Revisiting Titius-Bode

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. Note on v5.0 In the previous versions of this work we presented PVR as a new cosmological constant and Ksys as the 4th law of Kepler. Both were unintentionally deceptive and this has now been corrected. PVR is mathematical circular because the scaling of 1/√ appears in both numerator and denominator but the deviations from PVR=1 are real physics with the invariant Ksys as the source. Ksys was presented as a 4th law of Kepler but naming it Kepler’s 3rd-bis would have been more appropriate. Ksys is Kepler’s 3rd from a velocity perspective. This new approach offers new insights for the analysis of orbital velocity through a single invariant.