The beautiful Titius-Bode law about Solar planetary orbits discovered in 1766, is considered that it is a mathematical coincidence rather than an "exact" law, because it has not yet been physically proved. However, if we consider the disturbance restoration and the stability of the asteroid belt orbit and Saturn’s rings, there must be some underlying logical necessity. Planetary orbits are often computed by Newtonian mechanics with the kinetic energy and the universal gravitation energy. Nevertheless, 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 (discovered in 1915). Here, I mathematically demonstrated the Titius-Bode law, and also calculated the number of Saturn’s rings, maximum 31 for the first time by applying the principle of energy-minimum to the complicated energy equation which adopts mass, electric charge and rotation elements of the central core star and solving the sole differential equation.