A 1151-Year Quasi-Commensurability of the Solar System: Empirical Detection, Statistical Characterization, and the Anomalous Exclusion of Uranus

TL;DR

This study empirically detects a 1,151-year quasi-commensurability among most planets in the Solar System, revealing an anomalous exclusion of Uranus that may relate to its early impact history.

Contribution

It identifies a stable multi-planet quasi-commensurability period and highlights Uranus's unique orbital residue, suggesting a past catastrophic event affecting its orbit.

Findings

A 1,151-year period minimizes planetary angular displacements.

Uranus's orbital residue significantly deviates from other planets.

The period aligns with historical Venus return cycles.

Abstract

We report the empirical detection of a multi-planet quasi-commensurability in the Solar System and identify an anomalous exclusion that may bear on the dynamical history of Uranus. An exhaustive search identifies T* = 420,403 days (approx. 1,151 years) as the global minimum of a series-comparison similarity metric applied to daily heliocentric ecliptic longitudes of seven planets -- Mercury, Venus, Earth, Mars, Jupiter, Saturn, and Neptune -- computed from the DE441 ephemeris over +/-1,300 years. At this interval, the mean simultaneous angular displacement of all seven planets is 13.4 degrees, with a standard deviation of 0.65 degrees sustained over a century-long window and stable across 1,200 years of reference epochs. T* ranks first among all 2,600 candidates, with a gap of 1.09 degrees to the second best. No sub-multiple produces a comparable result. Seven of the eight planets participate in the synchronism. The sole exception is Uranus, whose sidereal residue at T* is -108.3 degrees -- nearly one-third of a full orbit -- while Neptune's residue is only -5.2 degrees, one of the smallest among all seven planets after Earth's. This sharp asymmetry between the two ice giants constitutes an independent empirical signature consistent with the hypothesis that Uranus's orbital period was substantially modified by a catastrophic early impact. The interval 1,151 years was identified by Babylonian astronomers as the Venus return period (de Jong 2019); the present work shows it is simultaneously optimal for six additional planets. Source code and data are publicly available.