Eclipse Prediction on the Ancient Greek Astronomical Calculating Machine Known as the Antikythera Mechanism

Abstract

The ancient Greek astronomical calculating machine, known as the Antikythera Mechanism, predicted eclipses, based on the 223-lunar month Saros cycle. Eclipses are indicated on a four-turn spiral Saros Dial by glyphs, which describe type and time of eclipse and include alphabetical index letters, referring to solar eclipse inscriptions. These include Index Letter Groups, describing shared eclipse characteristics. The grouping and ordering of the index letters, the organization of the inscriptions and the eclipse times have previously been unsolved. A new reading and interpretation of data from the back plate of the Antikythera Mechanism, including the glyphs, the index letters and the eclipse inscriptions, has resulted in substantial changes to previously published work. Based on these new readings, two arithmetical models are presented here that explain the complete eclipse prediction scheme. The first model solves the glyph distribution, the grouping and anomalous ordering of the index letters and the structure of the inscriptions. It also implies the existence of lost lunar eclipse inscriptions. The second model closely matches the glyph times and explains the four-turn spiral of the Saros Dial. Together, these models imply a surprisingly early epoch for the Antikythera Mechanism. The ancient Greeks built a machine that can predict, for many years ahead, not only eclipses but also a remarkable array of their characteristics, such as directions of obscuration, magnitude, colour, angular diameter of the Moon, relationship with the Moon’s node and eclipse time. It was not entirely accurate, but it was an astonishing achievement for its era.

Revising the eclipse prediction scheme in the Antikythera mechanism

“…The glyphs are indexed by two alphabets: the first is the usual 24 letters of the Greek alphabet; the second is the same, except that the letters have bars on top (indicated in this paper by subscript 2 for typographical reasons.) Since there were almost certainly 51 glyphs in all (Freeth, 2014), this leaves three additional glyphs that need to be indexed. Previous research (Freeth, 2014) has proposed that this was done with three extraalphabetical characters, which follow the first two alphabets.…”

“…Since there were almost certainly 51 glyphs in all (Freeth, 2014), this leaves three additional glyphs that need to be indexed. Previous research (Freeth, 2014) has proposed that this was done with three extraalphabetical characters, which follow the first two alphabets. These are the index letters for Glyphs 213, 214 and 219.…”

“…1, these Index Letter Groups are underlined in white and have white line numbers: they occur in Lines 9, 18, 29 and 36. They all reference solar eclipse inscriptions (Freeth, 2014). The user finds the Index Letter Group that contains the letter and then reads the lines of inscriptions above to discover the characteristics of the eclipse.…”

“…The Index Letter Groups are written in a non-alphabetic ordering, which was for a long time very perplexing. An understanding of their organization was published in Freeth (2014). The explanation is an application of a signed distance from node principle, which distinguishes whether the distances from node are North (positive) or South (negative) of the ecliptic.…”

“…The ecliptic latitude of the Moon at eclipse largely determines the character of the eclipse. The resulting Eclipse Year Model (EYM) (Freeth, 2014) explained both the distribution of the glyphs round the Saros Dial and the structure of the Index Letter Groups. The key idea is to calculate the distance of each eclipse from the node point, North or South of the ecliptic.…”