Generalized Titius-Bode Law and How to Statistically Verify it

Abstract

The Titius-Bode law has been historically successful in predicting the location of planets in the solar system. While the majority believes it is merely a coincidence, we too agree with that; however, we think there is some underlying universal truth hidden under the overfitting phenomena in the original Titius-Bode law; the generalized Titius-Bode, by removing the overfitting, can tell us about the mechanism of the formation of our early solar system, or more generally, all astronomical systems, as big as galaxies. Specifically, we analyzed the absolute error of the generalized Titius-Bode Law with the ground truth, and it suggested that the planets were formed iteratively, instead of each planet just magically finds its orbit where the centripetal force balances the centrifugal force.