The Initial Calibration Date of the Antikythera Mechanism after the Saros Spiral Mechanical Apokatastasis

This work analyzes the phase correlation of the three lunar cycles and the Exeligmos/(Saros) Cycle, after the study of the chapter “About Exeligmos” in “Introduction to the Phenomena” by Geminus. As Geminus reports, each Exeligmos Cycle began on very specific and rare dates, when the Moon was positioned at the starting points of the three lunar cycles: New Moon (Synodic), at Apogee (Anomalistic), and at the Node (Draconic). The extremely large duration of the Annular Solar eclipse occurred on December 22, 178 BC (Saros series 58) marks the start of the “Prominent Saros Cycle Apokatastasis”. The next day, December 23, 178 BC, the Winter Solstice occurred. During these two neighboring dates, the celebration of the religious festival of Isia started in Egypt and Hellenistic Greece. Based on the analysis of the specific position of the Mechanism’s Parapegma events, December 22/23 178 BC appears as the ideal starting date, i.e. functional and representative, in order to calibrate the initial position of the Mechanism’s pointers.