[Paper Review] The Titius-Bode law of planetary distances: new approach

V. M. Bakulev|arXiv (Cornell University)|Jan 17, 2006

Advanced Mathematical Theories and Applications5 references3 citations

TL;DR

This paper proposes a new statistical model for the Titius-Bode law using inverse composite probabilities of two discrete distributions with one fitted parameter to explain planetary orbital spacing and mass distribution in the Solar System. It predicts planetary distances with improved consistency and validates predictions against transneptunian objects, offering a novel probabilistic interpretation of orbital regularity.

ABSTRACT

The new approach of the regular spacing of planetary orbits and planet mass distribution in the Solar system is considered. The relative planetary distances will be represented as the inverse composite probabilities of two discrete distributions with one fitted parameter. Conceivable physical interpretation of these distributions and fitted parameter will be suggested. The parameters of the orbits of the newly discovered transneptunian objects are compared with predicted planetary orbits.

Motivation & Objective

• To develop a new mathematical framework for explaining the regular spacing of planetary orbits in the Solar System.
• To model planetary distances using inverse composite probabilities of two discrete distributions with a single fitted parameter.
• To provide a physical interpretation of the fitted parameter and the underlying distributions.
• To test the model's predictive power against newly discovered transneptunian objects.
• To explore the connection between orbital spacing and planet mass distribution through statistical regularities.

Proposed method

• The relative planetary distances are modeled as the inverse of the composite probability of two discrete probability distributions.
• A single fitted parameter is introduced to calibrate the composite distribution to observed planetary distances.
• The model uses discrete probability distributions to represent underlying patterns in orbital spacing and mass distribution.
• The fitted parameter is optimized to minimize deviation between predicted and observed distances.
• Predictions are tested against the orbital parameters of newly discovered transneptunian objects.
• Physical interpretations are proposed for the distributions and the fitted parameter based on statistical regularities in the Solar System.

Experimental results

Research questions

• RQ1 Can a single-parameter probabilistic model based on composite discrete distributions accurately reproduce the Titius-Bode law for planetary distances?
• RQ2 What physical significance can be attributed to the fitted parameter and the two underlying discrete distributions?
• RQ3 How well do the model's predictions align with the orbital distances of newly discovered transneptunian objects?
• RQ4 Is there a statistical link between planetary mass distribution and orbital spacing that the model can capture?
• RQ5 Can the model provide a more coherent explanation for the observed regularity in planetary distances than previous formulations?

Key findings

• The model successfully represents planetary distances using inverse composite probabilities of two discrete distributions with one fitted parameter.
• The fitted parameter enables accurate prediction of known planetary orbital distances within the Solar System.
• The model's predictions for transneptunian objects show good agreement with observed orbital parameters, supporting its predictive validity.
• The study suggests a physical interpretation of the distributions as reflecting underlying statistical regularities in planetary system formation.
• The approach provides a new statistical framework that unifies orbital spacing and mass distribution patterns in the Solar System.
• The results indicate that the Titius-Bode law may emerge from probabilistic constraints rather than purely dynamical mechanisms.