τ-Mercury Perihelion Precession

τ-Mercury perihelion precession (`V.T29`) is the τ-categorical theorem that the τ-Einstein equation predicts a per-orbit precession δφ = 6π G M_⊙ / (a(1−e²)c²) for a planet in a Keplerian orbit, with G = (c³/ℏ) · ι_τ². For Mercury this gives 43.0 arcseconds per century, matching the observed 42.98 ± 0.04 arcsec/century with no free parameters.

Categorical invariant. Per-orbit precession from V.D52 (linearized τ-Einstein) on a Keplerian orbit; 43.0 arcsec/century for Mercury.

Primary registry anchor: V.T29

Supporting items: V.D51, V.D52, V.T28

1. I.K0 — Universe Postulate
2. V.D51 — τ-Einstein equation R^H = κ_τ · T^mat
3. V.D52 — Linearized τ-Einstein equation (weak-field expansion)
4. V.T28 — Newtonian limit recovery — fixes G = (c³/ℏ) · ι_τ²
5. V.T29 — Mercury precession from τ-Einstein — δφ = 6πGM_⊙/(a(1−e²)c²); 43.0 arcsec/century

Lean modules referenced: TauLib.BookV.GravityField.LinearEinstein

Numerical value: 43.0 ± 0.04 arcsec/century

Calibration anchor: PG-P01-neutron

Calibration chain:

1. G = (c³/ℏ) · ι_τ² from the τ-cascade
2. M_⊙, a, e, c from solar-system data + cascade scales
3. SI bridge via m_n anchor for masses, τ-second for time

Manuscript reference: manuscript-sources/book-05/part02/ch14-linear-tau-einstein.tex

Status: Formalized

Module: TauLib.BookV.GravityField.LinearEinstein

Lean kind: theorem

Lean symbol: Tau.BookV.GravityField.MercuryPrecessionFromTaueinstein

Related glossary entries

• PG-L04-tau-einstein-equation τ-Einstein Equation
• PG-L05-tau-newton-gravity τ-Newton's Law of Gravity