A copy of an old notebook entry that follows is included both for the historical record and for its relevance to cosmology. It is from the writer's unpublished files. It logically belongs in [an earlier chapter], but is best understood in the context of the exchange of angular momentum described [earlier in this paper]. If it seems a bit disjointed, the reason is that it was only a reminder for further effort. Only after 35 years working on interplanetary transfer trajectories and solar system mechanics has the writer acquired the self confidence to tackle the problem of the "repulsion" between protons and electrons.
Orbit Mechanics - Binding Forces in Atomic Nuclei
Project Arc - 12 November 1960, Rollin W. Gillespie
About a month ago I was lead in my speculation on rendezvous problems of space rockets on orbit to a startling relationship. For simplicity consider two circular orbits around a point mass large compared with the masses of the particles in the orbits. Let the orbits be coplanar and concentric, but let them have different radii, and therefore different periods. Then the inner particle will move ahead of the outer one. The same will be true if the particles are attached to one another. Therefore, a sphere, for example, will be forced to rotate around an axis parallel with the axis of the orbit.
If the particle is large compared with the radius of its orbit, the rotation will be rapid, and account for a large part of the angular momentum of the system. So it would be in a large particle revolving at close range around a small particle of large mass. It seems apparent that there must be coupling of the moments of revolution and rotation, so that neither is independent of the other.
The energy released when the charged particles fall together is finite, and the energy that must be imparted to the rotation of the falling particle is large. There should be a point where the two are equal. Thus the means exists to hold the charges apart. By the same reasoning, like charges would inevitably be held together, once set revolving around one another at close range.
At the earliest time I will have available, I wish to explore the problem numerically.
A neutron may be regarded as a degenerate hydrogen atom. Every neutron in the universe is in a conic section orbit about every other neutron. The equipartition of energy should bring all neutrons to an equal level of mass and energy. That level determines the orbit radius of the electron. By the exchange of angular momentum the proton must rotate at an angular rate twice that of the angular orbital rate of the electron. Any departure from the 2/1 ration would be resisted, causing the electron to maintain its distance. This may be the origin of the "strong force." Another possible explanation may lie in the structure of the neutron. If it is indeed a configuration of quarks, it constitutes a multibody system. It would be prevented from collapse by the same principle which prevents the collapse of the solar system.