Ancient Maya documents concerning the movements of Mars

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.