The Figure-Eight and the Blood Moon: Analemma Derivation and Lunar Eclipse Radiance Map from Torus Knot Topology on S³
Abstract
Two macroscopic observational phenomena — the solar analemma and the lunar eclipse radiance spectrum — are derived from the same torus knot register set that generates particle masses, mixing angles, and the gravitational coupling. The analemma follows from three derived quantities: the circuit angle ε = arctan(13/30), the tropical year Y = 365 + 7/29, and the dressed circuit eccentricity e = 1/60 + Γ/Σ. The obliquity component of the equation of time is derived at 9.865 minutes (observed: 9.87, deviation 0.053%) and the eccentricity component at 7.659 minutes (observed: 7.66, deviation 0.009%), both after applying the Γ-order medium dressing. The dressing type is categorical: angular observations are local measurements that transit the GRIN field and receive multiplicative point-dressing (×n₀), while orbital eccentricity is a global circuit parameter perturbed by the gravitational coupling distributed across the spectral budget (additive per-channel dressing +Γ/Σ). The lunar eclipse radiance map is derived from the differential GRIN coupling δ = 1/45, yielding a spectral transmission that predicts blood-red lunar eclipses with a natural Danjon scale gradient. Mean deviation across all analemma observables: 0.024%. Zero free parameters throughout.
Fields of Study & Subjects
History and Developments in Astronomy
Solar and Space Plasma Dynamics
Historical Astronomy and Related Studies
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 31 August 2026
- Document type
- Preprint