Eclipse Prediction and the Length of the Lunar Month in Mayan Astronomy

Abstract

One of the most remarkable achievements of Mayan calendrical astronomy was the in- vention of a lunar theory that combined a fixed lunar calendar with eclipse predictions. Eclipse predictions are shown in the Dresden Codex on pages 51-58. The lunar calendar is reflected in the Maya Lunar Series, which was attached to the chronological statements of Maya rulers displayed on monuments.

The so-called Eclipse Table covers 405 schematic lunar months, divided into 69 groups of 6 and 5 months each (D53a-D58b). It is preceded by a table of multiples of 11,960 days (D51a- D52a), the period covered by the table. The table structure generally exhibits three units with 23 eclipse possibilities each, of which twenty occur after six months and three after five months. Since each unit contains 135 months, the table includes 405 months (= 3 x 135) or three tritos series. Considering that each units warns about the possibility of 23 eclipses, the entire table allows warning about the possibility of 69 (= 3 x 23) eclipses. Some schol- ars, however, argued that the table originated from a tzolkinex, an eclipse period consist- ing of 88 synodic months. Both periods produce mean eclipse periods, which are more accurate than the saros.

Despite the Maya systematic alternation of 29- and 30-day lunar months, they devised a method to insert additional or leap days at regular intervals to track the lunar phases accu- rately. This method, known from the Lunar Table found at the Maya city of Xultun, is based on the record of 162 lunar months. The Xultun table is compatible with the intervals of 11960 days used in several Maya cities to perform lunar computations backwardly. in time.

This paper aims to provide a helpful and informative description of the records that are utilized to infer the mean values of the length of a half eclipse year and the average length of a lunation in Maya astronomy.