Solar-System-Calibrated Geometric Upper Bound for Planetary Multiplicity and Inclination Correlation
Year: 2026
Type: preprint
Abstract: Conventional planetary formation theory attributes planetary multiplicity primarily to primordial nebula mass, initial density fluctuations, and stochastic collisional accretion history. Such material-determined paradigms cannot provide a strict upper limit for long-term stable planetary systems and fail to yield deterministic statistical correlations between planetary number and orbital architecture (Winn & Fabrycky, 2015). Under the continuous-medium dynamical framework, stellar systems are governed by background potential gradient cascading locking rather than nebula material abundance. This study derives a geometric upper bound for stable major planet multiplicity controlled by the perturbation-bearing capacity of the stellar background potential field. The theoretical upper limit follows a base-2 logarithmic scaling relation determined by the ratio of the outer locking cutoff radius to the inner stable locking radius. A paradigm-exclusive falsifiable prediction: within stable limits, system-averaged mutual orbital inclination increases monotonically with major planet number, originating from cumulative secondary perturbation distortion. For Solar-like G-type stars, calibrated with observed boundary parameters, the theoretical stable upper multiplicity range is approximately 8 to 10 major planets. We further discuss the physical implications of the radial thermodynamic gradient, which dictates planetary compositional zonation and establishes a narrow rocky habitability window essential for the emergence of complex dissipative structures. This statistical signature is testable with PLATO, extended TESS catalogs, and the Vera C. Rubin Observatory.
Author: Shuai Sheng
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7224905987