Artificial Intelligence-Assisted Exploratory Modeling of Planetary Distance Patterns: A Standing-Wave Grid Analysis of the Solar System

Source abstract

This study investigates the use of artificial intelligence-assisted exploratory modeling for the analysis of radial regularities in planetary distances within the Solar System. The proposed approach combines hypothesis generation and structural interpretation supported by artificial intelligence with numerical fitting of a standing-wave grid model and comparative evaluation against the classical Titius-Bode rule. The model represents planetary orbits as approximate positions of minima in a linear radial grid defined by a constant step and a fixed phase shift. Using the observed heliocentric distances of the eight major planets, the study estimates the grid parameters, assigns each planet to the nearest node, and evaluates model performance by means of absolute and relative error metrics. For the selected configuration, the fitted model with Δ = 0.2845 AU and φ = 0.5 yields lower average approximation errors for the eight-planet sample than the classical Titius-Bode relation. However, this result is interpreted as evidence of numerical fit only and does not by itself establish the physical validity of a wave-based mechanism for planetary orbital architecture. The fitted grid formally corresponds to a wavelength of 0.569 AU and an associated frequency of approximately 3.52 mHz, which is numerically close to the range of observed solar five-minute oscillations. This proximity is treated as a heuristic observation relevant to model development rather than as confirmation of a causal connection between solar oscillatory phenomena and planetary distances. An extended two-resonator version of the scheme is also examined for selected trans-Neptunian objects, several of which show close numerical alignment with the calculated grid nodes in the outer region of the model. At the same time, the approach remains limited by the presence of numerous unoccupied nodes, sensitivity to boundary assumptions, and the absence of an independently verified physical mechanism. The results indicate that artificial intelligence can serve as a useful research-support instrument for hypothesis formulation, parameter exploration, structured model comparison, and pattern-oriented analysis in astronomy. In this context, the standing-wave grid is best regarded as a heuristic computational framework that warrants further statistical testing and critical physical assessment rather than as an established theory of Solar System structure.