A geometric–temporal eclipse prediction model on a stationary flat Earth
using analemma-based time geometry and UTC anchoring
This repository presents a deterministic celestial clock model that represents the Earth as a stationary plane and the Sun and Moon as local moving luminarias governed by temporal geometry rather than orbital mechanics.
The purpose of this project is not cosmological ontology, but the construction of a mathematically coherent predictive system capable of determining solar and lunar eclipses through:
- harmonic solar analemma,
- synodic lunar phase synchronization,
- nodal temporal windows,
- and explicit UTC-based geodetic anchoring.
The system behaves as a celestial chronograph:
a geometric clock in which time determines form, not the inverse.
-
Stationary Plane
The Earth is modeled as a Euclidean disk.
No rotation, axial tilt, or translational motion is introduced. -
Local Luminarias
The Sun and Moon follow circular trajectories above the plane, with variable effective radius. -
Time as the Primary Variable
Spatial geometry is derived from UTC time.
There is no kinematic causality from space to time. -
Eclipses Without Terrestrial Shadow
Eclipse detection is performed via temporal–angular alignment and relative altitude geometry, not via Earth-cast umbra.
These hypotheses define a self-consistent mathematical framework, evaluated solely by predictive capability and internal stability.
The Earth is projected using an azimuthal equidistant projection centered on the pole of the plane.
Each geographic coordinate (lambda, phi) is mapped to polar coordinates:
-
Angular position
theta = -lambda - (pi / 2) -
Radial distance
r = R * ((90° - phi) / 180°)
This preserves radial distance and allows the superposition of a 24-hour temporal dial.
Fixed anchor points are used to validate temporal coherence:
- Santiago (UTC −3)
- London (UTC 0)
- Sydney (UTC +11)
These anchors are references, not calibration parameters.
Instead of raw UTC, the system employs a symmetrically reindexed temporal dial (System B).
This bijective remapping:
- preserves 24-hour periodicity,
- removes discontinuities at the meridian,
- simplifies detection of angular opposition and conjunction.
System B is a reading system, not a time modification.
The solar analemma is modeled as a harmonic function of annual phase:
Z_sun(f) =
a1 * sin(2*pi*f)
+ a2 * sin(4*pi*f)
+ a3 * sin(6*pi*f)
Where f is the fractional solar year.
- The fundamental term captures annual variation.
- Higher harmonics correct asymmetry.
- Geometric meaning:
Z_sunmodulates the effective solar radius above the plane.
This transforms the analemma from a descriptive artifact into an active geometric parameter.
The synodic phase is defined as:
phi = frac((t - t_ref) / M)
Where M is the synodic month.
phi ≈ 0: New Moonphi ≈ 0.5: Full Moon
In the planar model, the Moon’s angular separation from the Sun is phase-determined, not orbit-determined.
Instead of tilted orbital planes, the model introduces an effective draconic year that defines temporal nodal windows:
psi = frac((t - t_ref) / E)
Distance to node:
d_node = min(psi, 1 - psi, abs(psi - 0.5))
Only when d_node falls below a defined threshold can eclipses occur.
This translates inclination into time, preserving planar geometry.
Conditions:
- New Moon (
phi ≈ 0) - Within nodal season
- Relative altitude geometry permits occultation
Classification by nodal proximity:
- Annular
- Total
- Partial
Conditions:
- Full Moon (
phi ≈ 0.5) - Within nodal season
- Exact angular opposition
Classification:
- Total
- Partial
- Penumbral
No Earth shadow is projected.
Lunar eclipses arise from temporal–angular opposition modulated by analemma height.
Detected events are locally refined to minimize nodal distance.
Long-term recurrence emerges naturally from the quasi-resonance of:
- Solar year
- Synodic month
- Draconic year
This reproduces Saros-like behavior without spatial precession.
The visual interface is not illustrative — it is instrumental.
- Planar map → geometric substrate
- Temporal dial → time-angle mapping
- Dynamic Sun & Moon → radius modulation by analemma
- Complication panels:
- Solar analemma (Z-offset)
- Synodic lunar phase
Together they form a celestial clock, where each element is a measurable variable.
By reinterpreting the sky as a precision time system, this model demonstrates that eclipses can be described as synchronization events between harmonic cycles and planar geometry.
This repository presents a Flat Earth Celestial Clock:
a deterministic mathematical machine where time governs form.
Keywords
flat earth, analemma, synodic phase, draconic year, eclipses, temporal geometry, celestial clock
Para facilitar mantenimiento y auditoría, el repositorio incluye documentación
en línea en los módulos de simulación (notebook/*.py) y en los motores de
visualización (index.html y page/*.html).
Cada bloque principal documenta:
- propósito matemático o visual,
- entradas/salidas esperadas,
- relación con constantes del modelo temporal.
Además, se verificó el contenido del proyecto para confirmar que no existan emojis en código ni en textos de interfaz.