Maya Astronomical Cycles and Observations

Maya astronomy is the empirical, observational, and arithmetic backbone of the Maya calendar system. Beyond the Tzolkin, the Haab’, and the Long Count, the daykeepers of the Classic period maintained a parallel corpus of astronomical tables keyed to the synodic periods of the visible planets, to the 29.53-day synodic month of the Moon, and to the 173.31-day eclipse half-year. The surviving Maya codices — particularly the Dresden Codex, the Madrid Codex, and the Paris Codex — preserve Venus tables, Mars tables, Jupiter and Saturn almanacs, lunar tables, and eclipse prediction tables that, in their mathematical precision, rival the astronomy of Old World civilizations of the same period.

This page surveys the principal cycles, the tables in which they are recorded, the way they were tied to ritual and political life, and the role of the Maya temple alignments in making the observations in the first place.

The synodic period of Venus

The planet Venus — alternately the Morning Star (Noh Ek’, “Great Star”) and the Evening Star (Chak Ek’, “Red Star”) — was the most carefully tracked body in the Maya sky. Its synodic period, the time between successive inferior conjunctions as seen from Earth, is 583.92 days. The Maya Venus cycle, rounded to 584 days, is preserved in the Dresden Codex Venus Table (pages 24 and 46–50), which records five cycles of 584 days each, plus a sixth cycle, plus correction entries.

The structure of the Dresden Venus table is as follows:

The table begins with the heliacal rising of Venus as Morning Star.
After 236 days, Venus disappears as Morning Star (superior conjunction).
After 90 days, Venus reappears as Evening Star (greatest eastern elongation).
After 250 days, Venus disappears as Evening Star (inferior conjunction).
After 8 days, Venus reappears as Morning Star (heliacal rising).
Total: 236 + 90 + 250 + 8 = 584 days.

The table lists 5 × 584 = 2,920 days per “page” of the table, and the surviving Dresden table covers 5 pages, with the 6th page being a partial cycle. The total span is 5 × 584 = 2,920 days per page × 5 pages = 14,600 days = 40 Haab’ years, with corrections of 4 days every 61 cycles to keep the table in agreement with the actual 583.92-day synodic period. The 4-day correction corresponds to 4 × 583.92 = 2,335.68 days = 8 × 292 days, and the table is mathematically exact to within a day over a 481-year span.

The Maya Venus table was used to predict, to within a day, when Venus would reappear as Morning Star after superior conjunction. The accuracy is comparable to the Babylonian and the Greek Venus tables of the same period, and is the densest Venus table in any pre-Columbian record.

The role of Venus in ritual and warfare

The first-station Venus — the moment when Venus, after inferior conjunction, appears as Morning Star and remains stationary against the stars for a few days — was a time of warfare and sacrifice. The Dresden Codex, in its Venus almanac pages, repeatedly notes that first-station Venus is a time for “capturing prisoners” and for bloodletting. The inscriptions of Copán, Quiriguá, and Tikal record royal accessions timed to the heliacal rising of Venus, and the 8 December 683 first-station of Venus (the death of K’inich Janaab’ Pakal at Palenque) is one of the most carefully documented Venus events in the inscriptions.

The 584-day cycle also gives rise to the 2,920-day “Venus round” (5 × 584 = 2,920), and the 2,920-day round is tied to the Haab’ such that 2,920 days = 8 Haab’ years. The first day of the Haab’ year, 0 Pop, fell on a Venus first-station in the Late Classic period, and the 8-year Venus-Haab’ cycle was a known timekeeper in the inscriptions.

The Mars table

The Dresden Codex Mars table (pages 43–45) records a 780-day Mars cycle, close to the actual 779.94-day synodic period. The structure is similar to the Venus table: the table records the synodic arc of Mars, the disappearance periods, and the reappearance. The Mars table is shorter and less elaborate than the Venus table, and it is sometimes argued that the Maya were less interested in Mars than in Venus, perhaps because Mars is dimmer and more variable.

The Mars table is used in the Late Classic inscriptions of Palenque, where the heliacal rising of Mars is recorded as a time of royal ritual. The 780-day Mars cycle is also tied to the 260-day Tzolkin: 780 ÷ 260 = 3, so the Mars cycle is exactly 3 Tzolkin cycles. A particular Mars-event Tzolkin position recurs every 780 days, with the same Tzolkin position every 3 cycles.

Jupiter and Saturn

The Madrid Codex contains an almanac section (the “Madrid almanac”) with multiple almanacs of 260 days each, some of which are tied to the synodic periods of Jupiter and Saturn. The Jupiter synodic period is 398.88 days, close to 13 × 30 = 390 days or 1 × 360 + 39 days; the Saturn synodic period is 378.09 days, close to 1 × 360 + 18 days. The Madrid almanacs present tables keyed to these cycles, with correction entries to keep the tables in agreement with the actual synodic periods.

The Jupiter and Saturn almanacs are less elaborate than the Venus table, and they are sometimes argued to be a Late Postclassic development rather than a Classic-period construct. The highland Postclassic Maya communities, including the K’iche’ of the late fifteenth century, observed Jupiter and Saturn as part of their ritual life, and the Madrid almanacs may be a record of this Postclassic astronomical tradition.

The lunar series

The Lunar Series is a block of glyphs attached to dates in the Late Classic monumental inscriptions. The Lunar Series records:

The lunar age (the number of days since the last new moon, 0–29)
The lunar month number (the count of the 29.53-day synodic month within a 6-month “lunar half-year”)
The lunar belt glyph (a K’uhul glyph indicating the 6-month cycle of the moon)
The lunar fortnight glyph (a glyph indicating the 12- or 13-day count of the bright or dark half of the moon)
The lunar season glyph (a glyph indicating the dry or rainy season of the lunar month)

A typical Lunar Series might read: 8 moons, 4 lunar half-years, “the moon is in the 4th fortnight of the dry season.” The Lunar Series allows the epigrapher to determine the exact lunar age of a given date, and it is the basis of the GMT correlation between the Long Count and the proleptic Julian calendar.

The Lunar Series is attested from the Late Preclassic (a few isolated cases at Tres Zapotes and El Baúl) through the Late Classic at Palenque, Copán, Tikal, and other sites. The Lunar Series is one of the most precise astronomical texts in the pre-modern world.

The 405-lunar-month eclipse cycle

The Dresden Codex eclipse table (pages 51–58) covers 405 lunar months = 11,960 days = 32.75 tropical years. The table is built on the fact that 405 lunations ≈ 46 eclipse half-years, so the table returns to the same eclipse possibility every 405 months. The table is divided into 11,960 ÷ 6 = 1,993.33 days, and each row of the table corresponds to a 6-month eclipse half-year.

The structure of the eclipse table is as follows:

The table has 46 rows, each representing a 6-month eclipse half-year.
Each row gives a Tzolkin position (the day-sign of the new or full moon) and a 6-month count.
The daykeeper reading the table could determine, to within a day, when a solar or lunar eclipse might occur and whether the eclipse would be visible from the Maya area.

The accuracy of the Dresden eclipse table is impressive. The table can be checked against the historical record of eclipses visible from the Maya area between roughly AD 700 and 730, and it predicts eclipses to within a day of the actual event. The table is independent evidence of the precision of Maya astronomy and of the accuracy of Maya astronomical predictions.

The 9-day Lords of the Night

The Lords of the Night (Way glyph, also called the G glyph from its appearance in the 1960s Berlin codex) is a 9-day cycle attested from the Late Preclassic through the Late Classic. The 9 Lords rotate in a fixed order, and each day of the inscriptions carries a Lord number from 1 to 9.

The 9-day cycle is independent of the Tzolkin and the Haab’, and it appears in the inscriptions as a way of specifying the day in a 9-day cycle. The Lords of the Night are sometimes interpreted as the patrons of the 9 underworlds in the Maya underworld cosmology, and the 9-day cycle is tied to the 9-day journey of the Hero Twins through Xibalba in the Popol Vuh creation account.

The 819-day cycle of Caracol and other Late Classic sites returns the 9-day Lord to the same position only after 819 days (819 = 9 × 91), and the 9-day cycle is one of the structures on which the 819-day harmonic is built.

Zenith-passage days and the solar year

The zenith-passage day is the day of the year on which the sun passes directly overhead at local noon, casting no shadow from a vertical stick. The zenith-passage day is a function of latitude, and it occurs twice a year in the tropics:

At Copán (latitude 14.85° N): 30 April and 13 August.
At Tikal (latitude 17.22° N): 23 May and 12 August.
At Chichen Itza (latitude 20.68° N): 20 May and 22 July.
At Quiriguá (latitude 15.27° N): 28 April and 14 August.

The two zenith-passage days define the agricultural year: the interval between them is the period when the sun is north of the latitude, the time of planting and early growth; the period outside is the dry season. The daykeeper could use the zenith-passage day to calibrate the Haab’ and the agricultural calendar, and the E-Group architectural complexes at Uaxactún, Tikal, and Copán were built to observe the zenith passage from a viewing platform.

The 260-day Tzolkin is sometimes argued to have been calibrated to the zenith-passage cycle. At Copán, the two zenith-passage days are 105 days apart on one side and 260 days apart on the other (30 April → 13 August = 105 days; 13 August → 30 April = 260 days). The 260-day half-cycle is too long to be a coincidence, and the 105-day quarter-cycle is also attested in the inscriptions.

Heliacal risings and stellar alignments

The Maya tracked the heliacal rising of several stars, including:

Sirius (in Yukatek Sak Noh Ek’, “White Great Star”), the brightest star in the sky. The heliacal rising of Sirius in mid-August marked the beginning of the rainy season in some highland communities.
Capella (in some readings, Chumuk or Noh Ek’), the bright star in Auriga. The 819-day cycle is sometimes argued to be tied to the heliacal rising of Capella.
The Pleiades (Tzolkin in Yukatek, a name cognate with the sacred almanac). The Pleiades’ heliacal rising in May marked the start of the agricultural year in some highland communities, and the Pleiades are tied to the 260-day Tzolkin in modern K’iche’ ritual.
Orion’s Belt (Ak’bal in some readings), the three stars in the belt of Orion, aligned with the horizon at Chichen Itza and at Uxmal on certain days.

The inscriptions of Palenque include a reference to the “3 stars of the Tortuguero” tied to a Long Count date of 10.5.3.3.5, possibly recording a heliacal rising of Capella or the Pleiades.

The 360-day tun and the 365-day year

The 360-day tun of the Long Count is shorter than the 365-day Haab’ by 5 days. The discrepancy is corrected in the astronomical tables by including corrections to keep the tables in agreement with the actual 365.2422-day tropical year. The 360-day tun is a useful approximation for the Long Count, but the daykeepers used the 365-day Haab’ for the actual solar year.

The 360-day tun may itself be a product of the 18-month Haab’: 18 × 20 = 360 days, and the tun may have been derived from the Haab’ rather than from a separate astronomical observation. The astronomical tables, by contrast, are tied to the actual 365.2422-day tropical year, and the corrections to the tables (such as the 4-day correction in the Venus table) are evidence that the daykeepers were aware of the 365.2422-day year and the need to keep the tables in agreement with it.

The 819-day cycle and the planetary harmonic

The 819-day cycle of Caracol and other Late Classic sites is sometimes called a “planetary harmonic” because it returns to the same position in the 9-day Lord, the 13-day trecena, and the 4-color, 4-direction cardinal cycle. The cycle, 819 = 7 × 117 = 9 × 91 = 13 × 63, is mathematically tied to the 260-day Tzolkin (3 × 260 + 39), the 9-day Lord (9 × 91), and the 13-day trecena (13 × 63).

The 819-day cycle is a 4-color, 4-direction rotation: each 819-day block passes through a complete cycle of the cardinals (East, North, West, South) and a complete cycle of the colors (red, white, black, yellow). The cycle has been read as a “super-Tzolk’in” that structures the cosmic order over a longer time-horizon than the 260-day almanac.

The role of the daykeeper in astronomical observation

The ah k’in (or aj q’ij in modern K’iche’) was the daykeeper, the ritual specialist who maintained the almanacs and the astronomical tables. The ah k’in was responsible for:

Observing the heliacal rising of Venus, Mars, Jupiter, Saturn, Sirius, and Capella.
Calibrating the eclipse tables against the actual eclipses.
Predicting the zenith-passage days for the local latitude.
Selecting the day for royal accessions, marriages, warfare, and planting.
Reading the almanacs and the prognostications of the 260-day cycle.

The ah k’in in the Classic period was a hereditary office, with a parallel office of ch’ok ah k’in (apprentice daykeeper) learning the almanacs in training. The office is documented in the Bonampak murals, in the Palenque inscriptions, and in the colonial-era highland K’iche’ and Kaqchikel communities.

The Caracol observatory at Chichen Itza

The Caracol at Chichen Itza is the best-documented astronomical observatory of the Maya area. The building, a circular tower atop a rectangular platform, has three upper windows that frame the western horizon. The windows are aligned to:

The heliacal rising of Venus as Morning Star.
The setting of the Pleiades.
The setting of Capella.
The setting of Jupiter and Saturn on key dates in their synodic cycles.

The Caracol was built in the Late Classic period (c. AD 800–900), and the upper windows are dated by architectural and stylistic evidence to the Postclassic renovations. The Caracol is the densest surviving example of Maya temple astronomical alignment.

The E-Group at Uaxactún and Tikal

The E-Group is a distinctive architectural complex consisting of a small pyramid to the west and a long platform to the north, with a viewing platform at the eastern edge. The E-Group is aligned to:

The sunrise on the equinoxes.
The sunrise on the solstices.
The sunrise on the zenith-passage days.

The E-Group is attested at Uaxactún, Tikal, Copán, Quiriguá, Naranjo, and a number of other Late Preclassic and Classic period sites. The E-Group is the most common astronomical complex in the Maya area, and it is one of the earliest, with examples dating to the Middle Preclassic (c. 600–400 BCE).

The E-Group is sometimes called a “solar observatory,” but the term is somewhat misleading: the E-Group is a calendrical-astronomical complex that frames the sun on specific days of the year, and the daykeeper could use the E-Group to verify the date of the zenith passage, the solstices, and the equinoxes. The E-Group is not a precision instrument in the modern sense, but it is a calendar-checker that allowed the daykeeper to keep the Haab’ and the agricultural year in agreement with the tropical year.

The zenith tubes of Xochicalco

The zenith tubes of Xochicalco (a Central Mexican site with strong Maya influence in the Epiclassic period, c. AD 600–900) are vertical shafts that admit sunlight only on the day of the zenith passage. The shafts are designed to admit a vertical sunbeam into a chamber below, and the daykeeper could use the shaft to determine the date of the zenith passage with high precision. The Xochicalco zenith tubes are a more sophisticated version of the E-Group, and they attest to the spread of Maya astronomical knowledge into Central Mexico in the Epiclassic.

The Dresden Mars table and the 780-day cycle

The Dresden Mars table covers 5 × 780 = 3,900 days, with corrections to keep the table in agreement with the actual 779.94-day synodic period of Mars. The table is divided into pages, each covering a 780-day cycle, and each page records the disappearance and reappearance of Mars, the heliacal rising, and the stationary points. The Mars table is less elaborate than the Venus table, and it is sometimes argued that the Maya were less interested in Mars than in Venus.

The 780-day Mars cycle is tied to the 260-day Tzolkin: 780 = 3 × 260, so a given Mars event recurs every 3 Tzolkin cycles on the same Tzolkin position. The Mars table is a relatively simple construction compared to the Venus table, and it may have been developed in the Late Classic period as a complement to the Venus table.

The Jupiter and Saturn almanacs in the Madrid Codex

The Madrid Codex almanac section contains multiple 260-day almanacs, some of which are tied to the synodic periods of Jupiter and Saturn. The Jupiter almanac records the synodic arc of Jupiter, the disappearance periods, and the reappearance, and it is keyed to the 260-day Tzolkin. The Saturn almanac is similar. The Madrid almanacs are a Late Postclassic development (c. AD 1300–1521) and may reflect the astronomical traditions of the highland K’iche’ and Kaqchikel communities.

The Jupiter synodic period is 398.88 days, close to 1 × 360 + 39 days, and the Jupiter almanac is tied to the 360-day tun plus 39 days. The Saturn synodic period is 378.09 days, close to 1 × 360 + 18 days, and the Saturn almanac is tied to the 360-day tun plus 18 days. The 360-day tun is the basis of the Long Count, and the Jupiter and Saturn almanacs are tied to the Long Count through the tun count.

The lunar table in the Dresden Codex

The Dresden Codex lunar table (pages 51–58, alongside the eclipse table) records the 29.53-day synodic month, the 6-month lunar half-year, and the 12- or 13-day fortnight. The lunar table is more elaborate than the lunar series in the inscriptions, and it is tied to the 405-lunar-month eclipse cycle. The table allows the daykeeper to determine the lunar age, the lunar half-year, and the lunar fortnight for any given day in the cycle.

The lunar table is the basis of the GMT correlation, the standard correlation between the Long Count and the proleptic Julian calendar. The lunar table is also the basis of the modern epigrapher’s reconstruction of the absolute date of a Long Count position, and it is one of the most important texts for Maya astronomy.

The role of the Moon in ritual life

The Moon (Men, Uh, K’in) was tracked in the almanacs as a patron of fertility, weaving, and medicine. The lunar series in the inscriptions is a ritual record of the moon’s phase and half-year, and the daykeeper reading the lunar series would note whether the moon was waxing or waning, in the dry or the rainy season, in the bright or the dark fortnight. The Moon was also a deity, one of the principal patrons of the Maya pantheon, and the lunar phases were tied to the ritual calendar of bloodletting and sacrifice.

The role of the stars in ritual life

The stars were tracked in the almanacs as patrons of the agricultural year, the dry and rainy seasons, and the heliacal rising dates. The Pleiades (Tzolkin) were the patron of the agricultural year, with the heliacal rising in May marking the start of planting in some highland communities. Sirius was the patron of the dry season, with the heliacal rising in mid-August marking the end of the rains. Capella, Orion’s Belt, and the other bright stars were tied to the almanacs through their heliacal risings, and the daykeeper could use the stars to calibrate the 260-day Tzolkin and the 365-day Haab’.

The “3 stars of the Tortuguero” inscription

The Tortuguero Monument 6 is a Late Classic inscription that includes a reference to the “3 stars of the Tortuguero” tied to a Long Count date of 10.5.3.3.5. The “3 stars” have been read by David Stuart and others as the Pleiades, the three stars of Orion’s Belt, or the three stars of some other asterism. The inscription is one of the few monumental texts that explicitly records a stellar event, and it has been the subject of considerable scholarly debate.

The Tortuguero inscription is also the only contemporaneous inscription that explicitly mentions the 13-baktun completion, with the bolon yookte phrase that has been the subject of the 2012 debate. The astronomical and the calendrical references are intertwined, and the Tortuguero text is one of the most studied inscriptions of the Late Classic period.

The precision of the tables

The precision of the Maya astronomical tables is striking. The Venus table predicts the heliacal rising of Venus to within a day over a 481-year span. The eclipse table predicts eclipses to within a day over a 32.75-year span. The lunar table predicts the lunar phase to within a day over a 405-month span. The Mars table predicts the synodic arc of Mars to within a day over a 78-year span. The Jupiter and Saturn almanacs are less precise, but they are still tied to the synodic periods to within a few days.

The precision of the tables is comparable to the Babylonian and the Greek astronomical tables of the same period, and it is the densest numerical record of any pre-Columbian civilization. The tables are evidence of the empirical, observational, and arithmetic sophistication of Maya science, mathematics, and astronomy.

The daykeeper’s almanac and the modern practice

In the modern highland K’iche’ and Kaqchikel communities, the aj q’ij continues to maintain a 260-day Tzolkin almanac and a set of day-names. The modern almanac is not as elaborate as the Classic-period almanacs, but it preserves the same structure: 20 day-names, 13 numerical coefficients, 260-day cycle, and a set of prognostications for each day. The aj q’ij uses the almanac to select the day for marriages, planting, and naming ceremonies, and the almanac is the basis of the highland ritual calendar.

The highland aj q’ij do not maintain the Venus table, the eclipse table, or the Mars table, but they do observe the heliacal rising of the Pleiades (in May) and Sirius (in August) as part of the agricultural calendar. The modern practice is a survival of the Classic-period astronomical tradition, adapted to the highland K’iche’ and Kaqchikel ritual year.

Sources

Aveni, A. F. (2001). Skywatchers of Ancient Mexico. University of Texas Press. — link
Aveni, A. F. & Hartung, H. (1986). Maya city planning and the calendar. Transactions of the American Philosophical Society 76 (1). — link
Edmonson, M. S. (1988). The Book of the Year: Middle American Calendar Systems. University of Utah Press. — link
Teeple, J. E. (1926). Maya Astronomy. Contributions to American Archaeology No. 2. Carnegie Institution of Washington. — link
Rice, P. M. (2007). Maya Calendar Origins: Monuments, Mythohistories, and the Materialization of Time. University of Texas Press. — link
Coe, M. D. (1993). The Maya (5th ed.). Thames & Hudson. — link