My friend Mario Rabinowitz just revived my interest on this relation, which the Mexican Astronomer Poveda has been studying for many years now.
Arcadio Poveda visited us at the Physics school of the University of Puebla (UAP) many years ago. Tapan Kumar Chatterjee invited him, when Dr. Chatterjee was a professor there. Poveda has been an original astronomer, and I have followed his work. Recently Dr. Poveda analyzed extra-solar planetary systems with the so-called Titius-Bode Law, which Rabinowitz told me was discovered by Johann Daniel Titius.
I believe that they are bound to be regularities for objects moving close to a plane, because they exert forces on each other. This is a formation issue, that likely requires computer calculations to derive. The main idea though, is that a planar many body problem follows regularities, as has been observed by the hexagonal structure in Jupiter. From those hexagons to some radius relation for planetary orbits, I just see computer work directed to finding it. One planet, pulling a nearby one, competing with other planets on the other side of the orbit, could produce an orbit, not too close, and not too far, like in the Goldilocks fairy tale. Order out of Chaos.