Authors: Fumitaka Inuyama.
The beautiful Titius–Bode law (ξ=0.4+0.3×2^n ) , discovered 250 years ago, is considered to be a mathematical coincidence rather than an "exact" law, because it has not yet been physically proved. However, considering the disturbance restoration and the stability of the asteroid belt orbit, there must be some underlying logical necessity. Planetary orbits are often computed by Newtonian mechanics with the kinetic energy and the universal gravitation energy. However, applying the principle of energy-minimum to the Newtonian mechanics leads to the result that the stable orbital radius is only one value, which is totally incompatible with actual phenomena. This discrepancy must result from the shortage of elements which rule over the planetary orbits. Other elements to rule over the planetary orbits are the electric charge energy and the rotation energy, both of which are guided by the Kerr-Newman solution (discovered in 1965) of the general relativity theory. Here, I mathematically demonstrated the Titius-Bode law, and also calculated the number of Saturn’s rings, maximum 31 and the radius of Fine-Ring, by applying the principle of energy-minimum of Newtonian methods to the complicated energy equation which adopts mass, electric charge and rotation elements of the central core star and solving sole differential equation.
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