Caracol at Chichen Itza: A Maya observatory?

Accuracy without instruments "We now know that the Maya knew the exact length of the true solar year as 365.2420 days, that is, with a minus error of 0.0002, while our present Gregorian calendar has it at 365.2425, or a plus error of 0.0003." (William Gates,  Yucatan Before and After the Conquest) Maya astronomers determined astronomical constants with remarkable accuracy.  In our technological age, their feats seems incredible, if not impossible, without telescopes, clocks and measuring devices. But we have forgotten what can be achieved by careful naked eye observation using simple instruments, or even no instruments at all.

Dresden Eclipse table

Maya sky watchers used methods similar to those of other ancient astronomers.  The Greek astronomer Ptolemy would have understood and appreciated the star craft of a Maya scribe from Copan. What was required, above all else,  was careful observation over long periods of time.  For example, the Dresden Codex eclipse table tracks the phases of the moon over 405 lunar months, 11,960 days. If you watch the moon for a few months, you'll discover that the lunar month  (the time from new moon to new moon) usually alternates between 29 and 30 days, giving an average of 29.5 days. Watch  longer, and you'll discover that two 30 day lunar months sometimes occur in succession: The 29.5 day average isn't quite correct.  If you watch long enough to discover that the 405th new moon arrives 11,960 days after the 1st,  you will achieve the accuracy of the eclipse table:  11,960/405 =  29.53086 days.

Were the Maya really more accurate than other ancient astronomers?
 

Admiring statements about the accuracy of Maya astronomy (like Gates' quoted above) may distort what the Maya were trying to achieve. They were not interested in accuracy for its own sake, and had nothing like the modern notion of standard deviation to serve as a benchmark of accuracy.  Like many peoples, they wanted to be able to predict future astronomical events to time rituals and make auguries. They needed reasonably good measures of such things as the lunar month and the period of Venus to do so, but the accuracy of a modern ephemeris would not have been required for this purpose. But there is another aspect of Maya sacred astronomy that was almost unique among civilizations at a similar level of technology. The Maya were intensely interested in making astronomical cycles commensurate with their calendar. They carried out observations over long periods of time to fit astronomical and calendrical cycles together. The eclipse table in the Dresden Codex is not carried out 11,960 days to achieve extreme accuracy, but because nothing less than 405 lunations can be fitted into a whole number of 260 day.tzolk'in cycles. The Venus table is carried out even further, but only to ensure that it runs from a tzolk'in date of 1 Ahaw to another occurrence of 1 Ahaw on a day when Venus again rises with the sun.

So while the values of the lunar month, Venus period, and tropical year implied by Maya records are more accurate than those calculated by Ptolemy using Greek and Babylonian records,  the difference was dictated by the Maya calendar, not a scientific desire for high accuracy.  The Maya measurement of the synodic period of Mars is quite good, but not as accurate as the Greeks'. Mars' period is almost exactly three tzolk'in cycles, which required only a bit more than two years of observation to fit into the calendar. The short period of observation required to make a good match with the calendar produced a measure of Mars' period less accurate than the estimates of lunar and Venus periods.
 

This should not diminish respect for Maya astronomers, but it does put their achievement in proper context. The Maya regarded time as a meshing of sacred cycles. Their astronomy was a monumental effort to encompass the motions of the heavens in a mathematically perfect system.  Its purpose was ritual and augury, not scientific description in the modern sense.
 
 

Observing with simple instruments

In the tropics, the sun stands directly overhead at noon twice each year. In the Yucatan, these zenith passages occur in May and July, and mark the times when crops are planted. The 365 day Maya year, the haab, makes no allowance for leap year, but the Maya also tracked the solar year. The post-conquest Books of Chilam Balam suggest that July 26 in the Gregorian calendar, close to the time of a zenith passage in the Yucatan, was regarded as the beginning of the solar year.

Right  Vincent Malmström suggests that this monument at Izapa may have been used as a gnomon to determine the altitude of the sun and mark zenith passages.
 
 

Zenith tube at Xochicalco (left) aperture of the tube (right) entrance to  the artificial cave containing the zenith tube. Determining the zenith passage of the sun is a simple matter: A pole or standing stone trued to vertical with a plumb line will cast no shadow when the sun is directly overhead. The solar zenith and zenith passages of other objects can also be determined by observing through a vertical tube in the roof of a building.  At Monte Alban in Oaxaca and Xochicalco in Central  Mexico, zenith tubes appear to have been built into artificial caves beneath monuments. The Maya Madrid Codex likely illustrates a similar observing tube in use.

The time of zenith passage was apparently determined by observation. The Castillo at Chichen Itza faces to within a degree of the direction of sunset on the day of zenith passage sunset.  Other zenith passages were also important to the Maya and other Mesoamerican peoples. The Aztecs timed the "new fire" rituals at the end of the 52 year calendar round to the zenith passage of the Pleiades.     Maya skywatcher (Madrid Codex, p.34) observing with viewing tube. The symbols about the figure are similar to icons known to represent stars in Central Mexican codices.

At least one phenomenon that interested Maya scribes could most easily have been made with a simple angle measuring instrument. This is the maximum elongation of Venus. After heliacal rise of Venus, when it first appears above the horizon at sunrise, the planet moves further from the sun, rising earlier and reaching a higher point in the sky before dawn each night. At maximum western elongation, it is 45-47 degrees from the sun. It then moves closer to the sun each night, until it fails to rise before the sun again. After reappearance as evening star, it similarly moves toward maximum eastern elongation before again retreating toward the sun.   Right:  The Chinkultic Disk.  The text on this ball court marker records that the court was dedicated on  the long count date 9.7.17.12.14 11 Ix 7 Sotz' =  21 May 591 AD.  The Mesoamerican ball game was a metaphor for the movements of the heavenly bodies, particularly the sun and Venus.  The dedication date was likely chosen because it was close to both the zenith passage of the sun and maximum western elongation of Venus.

more about the disk

Bodley Codex (from pages 19 and 32)

Illustrations from Central Mexican codices show a cross-staff device that was likely used to estimate angular distances between objects in the sky. According to Nuthall, the cross-staff symbol represented foresight in the Mixtec codices.  The ends of the cross-piece on the staff will measure an angular distance (determined by the dimensions of the instrument) when the observer sights along the main staff.

Simple cross-staves were used by ancient astronomers in many parts of the world. Greek astronomers at Alexandria produced the first catalog of star positions in 284 BC using a cross-staff.
 
 

Ptolemy with cross-staff

In Medieval Europe, an improved version, called Jacob's staff, was known. It remained in use as a  navigational instrument into the 18th C.   Jacob's staff was a long, square staff, with a shorter cross-piece, which slid up and down the staff. The staff  was placed close to the eye and the crosspiece was adjusted so as to fill the apparent distance between Polaris or the sun and the horizon. The angular measurement was taken on a scale on the edge of the staff. It is unlikely that the Mexican cross-staff had a sliding cross-piece, but the possibility cannot be ruled out.

Jacob's staff

Building alignments

For observing the position of an event on the horizon such as sunrise or sunset, nothing works quite as well as  a long line of sight.  The observer sights across a distant object, a natural feature such as a boulder or the cornice on a building, to the horizon. Maya buildings were frequently aligned so they could be used to sight events such as sunrise on the equinoxes and solstices.  As a practical matter,  sunrise occurs at the north most point it ever reaches at a particular latitude at the Summer solstice, about June 21.  At the winter equinox on December 21, the sun rises at the south most point. At the Equinoxes on March 21 and September 23, the sun rises due east.

Uaxactun Pyramid E-VII

One of the best examples of alignments to the equinoxes and solstices is the pyramid and temples of  "Group E" at Uaxactun in the lowlands of Guatemala. From the pyramid, there are lines of sight to both equinoxes and solstices across cornices on the temples, located across a broad plaza. Monuments erected below the temples (stelae 18,19, and 20) bear long count dates separated by 7 katuns, just 3.48 days short of 138 solar years. This suggests that sightings made using the alignments  were used to determine the length of the solar year

Alignments to equinoxes and solstices seem to be a quite common feature of Classical Maya buildings, but others have also been discovered. The Caracol at Chichen Itza is recognized as an astronomical observatory. It appears to have three Venus alignments. The building as a whole is aligned  to the northerly extremes at which Venus rises. A pair of turret windows seem to point to places on the western horizon where Venus pauses and changes its direction of motion in the sky. The Caracol's platform, an irregular rectangle, has a diagonal directed toward the winter solstice sunset and summer solstice sunrise. (See on-line diagram of Caracol alignments)

But a caveat is necessary: Some alignments to astronomical events are bound to occur by accident at any large archaeological site.  Determining which alignments were intentional can be difficult. The classic example is Stonehenge, where so many possible alignments have been identified that the imagination boggles. Recent work by Anthony Aveni has cast doubt on some alleged Mesoamerican alignments.

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Bibliography and links
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Anthony Aveni,  Skywatchers (University of Texas Press, 2001). The best general introduction to astronomy in Mesoamerica, with good sections on observation methods, and a thorough description of Maya astronomy in the inscriptions and codices.  This is a new edition of Skywatchers of Ancient Mexico, one of the books that established the modern science of archaeoastronomy.

Anthony Aveni, "Archaeoastronomy in the Maya region: a review of the past decade", Archaeoastronomy No. 3 suppl. J. Hist Astronom. 12 (1981), S1--S16. Abstract on-line.

Anthony Aveni,  "Tropical archeoastronomy",  Science 213 (1981).  Abstract on-line.  Aveni demonstrates that cultures in the tropics appear in general to have adopted a horizon and zenith approach to the sky, as opposed to  the approach with the celestial pole and the ecliptic/celestial equator, which is more familiar to most of us.

Anthony Aveni and Horst Hartung, "The observation of the sun at the time of passage through the zenith in Mesoamerica", Archaeoastronomy no. 3 (JHA 12, 1981). Abstract on-line. On the zenith tubes at Monte Alban and Xochicalco. See also more images at Clive Ruggles  Archaeoastronomy Page.

Aveni, Anthony F. and Horst Hartung. "Uaxactun, Guatemala, Group E, and similar assemblages: an archaeoastronomical reconsideration", in A. Aven (ed.), World Archaeoastronomy ( Cambridge University Press, 1989).  On the alignments at Uaxactun.  

Aveni, Anthony F. and Horst Hartung.  "Archaeoastronomy and the Puuc sites" in  J. Broda, S. Iwaniszewski, and L. Maupomé, eds., Arqueoastronomía y Etnoastronomía en Mesoamérica (Inst. de Investig. Hist., Serie de Hist. de la Ciencia y la Technología, 4. México, 1991).  Discussion  of some possible alignments at Uxmal and elsewhere.  See also  Clive Ruggles  Archaeoastronomy Page and Rosenthal (below).

Jacobs, James Q. Mesoamerican Archaeoastronomy:  A Review of Contemporary Understandings of Prehispanic Astronomic Knowledge, 1999.  Good summary of astronomical periods measured by Maya astronomers.

Milbrath, Susan. 1988. "Astronomical images and orientations in the architecture of Chichen Itza" in A. Aveni (ed.), New  directions in American archaeoastronomy,  (BAR International Series, 454. Oxford, 1988).  On the Caracol as an observatory. See also more images at Clive Ruggles  Archaeoastronomy Page.

Milbrath, Susan. Stargods of the Maya: Astronomy in Art, Folklore, and Calendars.  Univ. of Texas Press, 1999.

Rosenthal, David. The Southernmost Rise of Venus at Uxmal, 1997.  See also Aveni (above). "This effort to document and photograph this  rare event may provide new insight into the architectural philosophy behind astronomically oriented Maya structures".

Schaefer,Brad.  Heliacal Rising: Definitions, Calculations, and Some Specific Cases, Archaeoastronomy & Ethnoastronomy News, No. 25. The problem of determining the time of heliacal rise.

Strobel, Nick. Astronomy without a telescope.  Part of Strobel's fine on-line astronomy text book. Explains solstices and equinoxes, lunar phases, eclipses, apparitions of planets etc.

Tedlock, Barbara. "Maya astronomy: what we know and how we know it", Archaeoastronomy: The Journal of
Astronomy in Culture, 14(1).

Astronomical Calculations of Crescents & Determination of The Beginning of Islamic Months. The problem of observing new moon

The Cross-staff Description of the use of  Jacob's staff from the NASA Stargazers page.
 

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