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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.
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