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ISAW Papers 11 (2016)

The Moon Phase Anomaly in the Antikythera Mechanism

Christián C. Carman and Marcelo Di Cocco

http://doi.org/2333.1/3ffbgd1v

Abstract: The Antikythera Mechanism is a mechanical astronomical instrument that was discovered in an ancient shipwreck at the beginning of the twentieth century, made about the second century B.C. It had several pointers showing the positions of the moon and sun in the zodiac, the approximate date according to a lunisolar calendar, several subsidiary dials showing calendrical phenomena, and also predictions of eclipses. The mechanism also had a display of the Moon’s phases: a small ball, half pale and half dark, rotating with the lunar synodic period and so showing the phases of the moon. The remains of the moon phase display include a fragmentary contrate gear. According to the reconstruction offered by Michael Wright, this gear is now pointing unintentionally in the wrong direction. In this paper we offer for the first time a detailed description of the remains of the moon phase mechanism. Based on this evidence, we argue that the extant contrate gear direction is the originally intended one, and we offer a conjectural explanation for its direction as an essential part of a representation of Aristarchus’s hypothesis that half moon phase is observably displaced from exact quadrature.

Library of Congress Subjects: Antikythera mechanism (Ancient calculator); Astronomy, Greek.

Contents

Introduction

The Antikythera Mechanism is a mechanical astronomical instrument that was discovered in an ancient shipwreck at the beginning of the twentieth century. The shipwreck has been dated around 60 B.C.1 A consensus does not exist on the question whether the Mechanism was built around that time or significantly earlier.2 After twenty centuries under water, it is incomplete, and broken into several fragments. The extant fragments are nevertheless enough for reconstructing the main structure and functions of the mechanism: it had several pointers, interconnected and worked by toothed gearing, showing the positions of the moon and sun (and probably also the planets) in the zodiac, the approximate date according to a lunisolar calendar, several subsidiary dials showing calendrical phenomena, and also predictions of eclipses.3

The longitudes of the sun and moon were shown on a single dial with two concentric rings: the inner one was divided into the twelve zodiac signs of 30 degrees each, and the outer one into 12 months of 30 days each plus five epagomenal days that constitute a year according to the Egyptian calendar. One pointer rotated one turn per year, showing the position of the sun in the zodiac; probably the same pointer4 showed also the day in the calendar ring. A second pointer rotated one turn per sidereal month, showing the position of the moon in the zodiac.

The moon pointer included a delightful and prominent detail, partially conserved in the back of Fragment C. See Figure 1. One half of a small ball was seen in a small circular window. The ball was half pale and half dark, and it rotated with the lunar synodic period and so showed the phases of the moon. The device was mounted on a small cap, rotating with the lunar sidereal period, to which the (lost) moon pointer was probably attached. See Figure 2. The moon ball was connected to a contrate gear through an arbor. This contrate was driven, either directly or indirectly, by a gear rotating with the solar period. Consequently the ensemble functioned as a differential gear, so that the contrate–and with it the little ball– rotated at a rate that was the difference between those of the sun and the moon pointers. Its period of rotation was therefore the synodic period, representing the elongation of the moon from the sun.