Revisiting Titius-Bode. A New Mathematical Framework for Planetary Architecture and Rotation

Part 1:

This part 1 of the paper here presented revisits the Titius-Bode Law through a modern empirical and theoretical lens,
introducing the TBB-JML-JOSL model (Titius-Bode-Birkeland, Jupiter Mass Limit, and Jupiter
Orbital Speed Limit), a unified framework that blends harmonic orbital structuring with
physical mass constraints.
Unlike the classical Titius-Bode law, which was purely numerical and lacked physical
justification, the TBB-JML-JOSL approach is grounded in plasma cosmology—particularly
Birkeland currents—and in the balance between Lorentz forces and gravity in a planetary
environment.
Orbital distances are modelled as harmonics of plasma structures, while the Jupiter Mass
Limit (JML) defines the ideal planetary mass at any orbital radius. JOSL defines the
corresponding ideal orbital speed.
This triple-layer model not only corrects classical anomalies but also enables predictive
insights into exoplanetary system architecture. By bridging orbital spacing with magneto-
gravitational dynamics, the model transforms an empirical rule into a physics-based
predictive framework for planetary science.
Applying the model to various planetary systems reveals a significant relationship between
Birkeland current density and orbital spacing. This leads to the proposal of a new theoretical
construct: the Birkeland Orbital Spacing Law (BOS). BOS encapsulates the influence of
plasma currents on planetary system architecture, offering new insights into the formation
and evolution of compact, stable planetary orbits.

Part 2:

The rotation rates of planets exhibit striking regularities and anomalies that remain poorly
explained by classical tidal or angular momentum conservation theories alone. In this part 2, we
introduce the Birkeland Spin Model (BSM) — a zonally partitioned framework that predicts
planetary spin rates (𝜔) through magnetospheric torque interactions, extending principles of
current coupling from plasma physics to planetary rotation.
BSM divides planetary systems into three torque regimes based on heliocentric distance.
The model incorporates empirically tuned but physically motivated parameters for current
strength, magnetic field scaling and drag coefficients, yielding spin predictions for all major solar
system planets within a ~5% margin. Notably, BSM captures retrograde spins for Venus and
Uranus through sign-reversed current terms and correctly limits tidal override cases such as
Mercury.

By integrating with the orbital framework developed in Part I — including the TBB, JML, JOSL and
BOS models — BSM completes a unified architecture for planetary systems, bridging orbital
structure with rotational dynamics. We conclude by extending BSM to 2 selected exoplanets,
demonstrating its predictive power across diverse stellar environments.