The Mayan Calendar:
260 Days & the Venus Orbit

Keith M. Hunter


The Ancient Mayan Calendar

Recently there has been a great deal of renewed interest in the Maya, and in particular their astronomical knowledge, including the Mayan calendar systems as developed from very ancient times. Indeed, within this area of study, much effort has been expended in the attempt to explain in particular why the Maya made use of a 260 day cycle. And why also they combined this time cycle with a calendar year period of 365 days, in order to generate a recurring 52 year period known as the ‘Calendar Round’. To date, from an overview of the relevant research concerning the Mayan use of a time cycle of 260 days, it would appear that its significance as an astronomical unit largely remains a mystery, with only a few tentative theories put forward. However, after careful study, this present author has developed what he believes is the answer; a full explanation as to why the Mayan calendar was devised in accordance with a 260 day cycle, and why this cycle was itself combined with a basic calendar year of 365 days.

Abstract

To summarise the theory in general, it is hereby put forward that the Maya specifically created, or rather invented, a 260 day cycle in order to allow them to accurately track the occurrence of successive conjunctions involving the Earth and Venus, over a full 2000 year grand cycle. So that this might be achieved, the 260 day period of the Mayan calendar was further combined with a basic Earth year of 365 days, as a means to generate an extended 52 year period of time, through which they were able to make subtle corrections to their calendar, to maintain harmony between it and the true astronomical observations i.e. Earth-Venus conjunctions.

The Primary Function of the Mayan Calendar: Tracking Venus

To the Mayan people, Venus was (and is) a very important planet, heavily tied in to their creation and ‘world-age’ mythologies. Indeed, the planet was in fact held to be a central character in the transition from one world age to the next. As a result of this, the ancient Maya were very much concerned with accurately tracking its passage though the heavens, most especially relative to the earth’s own orbit. And indeed, the primary method by which the Maya kept track of Venus was by noting the successive passage of conjunctions between it and the Earth.

Of course, it should be mentioned at the outset of this analysis, that in observing both the Earth and Venus over many thousands of years, the Maya determined a set of exceptionally accurate values for both the length of the Earth tropical year, and the Venus orbital period (year). One may cite in particular, concerning the former, the fact that the Maya were fully aware of the so called ‘year drift formula’, that relates the true length of the tropical year to a more basic calendar year of 365 days exactly. Essentially, the division between the true year and calendar year is almost exactly equal to the basic fraction of 1508 / 1507. This is shown below:

(365 x 1508) / 1507 = 365.24220305 days

In the modern age, the full duration of the tropical year is considered equal to about:

365.24218408 days

In terms of difference: (365.24220305 - 365.24218408) x 86400

= 1.6339968 seconds

As can be seen then from the above, the Maya did possess an exceptionally accurate value for the length of the earth tropical year. But one should also note that so too did they possess an accurate Venus orbital period; both values being carefully incorporated into the Mayan Calendar system. In proceeding therefore to an evaluation of the Mayan calendar with respect to both the Earth and Venus, an exacting set of modern values can be used. And they are as follows:

Earth Tropical Year = 365.24218408 days
Venus Orbital Period (Year) = 224.69526222 days

The Basic Conjunction Cycle

For any culture concerned with tracking periodic conjunctions between the Earth and Venus, it is readily apparent, in light of the values for the orbital periods of both bodies, that there is almost an exact re-alignment of the Earth and Venus every 8 tropical years. Thus, if one were to begin with an initial conjunction between both planets and the sun, after 8 tropical years, Venus will have completed (only) just over 13 orbits about the sun itself:

365.24218408 x 8 = 2921.93747264 days

2921.93747264 / 224.69526222 = 13.0040012582

From this, one can see then a basic 8/13 conjunction cycle between the Earth and Venus; one that is repeated at a relatively short celestial interval. However, as is quite obvious, the actual cycle itself is not perfect, for following precisely 8 tropical years, though the Earth will have returned to its initial position, Venus will have slightly outpaced the Earth, having already entered into its 14th orbit. Thus, there will be a distinct ‘Advance of Venus’ after 8 tropical years. Were one to express the advance in terms of actual days, it is as follows:

(13.0040012582 – 13) x 224.69526222 = 0.89906378 days

Therefore, the Venus Advance:

0.89906378 days, for every 2921.93747264 days (8 tropical years)

The Invention of a Time Cycle of 260 days

That the Mayan astronomers would have been aware of the noted advance of Venus goes without saying, and indeed, with accurate values for the orbital periods of both the Earth and Venus, they would have possessed a very accurate value also of the advance. Indeed, it is hereby suggested that it was directly due to the desire amongst the Maya to track the noted forward advance of Venus, that they invented a 260 day astronomical cycle.

Consider the Facts…

1) Accurate observations reveal that every 2921.93747264 days (8 years), Venus advances into its 14th orbit by 0.89906378 of a day, preventing a perfect 8/13 orbital re-alignment with the Earth.

2) There is a desire to track this forward advance accurately and successively.

3) But, looking at the actual numerical values, of 2921.93747264 and 0.89906378, it is readily apparent that such figures ‘lack simplicity’ and harmony.

And the Reasoned Solution…

Would it not be better if one could make use of a more basic set of time intervals to track the advance; employing some distinct measure of time expressed in a simple yet exacting number of whole days, over which the forward advance of Venus would itself correspond to a very basic time interval, such as say, a simple fraction of 1 day? INDEED IT WOULD!

And it was for this very reason, it is suggested, that the Maya deliberately INVENTED the 260 day astronomical cycle; a time interval which they themselves call a Tzolkin. The primary function of the Mayan calendar as based upon such a time cycle was therefore, to simply track the Venus advance; not in terms of a completed number of Earth tropical years, but instead, a smaller more basic cycle of exactly 260 days, wherein one finds the Venus advance to be almost an exact basic fraction of a single day:

260 / 2921.93747264 = 0.0889820546930

0.0889820546930 x 0.89906378 = 0.0800005424 days

Therefore, under the Mayan calendar the Venus Advance:

0.0800005424 days, for every 260 days (Tzolkin)

Based upon these figures, the Maya would have easily been able to keep track of the advance of Venus at regular intervals of 260 days. For upon completion of such a number of days, they will have known that the forward advance of Venus will have been almost exactly 0.08 of one solar day, or 115.2 minutes of time (0.08 x 24 x 60).

A 2000 Year Grand Conjunction Cycle of the Earth & Venus

In view of the above, it can be seen then how the 260 days of the Tzolkin cycle would allow the Maya to keep track of in a most elegant and simple manner, the ongoing orbital advance of Venus, responsible for the lack of perfection in the noted conjunction configuration based upon an exacting 13/8 ratio. Indeed, to go further still however; one must acknowledge that by way of tracking such an advance, one is able to generate and validate the physical existence of a long range Earth-Venus conjunction cycle based upon a period of almost exactly 2000 years in duration. This is brought to light when one considers carefully the mechanics of the noted forward advance of Venus.

Consider an initial starting configuration of the Earth and Venus, both in precise conjunction with the Sun. Every 8 (tropical) years the earth will return back to its original place (as of course it will indeed every year), with Venus being slightly advanced as per the noted measure of 0.89906378 days. How long then will it be before Venus advances all the way around to once more conjunct with the earth at its original starting point? The answer, to an exceptional level of accuracy, is almost precisely 2000 Earth years. A fact that is revealed with the following simple relations:

365.24218408 x 2000 = 730484.36816 days

730484.36816 / 224.69526222 = 3251.00031457174

Examined carefully, one can see that the critical ratio, manifested almost with precision, is 2000 / 3251. That is to say that after the Earth has completed 2000 orbits about the Sun, Venus will have completed 3251 orbits, and thus itself be back in conjunction with the Earth and Sun. The key point to note here is the fact that in evaluating this fraction, if one were to subtract 1 cycle from the Venus total to reduce it to 3250, then this number when set against the Earth total of 2000, is fractionally identical to a perfect 13 / 8:

3250 / (5 x 5 x 5 x 2) = 13
2000 / (5 x 5 x 5 x 2) = 8

Indeed, the extra cycle as noted is due to the very forward advance of Venus. And this is what generates the larger astronomical cycle of 2000 years*. Without the advance, the basic fraction of 13 / 8 would apply.

In Conclusion

Based upon the invention of the 260-day Mayan Calendar cycle; that they were interested in the forward advance of Venus is beyond doubt. However, in boldly going further, and certainly in light of the fact that there are many Mayan Calendar Systems in existence that track time cycles of vastly greater length – even millions of years – that they would have actively known about a 2000 year Grand Conjunction Cycle involving the Earth and Venus, due to the advance of the latter, would seem highly likely.


Proceed to Part 2: Mayan-Aztec Calendar: The Century Cycle & Earth-Venus Conjunctions


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Notes

*Of course, to those readers who know their celestial cycles, it will be apparent that in terms of such ‘lowest common multiple’ based - as opposed synodic conjunctions - a 243 to 395 Earth-Venus conjunction cycle does also exist. However, a careful review of the time measures involved in this reveals that the noted 2000 year cycle as given in this essay is vastly more refined and more accurate than the commonly recognised and far shorter 243 years. A proposed Mayan Calendar system based then upon a 2000 year cycle would seem far superior then.


Mayan Calendar Further Reading

For more insight on the matter of Venus as it relates to the Mayan Calendar cycles, one may consult a further essay by J. M. Jenkins: Toward Reconstructing the Ixil/Quiche Venus Calendar, at this link:
Mayan Calendar