Riadh Al Rabeh

Great question!

The answer is that the phenomenon of gravitation can be seen and measured, whereas the atoms are still too small to be seen. The electron is a small particle, it's not a wave or a probability distribution.

The problem reside in the lack of knowledge of the behavior of the electron within an atom. If you look at the relative distance between the electrons within an atom, you find that the interaction must be purely electromagnetic.

So, that means that there is a problem with our understanding of electromagnetics, especially the electromagnetic induction is not understood.

JES

No. The reason that electrons occupy shells is because they are quantum, not classical, objects. The inverse square dependence on the distance leads to the property that the quantum system of a charge bound to a center possesses a ground state-which the classical system does not-this was noticed by Fock in 1935.

Stam Nicolis

The shell structure is due to the associated wave phenomena, which is just a trajectory looking like a spiral. As usual, the problem is that the quantum properties are not understood.

JES

Let me throw in another observation, I've noticed, that may be entirely coincidental. Mercury and Venus -- Barely rotating/tidally locked. Earth and Mars -- 24 and 25 hour rotation. Jupiter and Saturn: Around 10 hour rotations. Uranus and Neptune: Around 16.5 hour rotations.

Question: Is there a spin-coupling phenomenon in solar system formation, just as there is spin-coupling in atoms? Of course we don't know if this pairing happens in other solar systems. But I still think it is worth considering if there could be a mechanism whereby the four pairs of planets may have formed from four disks of gas and dust, and somehow the coalescence led to pairs with similar rotational periods.

Jonathan Doolin

Spin is a phenomena of charged particles, a completely neutral object has no spin.

JES

Stellan Gustafsson Thank you for your interest in my answer.

An atom has a magnetic moment, measured in Coulomb.meter^2/second. The quantity of spin is a measure of that moment, or the difference in that moment between two different atoms. Unpaired electrons introduce a difference of 9.28x10^-24 Amp.meter^2 to the magnetic moment. This can be measured in two ways that I know of. In the Stern-Gerlach experiment, atoms of differing spins passed through a magnetic field will deflect at different angles depending on their magnetic moment. In the other, the evidence of the difference can be observed in emission line pairs. All the evidence consistently supports the view that the introduction of an unpaired electron in the atom contributes a quanta of magnetic moment.

Planets in orbit around stars, or disks of dust and gas if they are distinguishable, have an angular momentum, measured in kg.meter^2/second. While this angular momentum is not defined as "spin" by the physics community, it is known as "spin" by any English speaking person who has spun a quarter or a top. Physicists should be familiar with the "reduced Planck constant" denoted hbar, equal to 1.154x10^-34 kg.m^2/s which has units of angular momentum, and the Heisenberg uncertainty principle, saying Delta p Delta x > hbar, and Delta E Delta t > hbar. This implies that there are no changes in angular momentum that are smaller than Planck's constant. So while as a whole, planets coalesce out of gas and dust as a continuous process, if you get down to individual particle reactions, on the atomic scale, the changes in angular momentum would have some quantized quality to them.

Jonathan Doolin

Well, you can of course define a rotating planet as a spinning body. But, this is not the spin of a particle. A planet is too heavy to be influence by some particle's spin (or rotation).

But, you might have some connection with the initial condition of the solar system and the rotation of certain planets.

JES

To

“The inverse square force law governs both gravity and electricity.....”

- yeah, that is so, and Bohr model hat bases on ths law really is well scientifically rational – even comparing with modern QM, more see point 3 in the attached PDF.

However, this

“... Despite this we see that planets form discus around the central star whereas electrons form cloud shells around the nucleus. What is the mathematical/physical reason for this?…”

- is really incorrect. Atoms’ electrons fundamentally differ from planets in star’ planet systems in that exist and interacts with the “hosts” – atomic nuclei and stars - on different, i.e. QM and classical, scales, and, of course are created by fundamentally different ways.

Electrons interact with nuclei rather independently on something else [in H-atom – completely independently] than the nucleus,

- but formation of planet discs from some primary molecular cloud that was impacted by some wide shock so that the molecules got some angular momentum, M, which so determines the specific M-plane, happens at/by constant the molecules interactions,

- where the molecules in primary rather 4π symmetric cloud under star’s gravity force attracted , obtaining additional angular momentum, crossed the plane and at interactions with molecules that rotate in the M-plane loss their linear and angular momentums, obtain some parallel to M momentum and gradually rotate more and more closer to the plane.

The rotating in the plane molecules mutually interact much more rarely and weakly, so essentially by Gravity Force;

- and eventually so the observable planet systems appear.

Cheers

I interpret the question as asking why planetary systems are flat whereas atoms are not. The difference can be rephrased in terms of the angular momentun of either (probably reproducing in part previous answers). Well atoms can have large angular momenta, although they do not in their ground states. In the case of planetary systems, large angular momenta are the consequence of their formation process.