Revisiting Titius-Bode: From Kepler to Birkeland

Revisiting Titius-Bode: From Kepler to Birkeland

Abstract

We present a new approach to planetary system architecture in which orbital configurations emerge from a balance between gravitational and Lorentz forces. Using a 1/√r scaling law derived from plasma physics, we define a theoretical maximum mass for planets at each orbital radius, calibrated against the most massive planet in any system, e.g. Jupiter for the Solar System. Applying the same scaling to orbital velocities reproduces the results of Kepler’s and Newton’s laws without explicitly invoking them, introducing a new empirically derived constant that characterises planetary motion.

Extending this framework to planetary spacing reveals harmonic patterns across systems. For instance, Saturn’s rings follow a Fibonacci sequence related to the golden ratio, while the Kepler‑90 exoplanetary system exhibits orbital spacing consistent with prime-fraction harmonics. These patterns suggest that orbital mass limits, velocities and spacing may be governed by a universal electromagnetic–gravitational principle. This model provides a predictive framework for planetary system structure and offers testable hypotheses for both Solar System and exoplanetary architectures.

Most importantly from a pure Keplerian point of view we have discovered a "4th law of Kepler" hidden in plain sight for over 400 years. Even dismissing our hypothesis the discovered constant PVR=1 emerges from Keplers third law and remained unnoticed until now.