A particle of mass nm, carrying the electronic charge -e, revolves in an orbit through angle ψ at distances nr from a center of force
of attraction, with angular momenta nL perpendicular to the orbital plane, where n is an integer greater than 0, m the electronic
mass and r1 is the radius of the first circular orbit. The equation of motion of the nth orbit of revolution is derived, revealing
that an excited particle revolves in an unclosed elliptic orbit, with emission of radiation at the frequency of revolution, before
settling down, after many cycles of ψ, in a stable circular orbit. In unipolar revolution, a radiating particle settles in a circular
orbit of radius nr1 round a positively charged nucleus. In bipolar revolution, two radiating particles of the same mass nm and
charges e and –e, settle in a circular stable orbit of radius ns1 round a common center of mass, where s1 is the radius of the first
orbit. Discrete masses nm and angular momenta nL lead to quantization of the orbits outside Bohr’s quantum mechanics. The
frequency of radiation in the bipolar revolution is found to be in conformity with the Balmer-Rydberg formula for the spectral
lines of radiation from the atom hydrogen gas. There is a spread in frequency of emitted radiation, the frequency in the final
circle being the highest, which might explain hydrogen fine structure, as observed with a diffraction grating of high resolution.
The unipolar revolution is identified with the solid or liquid state of hydrogen and bipolar revolution with the gas state.
Circular orbits in the Taub–NUT and massless Taub–NUT spacetime
