Method and sources

Method

1. Ratios from teeth. The engine contains no astronomical formulas for the pointers: it contains the tooth counts of the surviving wheels and the trains that connect them. One turn of the crank turns b1 (223 teeth); every other wheel turns by the ratio imposed by the meshings. The sidereal Moon comes out at 254/19 turns per year, the Metonic dial at 5/19, the Saros at 940/4237, the Exeligmos at 235/12711, the anomaly group (pin-and-slot) at 477/4237.

2. Comparison with the true sky. Next to each pointer the site computes the real astronomical position with Meeus’s algorithms (low-precision Sun; Moon with ~27 longitude terms, 13 latitude terms and the distance terms). The difference is the machine’s error.

3. Calibration. The pointers can be zeroed on the entered date (immediate comparison) or on the epoch of 28 April 205 BC, start of the Saros dial according to Freeth 2014: in that case the visitor sees the error accumulated over 22 centuries.

4. Planets. They follow the Cosmos model (Freeth et al. 2021): period relations Mercury (1513, 480) and Venus (289, 462), with the tooth counts published in the text; for Mars, Jupiter and Saturn the counts are derived here from the same period relations and marked as such.

5. Local sky. Sidereal time, obliquity, ecliptic→equatorial→horizontal transformations, topocentric lunar parallax, rise/set by 48-hour scan.

What is measured, hypothetical or derived

Item	Origin	Status
Tooth counts of the 30 surviving wheels	Freeth et al. 2006, 2021 (Table S8)	measured
Radii, thicknesses, depths of the wheels	Table S8, 2021	measured
Back dials (Metonic, Games, Saros, Exeligmos)	Freeth et al. 2008	published
Lunar pin-and-slot, e/r = 0.1146	Freeth et al. 2006	published
Mercury and Venus tooth counts	Freeth et al. 2021, text	published
Mars, Jupiter, Saturn tooth counts	derived here from the period relations	derived
Epoch 28 April 205 BC	Freeth 2014	hypothesis
Solar slot e/r = 0.0334	project choice	to be verified
Axis layout of the 3D model	solved from the meshings	computed
Patina and appearance	colour calibration, not photogrammetry	aesthetic

Sources

Freeth, T. et al., “Decoding the ancient Greek astronomical calculator known as the Antikythera Mechanism”, Nature 444 (2006) 587–591, and Supplementary Notes.
Freeth, T., Jones, A., Steele, J. M., Bitsakis, Y., “Calendars with Olympiad display and eclipse prediction on the Antikythera Mechanism”, Nature 454 (2008) 614–617.
Freeth, T., Jones, A., “The Cosmos in the Antikythera Mechanism”, ISAW Papers 4 (2012).
Freeth, T., “Eclipse Prediction on the Ancient Greek Astronomical Calculating Machine Known as the Antikythera Mechanism”, PLOS ONE 9(7) e103275 (2014).
Freeth, T. et al., “A Model of the Cosmos in the ancient Greek Antikythera Mechanism”, Scientific Reports 11:5821 (2021), Supplementary Tables S8–S9.
Meeus, J., Astronomical Algorithms, 2nd ed., Willmann-Bell 1998, chapters 7, 12, 13, 25, 40, 47.
Standish, E. M., Keplerian Elements for Approximate Positions of the Major Planets, JPL Solar System Dynamics (elements valid 3000 BC – 3000 AD).

Corrections

If you find an error in a datum or a ratio, write to info@antikytheramechanism.app citing the source: the correction will be logged under Project status.