good question, and mostly beyond my pay grade. Almost certainly based on models rather than direct observation, though informed by the latter.

I'm struggling to find a strong source, but this page, by M. Coleman Miller at the University of Maryland, describes properties suggesting modelling over observation. Specifically it describes "the guts of a neutron star":

Even further down, you mainly have free neutrons, with a 5%-10% sprinkling of protons and electrons.

With an subsequent 'graph:

Yes, you may say, that's all very well for keeping nuclear theorists employed, but how can we possibly tell if it works out in reality? Well, believe it or not, these things may actually have an effect on the cooling history of the star and their spin behavior!

What follows is more description of theory with a few points based in what is directly observable, largely spin (via radio astronomy) and some temperature observations largely in X-ray observations, and the occasional gamma-ray burst.

<https://www.astro.umd.edu/~miller/nstar.html>

Miller's bio at UMD emphasizes his theoretical work:

Cole Miller's research in the last few years has focused on theory and modeling of high-energy radiation from neutron stars and black holes.

<https://www.astro.umd.edu/people/miller.html>