MEGALITHICA Methodology

The MEGALITHICA engine is a novel 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 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.

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 horizon azimuth where a celestial body with declination δ rises or sets at latitude φ is given by spherical astronomy:

cos(Az) = sin(δ) / cos(φ)

Rising:  Az (eastern horizon)
Setting: 360° - Az (western horizon)

This formula assumes a flat horizon. Atmospheric refraction (34') and solar semi-diameter (16') corrections can be applied for higher precision.

The geodesic bearing from site A to site B uses the forward azimuth formula:

θ = atan2(
  sin(Δλ) · cos(φ₂),
  cos(φ₁) · sin(φ₂) - sin(φ₁) · cos(φ₂) · cos(Δλ)
)

Distance uses the Haversine formula, accurate to ~0.3% for distances under 100km.

The core algorithm scans a year grid from 15,000 BCE to 500 CE, computing the event's horizon azimuth at each epoch and comparing it to the bearing:

1. For each year in the grid (100-year steps):
2. Compute obliquity → event declination → horizon azimuth
3. Compute diff = bearing - eventAzimuth
4. When sign changes between steps → binary-search refine
5. Compute residual in arcseconds
6. If residual ≤ threshold → alignment match found

Both directions (A→B and B→A) are tested. Equinox and cardinal alignments are epoch-independent (declination = 0° or fixed azimuth).

The "Perfect Year" is the central concept of the MEGALITHICA methodology. For any alignment between two sites, it answers the question: in which historical year did a celestial event (sunrise, sunset, moonrise, or moonset) occur at exactly the bearing between the two sites?

     Site A                                        Site B
       ●━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━●
       │          bearing = 51.2°
       │
       │    In which year did the Sun rise
       │    at exactly 51.2° azimuth?
       │
       ▼
  ┌─────────────────────────────────────────────┐
  │  Year scan: 15,000 BCE ──────────▶ 500 CE   │
  │                                             │
  │  For each year:                             │
  │    obliquity(year) ─▶ declination ─▶ azimuth│
  │                                             │
  │  Match found: azimuth ≈ 51.2°               │
  │  ─────────────────────────────              │
  │  Perfect Year = 3050 BCE                    │
  │  Residual = 0.8 arcseconds                  │
  └─────────────────────────────────────────────┘

The algorithm scans 15,500 years of history (15,000 BCE to 500 CE), computing the horizon azimuth of each celestial event at every epoch. Because Earth's axial tilt (obliquity) changes slowly over millennia, the point on the horizon where the Sun rises and sets at solstice shifts gradually. The Perfect Year is the moment when the computed azimuth matches the bearing between the two sites, with a residual measured in arcseconds — a unit so small that 1 arcsecond equals roughly 0.5 metres at 100 kilometres.

Earth's rotational axis is not fixed in space. The tilt angle — called obliquity — oscillates between approximately 22.1° and 24.5° over a ~41,000-year cycle. Today the obliquity is about 23.44°, but in 7,500 BCE it reached its peak of approximately 24.2°. Because solstice declination equals the obliquity, the sunrise and sunset azimuths at solstice have been slowly drifting for thousands of years.

  Obliquity
  (degrees)
  24.5° ┤
        │           ╱ ╲                         peak
  24.2° ┤         ╱     ╲                    ≈ 7500 BCE
        │       ╱         ╲
  24.0° ┤     ╱             ╲
        │   ╱                 ╲
  23.8° ┤ ╱                     ╲
        │╱                        ╲
  23.6° ┤                           ╲
        │                             ╲
  23.4° ┤ · · · · · · · · · · · · · · · ╲· · · · today
        │                                 ╲    (23.44°)
  23.2° ┤                                   ╲
        │                                     ╲
  23.0° ┤                                       ╲
        │
  22.8° ┤
        └──┬───┬───┬───┬───┬───┬───┬───┬───┬───┬──▶
         -15  -13  -11   -9   -7   -5   -3   -1  +1
         000  000  000  000  000  000  000  000  000
                     Thousands of years (BCE/CE)

This slow drift is what makes astronomical dating possible. If two megalithic sites are oriented toward a summer solstice sunrise bearing of, say, 51°, that bearing only matches the solstice azimuth at one specific epoch — the Perfect Year. The obliquity at that epoch determines how far north the Sun rose, and therefore what the azimuth was.

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 toward the peak around 7,500 BCE) and once on the descending limb (peak toward the present). This creates a "mirror year" for most alignments.

  Obliquity
  (degrees)
  24.2° ┤          ╱ ╲ peak
        │        ╱     ╲
  24.0° ┤      ╱         ╲
        │    ╱             ╲
  23.8° ┤  A╱· · · · · · · ·╲B · · · same obliquity!
        │ ╱                   ╲         (23.8°)
  23.6° ┤╱                     ╲
        │                       ╲
  23.4° ┤                        ╲
        └──┬───┬───┬───┬───┬───┬──┬──▶
         -12  -10   -8   -6   -4  -2  (×1000 years)

  ┌──────────────────────────────────────────┐
  │  Point A: 10,500 BCE  ←── Mirror Year    │
  │  Point B:  3,050 BCE  ←── Perfect Year   │
  │                                          │
  │  Same obliquity ─▶ same azimuth          │
  │  ─▶ both are valid alignment dates       │
  └──────────────────────────────────────────┘

If an alignment's Perfect Year is 3,050 BCE (on the descending limb, obliquity ≈ 23.97°), there exists a mirror year around 10,500 BCE (on the ascending limb, same obliquity ≈ 23.97°). At both dates, the Sun rose at the same azimuth — so both are equally valid astronomical dates for the alignment.

The mirror year is displayed on site pages beneath the Perfect Year in italics. Archaeologists can use construction dates, artefact typology, and other evidence to determine which of the two dates is more historically plausible.

When MEGALITHICA detects an alignment, the result contains several key fields. Here is how to interpret them:

This means that someone standing at Carnac — Le Ménec around 3,050 BCE, looking toward Stonehenge (bearing 51.23°), would have seen the summer solstice Sun rise at almost exactly that direction — with an error of only 0.8 arcseconds, which is about 1.3 metres at that distance. The mirror year of 10,500 BCE suggests the same geometry also held during the late Ice Age.

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, an extremely small unit of angular measurement.

  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

An arcsecond is 1/3,600th of a degree. To put this in perspective: if you hold a coin (2 cm diameter) at arm's length (60 cm), it subtends about 1.9 degrees — roughly 6,800 arcseconds. A single arcsecond is the angle subtended by that same coin viewed from 2.4 kilometres away. The fact that many megalithic alignments achieve sub-arcsecond precision over distances of tens or hundreds of kilometres is what makes the PHOSPHERE results remarkable.

The residual directly determines the precision category of the alignment. A sub-arcsecond residual (< 1″) at a distance of 100 km means the computed azimuth and the site bearing agree to within less than half a metre — an astonishing level of precision that is extremely unlikely to occur by chance. Monte Carlo simulations show that MEGALITHICA alignments occur 1,200 to 1,500 times more frequently than would be expected from randomly placed sites.

MEGALITHICA can detect hidden geometric patterns formed by groups of sites:

• Triangles: Three sites forming equilateral, isoceles, or right triangles
• Rectangles: Four sites forming rectangles or squares (90° ± tolerance)
• Circles: Sites fitting a least-squares circle (Kasa method)
• Lines: Collinear arrangements of 3+ sites

Shape detection uses a 15% side-length tolerance. Rectangle angle tolerance is 5° by default.

Hub sites are central nodes with many alignment connections. The analysis:

1. Filter alignments by precision threshold
2. Build adjacency graph (site → connected sites)
3. Count unique connections per site
4. Compute average precision for each site
5. Assign confidence: Very High (20+), High (10+), Moderate (5+), Low (3+)
6. BFS to find connected hub clusters

• 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.
• MEGALITHICA. Database of 960,000+ megalithic and archaeological sites worldwide.
• IAU SOFA (Standards of Fundamental Astronomy). IAU 2006 precession model.
• Hofmann-Wellenhof, B. et al. (2001). Global Positioning System: Theory and Practice. Springer.

MEGALITHICA methodology and MEGALITHICA platform conceived and developed by Charlie Taillard (2025).

Data sources: Yale Bright Star Catalogue, NASA JPL Horizons, national heritage databases.