Was the Titius-Bode series dictated by the minimum energy states of the generic solar plasma?

It has been shown previously that the Bode numbers and measured velocity ratios of the planets are accurately predicted by the eigenvalues of the Euler-Lagrange equations resulting from the variation of the free energy of the generic plasma that formed the Sun and planets. This theory is reviewed and extended to show that the equations make accurate predictions for all the major planets out to and including Pluto. The semimajor axes and velocity ratios of Pluto and Neptune are predicted exactly. The Bode numbers are shown to correspond to the roots of the first-order Bessel functions. The extrema of the roots of the zeroth-order Bessel function predict the ratios of the measured planetary velocities almost without error for the outer planets. Both sets of roots correspond to the same eigenvalue solution of the force-free equation. The eigenvalues are set by the initial energy input to the plasma nebula. Both the Titius-Bode series and Kepler's harmonic law are predicted by the relaxed state solution of the free-energy equation for the generic plasma that formed the Sun and planets. Newton's law of gravitation is not used in the calculations. The solution makes exact predictions for the outer planets where the Titius Bode series fails completely.<
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