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.

Tropical archeoastronomy.

Too often, judged by the Westem cultural yardstick, astronomical systems developed by indigenous civilizations of the tropical latitudes are found to be both complex and fundamentally different from those originating in civilizations of the temperate latitudes. One explanation for this difference is the radically contrasting sky orientations that are viewed from different parts of the globe, a determinative environmental factor in the development of cosmological systems that should not be neglected by the anthropologist and cultural historian.

The pecked cross symbol in ancient mesoamerica.

Attention is directed to a design, possibly of Teotihuacan origin, carved both in rock and in the floors of ceremonial buildings throughout ancient Mesoamerica. Consisting generally of a double circular pattern centered on a set of orthogonal axes, the so-called pecked cross or quartered circle figure is shown to exhibit a remarkable consistency in appearance throughout its 29 reported locations, thus suggesting that it was not perfunctory. The metric properties of the symbols gleaned from field surveys are delineated, and several interpretations of their possible functions are discussed. These symbols may have been intended as astronomical orientational devices, surveyor's bench marks, calendars, or ritual games. Evidence is presented which implies that more than one and perhaps all of these functions were employed simultaneously, a view which is shown to be consistent with the cosmological attitude of the pre-Columbian people.

The caracol tower at chichen itza: an ancient astronomical observatory?

Although our investigations reveal a number of significant astronomical events coinciding with many of the measured alignments presented in Table 1, not every alignment appears to have an astronomical match which we can recognize. It may be that only some of the sighting possibilities we have discussed were actually functional. Moreover, our search of significant astronomical events to match the alignments has included only those which seem of obvious functional importance to us: sun, moon, and planetary extremes and the setting positions of the brightest stars. We have emphasized those celestial bodies which are documented in the literature as having been of importance. Perhaps hitherto unrecognized constellations were sighted in the windows, perhaps fainter stars, the heliacal rising and setting times of which could have served to mark important dates in the calendar. While we propose no grand cosmic scheme for the astronomical design of the Caracol it can be inferred that the building, apart from being a monument related to Quetzalcoatl, was erected primarily for the purpose of embodying in its architecture certain significant astronomical event alignments, in the same sense that a modern astronomical ephemeris exhibits information of importance to us in the keeping of the current calendar. There are examples in the Mesoamerican historical literature of deliberate attempts to align buildings with astronomical directions of importance. For example, Maudslay (33) quotes Father Motolinia, who tells us that in Tenochtitlan the festival called Tlacaxipeualistli "took place when the sun stood in the middle of Huicholobos, which was at the equinox, and because it was a little out of the straight, Montezuma wished to pull it down and set it right." According to Maudslay, worshipers were probably facing east to watch the sun rise between the two oratories on the Great Temple of Tenochtitlan at the time of the equinox. The directions of the faces of the Lower and Upper platforms of the Caracol seem to have been laid out deliberately to point to horizon events involving the sun and the planet Venus. Of the lines taken through the windows, the Venus setting points seem most plausible to us in view of both the accuracy with which they fit the architecture and the historical evidence bearing upon the importance of Venus to the Mesoamerican people. A specific connection between the Venus calendar in the Dresden Codex and the sighting of the extreme positions of the planet along the horizon, however, is yet to be established. It is especially significant that alignments in both the base and the top of the tower relate to Venus. The solar equinox alignment in window I remains problematical, although the arrangement probably functioned as an approximate means of determining the first day of spring and the first day of autumn. Lines pointing to individual bright stars undoubtedly should be given lower value. If one is willing to carry the matching game to its ultimate completion, a stellar object can always be found which, although very obscure, will fit an alignment. In our consideration of the problem we have attempted to single out bright stars which appeared or disappeared on significant calendar dates. Other round structures resembling the Caracol exist in Mesoamerica (20), although there are comparatively few built by the Maya. Nearly all can be attributed to the cult of Quetzalcoatl (34). To our knowledge none have been carefully measured and analyzed for astronomical orientations. The ruined tower Q-152 at Mayapan bore distinct similarities to the Caracol, both in shape and structure. It probably contained only a single doorway which faced west. Both structures possessed circular corridors. A circular tower is still standing at Paalmul on the coast of Quintana Roo north of Tulum. Pollock (20, p. 115) states that it has a single room in the turret. A window similar to No. I in the Caracol faces northwest, the same direction as the base of the front of the structure. It may be astronomically significant that the Yucatecan towers fronted in approximately the same direction. Andrews (34) reports the existence of a curious circular building located at Puerto Rico, Campeche, near Xpujil. His crosssectional view of the tower bears a close resemblance to Ruppert's sketch (6, figure 293) of a horizontal section taken through the windows remaining at the top of the Caracol. Hartung (12) has suggested a possible astronomical use for the Puerto Rico tower, but no analysis of the orientation of its "windows," which are much smaller than those of the Caracol, has yet been conducted. Other circular buildings are reported at Ake (20, p. 113) and Isla Cozumel (35, p. 557). We hope that future investigations of the remains of Yucatecan towers will shed further light upon the significance and use of the Caracol as an astronomical observatory.

Middle devonian lunar month.

Simple dynamical calculations regarding the number of lunar months in the Middle Devonian year differ slightly from results obtained from periodicities found in the breeding of corals.