Ancient Maya documents concerning the movements of Mars

Ancient Maya documents concerning the movements of Mars

^*Department of Anthropology, Tulane University, 1021 Audubon Street, New Orleans, LA 70118; and ^‡Department of Physics and Astronomy, Colgate University, 13 Oak Drive, Hamilton, NY 13346

Contributed by Victoria R. Bricker

Abstract

A large part of the pre-Columbian Maya book known as the Dresden Codex is concerned with an exploration of commensurate relationships among celestial cycles and their relationship to other, nonastronomical cycles of cultural interest. As has long been known, pages 43b–45b of the Codex are concerned with the synodic cycle of Mars. New work reported here with another part of the Codex, a complex table on pages 69–74, reveals a concern on the part of the ancient Maya astronomers with the sidereal motion of Mars as well as with its synodic cycle. Two kinds of empiric sidereal intervals of Mars were used, a long one (702 days) that included a retrograde loop and a short one that did not. The use of these intervals, which is indicated by the documents in the Dresden Codex, permitted the tracking of Mars across the zodiac and the relating of its movements to the terrestrial seasons and to the 260-day sacred calendar. While Kepler solved the sidereal problem of Mars by proposing an elliptical heliocentric orbit, anonymous but equally ingenious Maya astronomers discovered a pair of time cycles that not only accurately described the planet's motion, but also related it to other cosmic and terrestrial concerns.

Footnotes

↵ † To whom reprint requests should be addressed. E-mail: hbricker{at}tulane.edu.
↵ § Page M.2a of the Madrid Codex contains a remaining portion of what may have been another version of a 780-day synodic Mars table, but too little has survived to be sure of its structure (8).
↵ ¶ We exclude cycles in which any portion of the retrograde loop occurs at the starting longitude from which a given ESI is reckoned. For example, if Mars passed 0° longitude just before reaching first stationary, it would pass it a second time while in retrograde motion and a third time after having resumed prograde motion following second stationary. However, the two passages through 0° longitude in prograde motion would be separated by a relatively short interval, fewer than 200 days, which would not constitute an ESI; the passage of longitude 0° shortly after second stationary would be included in the new ESI.
↵ ‖ A sample of 88 long ESIs from the 2nd, 8th, and 11th centuries A.D. has a length mean and standard deviation of 706.67 ± 4.86 days. The 12 short ESIs associated with these series have a mean length of 543.17 ± 6.79 days, producing a difference between long and short means in this sample of 163.50 days. There are no significant differences among the samples from the three different centuries.
↵ ** All Western-calendar dates in this communication are expressed in the Gregorian calendar.
↵ ‡‡ The dates, which appear on pages 69, 70, and 73, are written in pictun, serpent-number, ring-number-plus-long-round, initial-series, and truncated initial-series notations (9, 11). All can be expressed in terms of the number of days elapsed since the start of the current Maya era, a day designated 13.0.0.0.0 4 Ahau 8 Cumku. This beginning day of the era fell on Julian Day Number 584,283, corresponding to 11 August 3114 B.C. in a back-reckoned Gregorian calendar (5).
↵ †† Pooled samples from three 7L + S + 7L + S + 8L + S sequences, one each from the 2nd, 8th, and 11th centuries, have means and standard deviations of 17,171.67 ± 0.58 and 11,679.00 ± 1.00 days, respectively.
Abbreviations:

ESI,

empiric sidereal interval;

UWT,

upper water table