A Digital (3D) Reconstruction of a Lost Planetarium: A Finishing Touch to the Antikythera Mechanism

Introduction

In 1901, some sponge divers, pulled out from an ancient Roman shipwreck near the coast of Antikythera island, pieces of a corrupted geared construction. After a more careful examination of the remnants, it was found that these pieces (fragments) belonged to a mechanism which since then was called Antikythera mechanism. Seven of the main survived fragments of this mechanism named from A to G and were dated around 150–100 BCE. In 2005, after the application of two revolutionary technological methods, on Antikythera mechanism, many constructional details came to light. The methods been applied are: a) 3D x-ray computed tomography (CT) by X-Tek Systems Ltd and b) polynomial Texture Mapping (PTM) by HP Labs. In the mechanism remains identified more than 30 gears meshed in complicated combinations, while engraved symbols and letters on the fragments’ surfaces were decoded. Since then scholars have concluded that this mechanical construction was consisted of an advanced gearing system, and it was capable of making astronomical calculations as well as capable of predicting astronomical celestial phenomena.

A decoded text on the back face of the Antikythera mechanism reveals many details about the characteristics and the functional capabilities of this amazing gearwork machine. According to (Anastasiou et al., 2016) “The texts give data on synodic cycles for the five planets, and it may be conjectured that lost lines described the behavior of the Sun and Moon.” According to (Freeth & Jones, 2012) there is a deciphered text in the back cover of the mechanism where unfinished words inside fragmentary expressions show names of the five known planets. Particularly noticeable are the repeated words (σφαιρίον) “little sphere”, one for every planet and (κύκλος) “circle” where the little sphere possibly belongs to.

All the above references testify that possibly the Antikythera mechanism, could have a constructive formulation, on its top, like a kind of planetarium. This planetary compartment is completely absent from the remains of the mechanism found in 1901. Speculated models of this planetary synthesis, have already been made and they all use the available space between the sun gear b1¹ and the top of the mechanism. The gearing of Antikythera mechanism was hosted inside a wooden case consisted from a front and a back door, engraved with the previously referred deciphered texts. Researchers have already presented various models of Antikythera mechanism equipped with planetary systems. In most of them, motion seems to be simulated by epicyclic gearing trains based on the famous “epicyclic theory,”¹¹ which was known in the era Antikythera mechanism was constructed. Although the implementation of this theory gives satisfying results for planets with negligible eccentricity³, fails to demonstrate satisfactorily the motion of planets with considerable eccentricity, like Mercury or Mars (eccentricity of Mercury orbit: 0.205 and eccentricity of Mars orbit: 0.0935). On the other hand, the gear couple of classic “deferent- epicyclic model” limits gear combinations due to the restricted available area and in some cases (especially for superior planets) is not so reliable. For these reasons, models which are using this epicyclic couple¹⁵, give a planetary motion illustration lacking in measurement accuracy though. Moreover, in Antikythera mechanism remnants, there is a sophisticated device with code name “pin & slot” which regulates the rotation of Moon pointer to simulate the abnormal Lunar rotation around the Earth, using Hipparchus⁴ eccentric model.¹⁴ According to (Moussas, 2009) “The difference between Kepler’s predictions on the angular velocity of the Moon during the month and the mechanism’s prediction is of the order 1/400…” The fact that moon’s eccentricity (0.0549) is 3.7 less than Mercury’s eccentricity which is 0.205, shows that the constructor could possibly use the same ellipse simulation for planets with considerable eccentricity like Mercury and Mars.

Particularly interesting is the constructor flexibility of handling complex gear combinations, to drive the desirable ratio between the meshed gears. According to a published article written by the authors “For example, in the moon train⁵ there are six gears used to transmit the rotation to the lunar pointer.

Figure 1.

Moon train of the Antikythera mechanism modeled (Freeth & Jones, 2012)