The Engine

MEGALITHICA Methodology

The complete technical reference for the computational archaeoastronomy engine behind MEGALITHICA.

Conceived and developed by Charlie Taillard · MEGALITHICA methodology: 2025 · Platform: 2006–present

Overview

PHOSPHERE is a computational approach to archaeoastronomy that identifies astronomical alignments between megalithic sites by exploiting the slow change in Earth’s axial obliquity over millennia. The analysis pipeline has six stages:

1.Compute geodesic bearing between two sites

2.Pre-filter: bearing bracket eliminates ~50–60% of pairs

3.Convert bearing to target declination

4.Build year grid: compute event declination via obliquity for each epoch

5.Sign-change detection to locate alignment year

6.Refine and compute residual in arcseconds

Earth’s Changing Tilt

Precession & Obliquity

Earth’s rotational axis precesses with a period of ~25,772 years. This changes the obliquity (tilt) from about 22.1° to 24.5° over a ~41,000-year cycle. At J2000.0 (year 2000), the mean obliquity is 23°26′21.448″ (≈ 23.4393°).

Because solstice declination equals the obliquity, the azimuth where the Sun rises and sets at solstice changes gradually over millennia — allowing us to “date” an alignment by finding which epoch makes the bearing match.

Key Parameters

Obliquity range: 22.1° — 24.5° · Precession period: ~25,772 years · Obliquity cycle: ~41,000 years · Lunar orbital inclination: 5.145°

Formula

Obliquity Formula (Laskar 1986)

The Laskar (1986) polynomial computes mean obliquity to ~0.01° accuracy over ±10,000 years:

ε₀ = 23° 26' 21.448" U = T / 100 (T = Julian centuries from J2000) Δε = -4680.93·U - 1.55·U² + 1999.25·U³ - 51.38·U⁴ - 249.67·U⁵ - 39.05·U⁶ + 7.12·U⁷ + 27.87·U⁸ + 5.79·U⁹ + 2.45·U¹⁰ ε = ε₀ + Δε / 3600

The Perfect Year

The “Perfect Year” is the central concept of PHOSPHERE. For any alignment between two sites, it answers: in which historical year did a celestial event occur at exactly the bearing between the two sites?

Site A Site B ●━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━● │ bearing = 51.2° │ ▼ ┌─────────────────────────────────────────────┐ │ Year scan: 15,000 BCE ──────────▶ 500 CE │ │ │ │ For each year: │ │ obliquity(year) → declination → azimuth │ │ │ │ Match: azimuth ≈ 51.2° │ │ Perfect Year = 3050 BCE │ │ Residual = 0.8 arcseconds │ └─────────────────────────────────────────────┘

Mirror Years

Mirror Years — Two Dates for Every Alignment

Because the obliquity curve rises to a peak and then descends, any given obliquity value is reached twice — once on the ascending limb (deep past) and once on the descending limb (toward the present). This creates a “mirror year” for most alignments.

Obliquity (degrees) 24.2° ┤ ╱ ╲ peak │ ╱ ╲ 23.8° ┤ A╱· · · · · ·╲B · · · same obliquity (23.8°) │ ╱ ╲ 23.4° ┤ ╲ └──┬───┬───┬───┬───┬──┬──▶ -12 -10 -8 -6 -4 (×1000 years) Point A: 10,500 BCE ←── Mirror Year Point B: 3,050 BCE ←── Perfect Year Same obliquity → same azimuth → both are valid dates

The Residual

Understanding the Residual

The residual is the most important number in any alignment result. It measures how closely the computed astronomical azimuth matches the actual bearing between two sites at the Perfect Year — expressed in arcseconds.

Residual = | computed azimuth − bearing between sites | Expressed in arcseconds (symbol: ″) 1 degree = 3,600 arcseconds 1 arcminute = 60 arcseconds 1 arcsecond = 1/3,600 of a degree

Distance between sites	1″	5″	30″
1 km	0.5 cm	2.4 cm	14.5 cm
10 km	4.8 cm	24 cm	1.45 m
100 km	48 cm	2.4 m	14.5 m
500 km	2.4 m	12 m	72.7 m

Worked Example

1. Bearing from Carnac to Stonehenge: 51.2300° (geodesic formula from GPS coordinates).

2. At Perfect Year (3,050 BCE), obliquity ~24.01° → summer solstice sunrise azimuth: 51.2298°.

3. Difference: |51.2300° − 51.2298°| = 0.0002° = 0.72 arcseconds

Result: Sub-Arcsecond precision. At 345 km, ≈ 1.2 metres of lateral offset.

Precision Categories

Sub-Arcsecond≤ 1″Extraordinary — equivalent to 0.5m at 100km

Excellent≤ 5″Consistent with intentional design

Very Good≤ 10″Strong indication of deliberate alignment

Good≤ 20″Plausible astronomical alignment

Moderate≤ 30″Within detection threshold

Event Declinations & Computation

Event Declinations

Event	Declination	Modern Value
Summer Solstice	+ε	+23.439°
Winter Solstice	−ε	−23.439°
Equinox	0°	0°
Lunar Major North	+(ε + 5.145°)	+28.584°
Lunar Major South	−(ε + 5.145°)	−28.584°
Lunar Minor North	+(ε − 5.145°)	+18.294°
Lunar Minor South	−(ε − 5.145°)	−18.294°

Azimuth Computation

cos(Az) = sin(δ) / cos(φ) Rising: Az (eastern horizon) Setting: 360° − Az (western horizon) Note: Atmospheric refraction (34') and solar semi-diameter (16') corrections can be applied for higher precision.

Great-Circle Bearing

θ = atan2( sin(Δλ) · cos(φ₂), cos(φ₁) · sin(φ₂) − sin(φ₁) · cos(φ₂) · cos(Δλ) ) Distance: Haversine formula, accurate to ~0.3% for distances under 100 km.

Detection Algorithm

Alignment Detection Algorithm

1. For each year in grid (100-year steps, 15,000 BCE to 500 CE): a. Compute obliquity → event declination → horizon azimuth b. Compute diff = bearing − eventAzimuth 2. When sign changes between steps → binary-search refine to 1-year resolution 3. Compute residual in arcseconds If residual ≤ threshold → alignment match found 4. Both directions (A→B and B→A) are tested 5. Equinox and cardinal alignments are epoch-independent

Reading Results

Reading an Alignment Result

Example alignment result

FromCarnac — Le Ménec

ToStonehenge

Event☀ Summer Solstice Sunrise

Bearing51.23°

Distance345 km

Perfect Year3050 BCE

Mirror Year10,500 BCE (italic on UI)

Residual0.8″

PrecisionSub-Arcsecond

Important Caveats

A mathematical alignment does not prove intentional construction — it identifies a geometric possibility requiring archaeological investigation. The Perfect Year indicates when the astronomy matched, not necessarily when the sites were built. Local horizon features can shift the effective sunrise/sunset point. MEGALITHICA currently assumes a flat horizon; DEM integration is planned.

References

Laskar, J. (1986). “Secular terms of classical planetary theories using the results of general theory.” Astronomy and Astrophysics, 157, 59–70.

Meeus, J. (1998). Astronomical Algorithms, 2nd ed. Willmann-Bell.

IAU SOFA (Standards of Fundamental Astronomy). IAU 2006 precession model.