Lunar Standstill Cycle
We can hypothesize a line of inquiry that might have occurred to early astronomers who were well aware that the longest cycle they tracked was the gradual north and south transit of the moon during approximately18.61 years. Although there are many orbital perturbations that can lengthen or shorten the basic cycle, individual cycles would have been easy to count and additional observations could have refined the understanding. By noting the position of the moon in the sky when eclipses occurred, the ancients were able to map the path that we know as the ecliptic. The ecliptic represents the plane of earth’s orbit about the sun. The plane of the moon’s orbit around earth is inclined 5.14 degrees to the ecliptic, causing the moon to cross the ecliptic about twice a month. As the moon’s orbit progresses north or south in relation to the ecliptic, the moon’s apparent travel is limited by standstill, when the lunar nodes (where the moon crosses the apparent path of the sun in the sky) are in the plane of the equator. Since eclipses occur when the moon and sun are in the plane of the ecliptic, eclipse positions are also nodes where the lunar orbit intersects the ecliptic. Solar eclipses can only occur during a new moon, while lunar eclipses can occur only during a full moon phase. Considering the value of predicting eclipses, the long-term cycle of the moon would be particularly important if other cycles could be measured by integer multiples of it.
Using the average value of 6,797 days for a lunar standstill cycle (Aveni 2001:347), we can factor the cycle by various values we have noticed from other observations. Length of a tropical year, lunar month, and lunar standstill cycle are each readily counted with sufficient accuracy. The eclipse year can be calculated by dividing the standstill cycle by the number of tropical years plus one.
6,797 days
= 365.2422×18.61 tropical year times the standstill cycle
= 346.62×19.61 eclipse year times number of eclipse years in the cycle
The standstill cycle of 6,797 days encompasses an integer number of potential eclipse opportunities, but more is needed to explain the structure of the calendar.
6,760 days
= 260×26 = 520×13 three eclipse half-years times thirteen
A cycle of 6,760 days seems auspicious since multiplying by 365:260 yeilds half the calendar round of 18,980 days. Counting cycles of 260 days by repetitions of 13 and 20 days may have made it possible to anticipate eclipses.
6,700 days
= 360×18.61 tun year times the standstill cycle
The tropical year of 365.2422 days divided by 360 degrees shows that multiplying by 1.01456 converts degrees to days. That conversion factor also transforms 6,797 days to 6,700 degrees. This leads very nicely to the structure of the Mesoamerican division of time, with a 360-day tun that can be counted as integer cycles without end.
Continuously counting by intervals of 260, 360, and 365 days avoids having to choose one optimum integer factoring scheme over another. That the numbers link comfortably with the lunar node, eclipse intervals, and Venus cycle is particularly convenient for linking cycles.