The formal analogy between electromagnetism (EM) and gravitation was noted by Maxwell and Faraday, and later on by Heaviside in the 1890s; the analogy was extensively used in the gravito-magnetism of the 20^{th} century. The connection between EM and fluid theory is explicit in Maxwell’s work, and the equivalence of Maxwell equations (ME) to various wave equations is explained in electrodynamics textbooks (say, Jackson’s); additionally, a little-known paper presented by Henri Malet to the Paris Academy of Sciences (1926), demonstrated that the validity of ME concurrently requires the validity of the vector and the scalar homogeneous wave equations.

In the 1990s the present author reported in Foundations of Physics Letters the existence of novel solutions for the homogeneous wave equation in spherical coordinates; it turns out that one class of our solutions (the nonharmonic functions of the first-kind, NHFFK) is equivalent to the unified force of nature proposed around 1760 by Boscovich from philosophical considerations, but without a formal mathematical basis. Our finding is significant because it lends a mathematical foundation to Boscovich’s force, which has extremely interesting properties, as quantization in energy and distance —noted by J. J. Thomson before Bohr’s quantum theory.

Associated with spherical surfaces in gravitational equilibrium, the family of even NHFFKs described here predict Titius-Body structures at different scales, as the solar system and the moons of Mars, Jupiter, Uranus, Saturn, and Neptune. Each calculated radius is compared to an average distance of moons/planets: the correlation and the R2 coefficients are quite high. The same NHFFK also predict the existence of ring structures, as those observed in Saturn, and in asteroids belts in our solar system. Newtonian gravity appears as the limit at very large distances from the center of force. The family of odd NHFFK exhibits a non-zero limit as distance tends to infinity, feature that immediately explains the flat rotation rate of some galaxies, problem that led to the ad hoc introduction of dark matter.

In the 1990s the present author reported in Foundations of Physics Letters the existence of novel solutions for the homogeneous wave equation in spherical coordinates; it turns out that one class of our solutions (the nonharmonic functions of the first-kind, NHFFK) is equivalent to the unified force of nature proposed around 1760 by Boscovich from philosophical considerations, but without a formal mathematical basis. Our finding is significant because it lends a mathematical foundation to Boscovich’s force, which has extremely interesting properties, as quantization in energy and distance —noted by J. J. Thomson before Bohr’s quantum theory.

Associated with spherical surfaces in gravitational equilibrium, the family of even NHFFKs described here predict Titius-Body structures at different scales, as the solar system and the moons of Mars, Jupiter, Uranus, Saturn, and Neptune. Each calculated radius is compared to an average distance of moons/planets: the correlation and the R2 coefficients are quite high. The same NHFFK also predict the existence of ring structures, as those observed in Saturn, and in asteroids belts in our solar system. Newtonian gravity appears as the limit at very large distances from the center of force. The family of odd NHFFK exhibits a non-zero limit as distance tends to infinity, feature that immediately explains the flat rotation rate of some galaxies, problem that led to the ad hoc introduction of dark matter.