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Mayan Astronomy

Note 17: The Dresden Codex Venus Table and Modern Astronomy. 8/23/99

On the first-day of the Dresden Codex Venus Table in the modern era, which is the first day reached in the table's structure after the base-day (1 Ahau 18 Kayab) when 236 days are added to that position, Venus reached 17.5* of elongation from the sun in the evening sky on June 30, 1917 A. D. This position was chosen for scrutiny by virtue of the fact that it is the final first-day of the Dresden Codex Venus Table counted forward in time from the Maya Classic Period before the end of the 13-Baktun sequence of the Long Count which they were counting in their own historical epoch. That LC notation reaches completion on August 14, 1955 using the correlation number 563334 as the zero base-day on April 29, 3171 B. C. The day in question would have been written as 12.18.1.5.16 3 Cib 9 Zac by the Mayas in the LC notation had they recorded it during the Classic Period. The interval between the Classic Period first-day (written as 9.9.10.9.16 3 Cib 9 Zac on May 21, 566 A. D.) and its modern day equivalent is 13 X 37,960 days, or 13 even turns of the Dresden Codex Venus Table without any corrections or alterations in the count.

The initial first-day position of Venus in the Dresden Codex Venus Table on May 21, 566 A. D. (Julian Day #1927930) places Venus at superior conjunction with the sun at 0.2* of elongation from it in the evening sky. After the completion of the first run of the Venus Table, or 37,960 days later, the same day-name (3 Cib 9 Zac) is recovered on April 25, 670 A. D. (Julian Day #1965890). On that day Venus reached a position of 1.3* of elongation from the sun in the evening sky after superior conjunction, for a maximum increase of 1.1* of elongation from the position it held 104 years earlier. Venus reached that position a total of 4 days after its conjunction with the sun, which occurred on April 21, 670 A. D. As noted elsewhere, the sun, the moon, Venus, and the Pleiades were in virtual conjunction with each other on this particular 3 Cib 9 Zac, where there was a differential of only eight minutes in the times of rising for the four objects on that morning. Taking the next Venus Table leap forward in time to the third 3 Cib 9 Zac first-day of the table, we reach March 30, 774 A. D. (Julian Day #2003850) 37,960 days later. On this day, Venus reached 2.5* of elongation from the sun in the evening sky after superior conjunction and had increased its differential from the previous position by a total of 1.2* of elongation. At the same time, this position for the planet occurred a total of 8 days after the superior conjunction itself which fell on March 22, 774 A. D. that year. The fourth 3 Cib 9 Zac in the Venus Table's count fell on March 4, 878 A. D. (Julian Day #2041810) with Venus standing at 3.8* of elongation from the sun in the evening sky after superior conjunction. The differential from the previous position is 1.3* of elongation and the number of days after SC has increased to 14 days, with the SC listed on February 18, 878 A. D.

A fair question, of course, is whether Maya astronomers during the Classic Period would have been able to calculate positions of Venus that were invisible to naked-eye observation, where superior conjunction with the sun is the relevant position in this context. While a definitive answer to this question might not ever rise above the level of speculation or conjecture, there is a certain amount of factual evidence in hand which tends to suggest they were able to do so with relative calendrical ease. If Maya astronomers understood the mechanics of Venus's invisibility at superior conjunction, and there is little reason to doubt otherwise, since they probably saw Venus during invisibility near superior conjunction during total solar eclipses at some point during the Classic Period or before, and since they were clearly able to count planetary motion quite accurately with their calendrical devices and structures, they would have known that Venus was invisible at SC for approximately 50 days. As I have suggested elsewhere, the likeliest possibility is that they employed a 52-day interval for that period, simply because it is a multiple of 13 and fashions a calendrical structure in the almanac day-name structure for last and first days of visibility before and after SC that also share the same almanac day-name coefficient with the day of conjunction itself. Since Venus moves both slowly and deliberately through its period of invisibility at SC, as opposed to its less consistent motion at inferior conjunction when it is between the earth and the sun, a 26-day interval to measure its last visible day before conjunction and from that point to its first visible day afterwards would work quite well more often than not to alert astronomers to its disappearance and reappearance cycles at SC.

The question any of this begs is whether or not there is evidence that the base-day of the Dresden Codex Venus Table was chosen to accommodate this calendrical astronomy in the first place. Like a lawyer, I never ask a question until I know the answer. In fact, 9.9.9.16.0 1 Ahau 18 Kayab was chosen as the base-day of the Venus Table, and it could have been attached to the Long Count notation anywhere at all, precisely because September 27, 565 A. D. (Julian Day #1927694) marked a position of Venus where it had reached a point exactly 236 days prior to the superior conjunction that occurred on May 21, 566 A. D. when the Maya Calendar Round reached 3 Cib 9 Zac. This is a reasonable assumption to make because two days after the base-day position the Calendar Round advanced to 3 Ik 0 Cumku. This is significant because Venus's first day of visibility after the superior conjunction marked by the Venus Table's first-day (3 Cib 9 Zac), which is reached by the addition of 236 days, fell on 3 Ik 15 Ceh, 26 days after the SC. The most compelling feature of this calendrical structure concerns the fact that 15 Ceh in the Maya Haab always occupies the 236th position of that sequence. Hence, the interval of extension in the Dresden Codex Venus Table (236 days) which carries forward from base-day to first-day (1 Ahau to 3 Cib) is the same as the calendrical position of the day-name (15 Ceh) in the Haab that marks the first day of visibility for the planet after its superior conjunction with the sun, a precise position that is marked by the extension of 236 days from the base-day in the first place. This calendrical circumstance cannot be the result of chance or coincidence; rather, it must be the result of design. This is Maya designer astronomy par excellence.

What the Mayas were doing with this structure, of course, was binding Venus's motion to the major components of their calendrical system. 260 days after the base-day of the Venus Table, which is the closest multiple of 13 to the actual length of Venus's period of visibility between solar conjunctions, set at 263 days on average, the day-name 1 Ahau (13 Ceh) is repeated. The choice of 1 Ahau, in the first place, marks a day on which Venus reaches 46.1* of elongation from the sun in the morning sky after it has passed its point of maximum elongation and has started to fall back toward the sun before superior conjunction: 236 days before that point in its synodic period precisely, as it turns out. These facts absolutely determine that the next occurrence of 1 Ahau will fall 2 days before Venus's reappearance in the evening sky after superior conjunction, when that interval is counted as 26 days. With respect to 365, the Haab interval itself, the same design principles are also true by virtue of the choice of 18 Kayab as the second half of the CR designation for the base-day. That extends inevitably to 15 Ceh (236) as the day of Venus's reappearance after the SC.

The one thing that has not been said here, of course, is that this calendrical astronomy works if, and only if, the zero base-day for the Maya Long Count notation is fixed at Julian Day #563334. This works if, and only if, these is a superior conjunction of Venus on the first-day of the Dresden Codex Venus Table on 3 Cib 9 Zac, on May 21, 566 A. D. (Julian Day #1927930). If any other position of Venus is used for the base-day, and there are 583 other choices in a single synodic period of the planet, the precision of this calendrical structure disappears. A final point to remember, the zero base-day was not determined on the basis of any planetary astronomy initially but was fixed in place because its forward extension places a preponderance of lunar and solar eclipses on the day-name triads of the Dresden Codex Eclipse Table precisely as the Mayas wrote it in the Classic Period.

Returning to the discussion of Venus's incremental motion away from superior conjunction with the sun that occurs as the calendrical system advances from the initial first-day of the Venus Table in 566 A. D. forward in time to the modern era, the following table expresses those values that seem most relevant to this discussion (all Maya day-names in the table are 3 Cib 9 Zac and the interval between each position is 37,960 days):

What this table demonstrates is that the superior conjunction which initiates the 3 Cib 9 Zac first-day sequence in the Dresden Codex Venus Table over extended periods of time regresses through the Maya calendrical system at a relatively constant rate. In a total of 13 extensions forward from the initial 3 Cib 9 Zac (566 A. D.) to the last one that can be counted before the terminal date of the 13-Baktun LC (1917 A. D.), the superior conjunction has regressed a total of 65 days over an interval equivalent 1,352 Mayan year (365 days each) and 845 average synodic periods of Venus (584 days each). The average rate of regression is 5 days every 104 years, with the lowest rate set at 3 days and the highest set at 8 days in each segment. Arguing that the Mayas became aware of this feature of their Venus Table during its Classic Period use is not an unreasonable assumption given the fact that they were able to observe these increments of regression relative to the last and first days of visibility before and after superior conjunction during every Venus synodic period they counted with their Venus Table over several 104-year runs of its duration. Whether they were actually able to predict that the regression would reach 65 days after 13 turns of the Table is less certain but the fact that the numbers themselves, 13 and 65, have such a positive resonance in the calendrical structure itself may suggest that the Table itself was designed in the first place in the way that it was to take advantage of this inescapable outcome.

A secondary consideration which cannot be ignored in this context concerns the fact that the differential between the day-name triads in the Classic Period sequence of eclipses and the modern equivalent of its expression, while there are some minor discrepancies between the two in terms of absolute accuracy, works out to being one of the difference between 64/196, as opposed to 65/195, in terms of the almanac structure of those two tabular expressions of eclipse occurrence. In other words, there is only a one day difference between one and the other where one-quarter and three-quarters of the almanac sequence of day-names is concerned. Given the 65-day regression from superior conjunctions in the Dresden Codex Venus Table, which the Mayas may have been able to anticipate, it seems more than just a coincidence that the day-name structure of the modern eclipse sequence is consistently offset from the original by one day more than three-quarters of the almanac sequence that gives it its essential structural reality.

Taking the discrepancy into account, and since several of the lunar eclipses in the modern sequence occur on the day after the third day of the triad, moving the triads forward by one day would place every eclipse on either the middle or the final day of each triad in the sequence; moving them forward two days would place every eclipse on either the middle or first day of each group. The point of saying so is to draw attention to the fact that Maya astronomers missed the mark by one or two days from a remove of 1300 years when they went about the task of predicting eclipse occurrences from their time to ours. All that remains for evaluation now is a comparison between the relationship between Dresden Codex Venus and Eclipse Tables from the ancient sequence to the present day.

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