Statistical Correlation Between Celestial Body Rotation Rate and Companion Abundance and Its Scientific Implications

This paper investigates the statistical correlation between rotation rate and satellite abundance based on grouped statistics of solar system bodies, introducing mass as a control variable. The sample is divided into two groups: a full sample including asteroids and dwarf planets (13 bodies), and a planetary sample retaining only the eight major planets (8 planets). Within each sample, bodies are divided into fast-rotating and slow-rotating groups according to their rotation rates, and the rotation rate ratios, mass ratios, and satellite abundance ratios between the two groups are calculated. The statistical results show: · · In the full sample, the fast-rotating group has a rotation rate 101 times that of the slow-rotating group, a satellite abundance 56 times that of the slow-rotating group, and a mass 524 times that of the slow-rotating group. · In the planetary sample, the fast-rotating group has a rotation rate 39.0 times that of the slow-rotating group, a satellite abundance rising to 95 times that of the slow-rotating group, and a mass dropping to 225 times that of the slow-rotating group. Two core observational facts: First, rotation rate and satellite abundance show a significant positive correlation within both samples, and APOGEE survey data independently corroborate that fast-rotating stars have a higher occurrence rate of companions [2]. Second, when transitioning from the full sample to the planetary sample, the mass ratio decreases from 524 to 225 times (a 43% reduction), while the satellite abundance ratio increases from 56 to 95 times (a 70% increase). This inverse variation presents a significant contradiction to the expectations of classical Hill sphere theory, pointing to a core scientific question: Is the contribution of mass to satellite abundance overestimated, while the contribution of rotation is underestimated? General relativity's frame-dragging effect has confirmed that rotation possesses a dynamical contribution, but its weak-field predictions are far too small to explain the above statistics. Based on this tension, this paper proposes the heuristic concept of "coupling gravity" – which aims to describe the possibility that "the contribution of rotation to spacetime curvature may be comparable in weight to that of mass" – and designs a Cavendish torsion balance experiment for systematic exploration. This experiment has dual value: if a signal is detected, it would indicate an unknown amplification mechanism for rotation's contribution to spacetime curvature; if only an upper limit is obtained, it would point the way for future experiments with higher speeds and larger masses.