Dynamical Degeneracy of Relativistic Orbital Observables

Dynamical Degeneracy of Relativistic Orbital Observables

This work investigates the uniqueness of dynamical reconstruction from relativistic orbital observables using direct numerical experiments on Mercury perihelion precession.

Several dynamically non-equivalent orbital models are constructed and calibrated to reproduce nearly identical relativistic-scale perihelion advance while exhibiting measurable differences in local temporal structure, orbital timing, phase-space evolution, Fourier composition, and sector traversal dynamics.

The results demonstrate that agreement with a single integrated observable does not uniquely determine the underlying dynamics. Distinct orbital evolutions may generate observationally equivalent secular effects while remaining distinguishable through local diagnostics.

The work introduces the concepts of dynamical non-equivalence, reconstruction dependence, and geometric versus reconstruction uniqueness, and discusses the informational content of geometric reconstruction in orbital mechanics.

No claim is made regarding inconsistencies of General Relativity or the construction of an alternative theory of gravity. The study is methodological in nature and focuses on the non-uniqueness of inverse dynamical reconstruction from integrated observables.

Source code and numerical experiments are included to ensure full reproducibility.