The Research Paper, "Mercury Orbital Dynamics in Extended Classical Mechanics: Phase- Frequency Advancement and Energy Redistribution" available at the DOI: https://doi.org/10.13140/RG.2.2.12884.67208
Introduction
Mercury’s anomalous perihelion advance has long served as a benchmark problem in gravitational physics. Historically, the unexplained residual precession beyond Newtonian predictions was taken as one of the earliest confirmations of general relativity, where spacetime curvature was introduced as the governing explanatory principle. More recently, various alternative analyses have revisited the problem using refined Newtonian calculations and numerical simulations, aiming to reduce or eliminate the discrepancy through improved accounting of planetary interactions.
Extended Classical Mechanics (ECM) approaches this problem from a fundamentally different conceptual foundation.
Limits of Force-Based Recalculations
Many alternative treatments of Mercury’s perihelion advance focus on improving the fidelity of Newtonian force models. These include accounting for planetary velocities, multi-body coupling, barycentric motion of the Sun, and higher-order numerical effects. While such efforts can alter the predicted magnitude of perihelion precession, they remain confined to the same underlying paradigm: gravity as a force acting between masses, accumulated geometrically over time.
From an ECM standpoint, these refinements—though mathematically sophisticated—do not address the deeper physical origin of the observed phase advance. They attempt to redistribute the numerical outcome within an existing framework rather than re-examining the mechanism responsible for orbital phase evolution itself.
The ECM Interpretation: Phase and Energy, Not Geometry
In Extended Classical Mechanics, Mercury’s perihelion advance is not treated as a correction to Newtonian gravity, nor as a consequence of spacetime curvature acting as a physical cause. Instead, it is interpreted as a manifestation of cumulative phase–frequency advancement arising from energy redistribution within a spatially varying gravitational environment.
Key to this interpretation is the role of negative gravitational potential energy (−ΔPEᴇᴄᴍ) and its dynamic exchange with kinetic and effective mass terms. As Mercury traverses a non-uniform gravitational field, subtle but continuous energy–phase shifts accumulate over each orbital cycle. Over time, this accumulated phase drift appears geometrically as a rotation of the orbital ellipse—observed as perihelion advance.
In this view:
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Geometry records the effect,
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Phase evolution drives the phenomenon,
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Energy redistribution provides the physical agency.
Reframing Spacetime Curvature
Within ECM, spacetime curvature—as used in general relativity—is not rejected outright, but reinterpreted. It is understood as a mathematical encoding of accumulated interaction effects rather than an independent causal entity. Curvature describes how trajectories appear once phase and energy redistribution have taken place; it does not generate those effects.
Thus, Mercury’s perihelion advance does not require spacetime itself to “act” on the planet. The observable precession emerges naturally from classical dynamics once phase, frequency, and energy manifestation are treated as primary physical quantities.
Conclusion
Analyses that seek to explain Mercury’s perihelion advance solely by refining Newtonian force calculations may successfully challenge simplified historical models, but they do not align with the dynamical foundations of Extended Classical Mechanics. ECM shifts the explanatory focus away from force summation and geometric correction toward phase-governed energy redistribution as the underlying physical process.
From this perspective, Mercury’s perihelion advance is not a numerical anomaly to be repaired, nor a curvature effect to be invoked, but a natural outcome of how energy, phase, and motion co-evolve in a gravitational field.
