The mechanism is computed. Every pointer follows from the real tooth ratios (Freeth et al. 2006 / 2008 / 2021) applied to the number of turns of the crank. Beside it, the true astronomical position, so the machine's error can be measured.
This is the machine turning: every gear with the real measurements read from the CT scan, driven by the same ratios as 2,100 years ago. Drag to turn around it; the controls are below.
The wheels move apart along the crank axis: in this model they sit on twelve different depths, from +3.0 mm for the big b1 down to −13.5 mm for the last plane. Turn the labels on and look for k1 and k2: two 50-tooth wheels on arbors that are not aligned, one carrying a pin that runs in the other’s slot — that is how the machine makes the Moon run faster near perigee and slower near apogee. The pale green wheels are the hypothetical ones: they are not in the artefact.
Drag to orbit · pinch or scroll to zoom · tap a wheel for its card, tap again for the one behind
The mechanism knows nothing of place: it computes longitudes on the ecliptic, valid anywhere. The place is needed to translate them into the sky one sees: rising and setting with azimuths, altitude above the horizon at the set hour, and whether the predicted eclipse is visible from there. Times in local mean time (UT + longitude/15), the same for every epoch.
sky dome seen from above: N at top, zenith at centre; the marks on the rim are the azimuths of rising and setting
The dial people looked at: the two hands are the Sun (gold) and the Moon (silver) on the zodiac; the outer ring is the 365-day Egyptian calendar. The small disc below shows the lunar phase.
The same hands, read as numbers. “Anomaly” is the correction the pin-and-slot applies to the Moon, because it does not move at constant speed.
19 years make exactly 235 lunar months: this spiral tells which month of the cycle we are in, and what it was called.
223 lunar months: after one Saros the eclipses repeat. The hand points to the cell of the cycle; the original machine had the eclipse months inscribed on it.
Three small dials: the year of the Panhellenic Games (Olympia, Nemea…), the 76-year Callippic cycle, and the Exeligmos that shifts eclipse times by 8 hours per Saros.
Everything this page computes starts from published measurements, not estimates. The 30 surviving gears — tooth counts, radii, thicknesses — come from the CT scan of the artefact kept at the National Archaeological Museum in Athens: counts in Freeth et al., Nature 2006; measurements in millimetres in Table S8 of Freeth et al., Scientific Reports 2021. The back dials — Metonic calendar, Games, Saros, Exeligmos — follow Freeth, Jones, Steele & Bitsakis, Nature 2008. The calibration epoch (28 April 205 BC, the start of the Saros dial) is the hypothesis of Freeth, PLOS ONE 2014, and remains a hypothesis. The planets follow the Cosmos model of Freeth et al. 2021 (period relations and Table S9); the tooth counts for Mars, Jupiter and Saturn are not published in readable form and are derived here, and marked as such.
The comparison with the sky uses Meeus’s formulae (Astronomical Algorithms) for Sun and Moon and JPL Keplerian elements for the planets: accuracy of a few arc-minutes. The design choices — the 3D layout, the layer depths, the eccentricity of the solar pin, the patina — are listed in the Expert view.
That distinction is the substance of this model, so it is declared line by line.
| Element | Source | Status |
|---|---|---|
| Tooth count, outer/inner/pitch radius and thickness of the 30 surviving gears | Freeth et al. 2021, Table S8 | measured |
| Radii of the 7 hypothetical gears (m3, n1, n2, n3, p1, p2, q1c) | mean module 0.495 × teeth / 2 | derived |
| Centre distance of every meshing pair | sum of the pitch radii | imposed by the mechanics |
| Metonic arbor (n) on the vertical above b; Saros arbor (g) on the vertical below | position of the two back dials | real constraint |
| Angular placement of the other arbors (c, d, e, f, h, i, l, m, o, p, q) | solved numerically: exact meshing, no collision between gears on the same layer | design choice — TO BE VERIFIED against the CT coordinates |
| Order and depth of the layers (z) | order imposed by the trains; depths chosen here, 1.5 mm pitch | approximate |
| Dimensions of plates, dials and spirals; pointer shapes | front cover ≈128.8 mm; the rest sized to contain the train | approximate |
| Artefact patina (surface colour and roughness) | procedural noise calibrated on the documented colours of corroded bronze: verdigris, cuprite, calcareous deposits; not a photograph | evocative |
| Direction of rotation, ratios, pin and slot | engine of the 2D pages (tested) | computed |
No planetary gearing survives: this part is reconstruction, not artefact. The period relations are those of Freeth et al. 2021; the Mercury and Venus tooth counts are printed in that text, while those for Mars, Jupiter and Saturn are derived here to satisfy the published relations and the shared-gear constraints. Table S9 of the paper confirms the design: the ratios between pin distance and axis distance (14.04/36.0 = 0.39 · 20.01/27.8 = 0.72 · 10.00/6.58 = 1.52 · 8.22/1.58 = 5.20 · 14.37/1.50 = 9.58) reproduce the planetary distances in astronomical units. The model is therefore one of concentric circles: synodic anomaly yes, zodiacal anomaly no.
| Body | Period relation | Epicyclic train | Ratio realized | Synodic period | Provenance |
|---|
The machine computes with fixed whole-number ratios. The sky does not. The deviation below is the object's real error, and it depends on how far you are from the calibration: the pointers are set by hand, and the operator would reset them. Calibrated to the ancient epoch, the Moon is more than 200° out at today's date and the Sun 14 days out — the effect of 22 centuries of cranking. Calibrated to the date entered, the machine is accurate again: that is how it would have been used.
| Quantity | Mechanism | Astronomy (Meeus) | Deviation | Note |
|---|
Every ratio below is recomputed by the browser from the tooth counts, not transcribed: were a count wrong, the ratio would not come out. The “status” column separates what was read from the CT scan from what is reconstruction.
| Function | Chain (teeth) | Ratio | Turns / year | Period | Status |
|---|
Thirty gears survive (27 in Fragment A). Table S8 of Freeth et al. 2021 for the survivors; the hypothetical ones come from Freeth 2006/2008 and are marked as such.
| Gear | Teeth | Status | Function |
|---|