Calculation of elementary particles' masses and planetary distances. The shape of the primordial universe

A primary equation, derived from the Schrödinger equation, can be employed to calculate the planetary distances. It can also be converted, according to a model which had been demonstrated in previous papers [L. Nahum, Adv. Phys. Theor. Appl. 5, 11 (2012); Phys. Essays 28, 167 (2015)], into a parallel equation to calculate the masses of elementary particles; its solution predicts that the logarithms of the masses must differ from one another by constant quantities or their multiples. The following masses have been calculated: top quark (172.567 ± 0.038 GeV/c ²), bottom quark (4.2764 ± 0.0009), and two Higgs bosons (126.221 ± 0.028 and 124.616 ± 0.030). The most probable masses of the other quarks have also been calculated. The results imply that the primordial universe had a lenticular shape with the equatorial axis measuring R bx = R by = 4 6 π   9 / 2 l p and with R bz = 9 l p π - 3 / 2 , l p being the Planck length. The solution of the primary equation demonstrates that also the differences between the logarithms of planetary distances from the sun are multiples of a constant quantity. The same equation could be applied to an extra-solar system (Pulsar PSRB1257+12). Comparing this equation with the Titius‐Bode empirical law, we try to explain why the latter fails in the case of Neptune.