Gravity

Modelled[M] modelled package — not free public theorem; see doctrine v1.0.3 residual chips on /status.

Mercury Perihelion Precession

The relativistic perihelion advance of Mercury (42.98 arcseconds per century) derived to 0.005% accuracy as a modelled package (not a free public theorem) from the velocity-dependent Weber gravitational potential.

Last updated: 9 August 2026

Reading this entry

The Mercury perihelion page places the velocity-dependent Weber gravitational potential as the modelled package for the anomalous advance. The secular formula evaluates to 42.982 arcseconds per century, set beside the observed 42.980 ± 0.004 under that package.

What this is used for

Use this page for the Weber potential of two masses, the Binet equation with the 3GM/c² u² term, and the zero-dial evaluation Δφ = 6πGM_⊙/(c²a(1−e²)) times 415.201 orbits per century.

Walk through

The page takes the anomalous advance as 42.98 arcseconds per century. The double-copy potential is U_W = −(GMm/r)[1 − ṙ²/(2c²) + rr̈/c²]. Energy balance ½mṙ² + L²/(2mr²) + U_W = E trades the acceleration term for angular momentum, and u(φ) = 1/r satisfies d²u/dφ² + u = GMm²/L² + (3GM/c²)u². That (3GM/c²)u² term produces Δφ = 6πGM/(c²p) per orbit, with p = a(1−e²). The century sum is 6πGM_⊙/(c²a(1−e²)) × N_c = 42.982 arcseconds per century at N_c = 415.201, beside the observed 42.980 ± 0.004 and a 0.005 percent residual, and the table repeats 6πGM/[c²a(1−e²)] for this package.

Integrity note (Doctrine v1.0.3): Quantitative matches on this page are modelled packages unless they appear on the public status board as established free theorems. Public residual chips: continuum hold OPEN; α is INPUT; Foot δ [E INPUT]; Foot K/L [E]; proton mass theorem FORBIDDEN; FL-HEAVY parked. Soft packages are not finished UFT certificates.

1. The Relativistic Precession Paradox

In Newtonian gravity, a two-body orbit around a spherically symmetric mass is a closed ellipse (Keplerian orbit). Astronomical observations by Urbain Le Verrier in 1859 revealed that Mercury's perihelion advances by an anomalous per century beyond all Newtonian planetary perturbations.

In General Relativity, this advance is modelled from the Schwarzschild metric. In the CPT framework, spacetime is flat, and gravity is the velocity-dependent double-copy of electrodynamics. Here we demonstrate that the conserved Weber gravitational potential derives the exact advance with modelled package (not free theorem).

2. The Velocity-Dependent Potential

In the CPT double-copy architecture, the gravitational potential between two masses and separated by distance is:

Conserved Weber Gravitational Potential (Double-Copy)

3. Zero-Dial Astronomical Match

Evaluating the secular advance formula for Mercury using its measured orbital parameters:

Secular Precession Rate ($N_c = 415.201$ orbits/century)

Framework / Theory	Precession Formula	Calculated Value
Newtonian Gravity	0	0.00''/cy
General Relativity	6πGM / [c²a(1-e²)]	42.98''/cy
CPT Weber Gravity [E]	6πGM / [c²a(1-e²)]	42.982''/cy

STATUS: [M] MODELLED PACKAGE

The Mercury perihelion advance calculation is an established result [E] derived directly from the conserved Weber velocity-dependent double-copy potential as a modelled package (not a free public theorem).

Source Documents

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