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Tikal, Guatemala

Latitude (DMS): 17° 13' 30 N
Longitude (DMS): 89° 36' 48 W
The erection of five great
pyramids, all of them more than 60 m (200 ft) in height and all of
them constructed without benefit of the wheel or crane, has to be
one of the most impressive accomplishments of any early people in
any part of the world.
The spectacular grandeur of
Tikal is in large part a result of this remarkable engineering
triumph. But what makes this accomplishment even more impressive is
that all five of these pyramids were conceived and built with such
exacting precision that they continue to function as a giant
astronomical matrix to this day!




While it may be of interest to
know that some of the pyramids of Tikal also served as the final
resting place of members of the Mayan elite, their primary function
was to serve as observation platforms for priests working with the
calendar.
Dr. Malmström discovered that pyramids had been constructed as an
astronomical matrix whose purpose it was to calibrate the most
important dates in the Maya year.

The five major pyramids of Tikal were all
constructed within a 40-year period beginning in the mid-eighth
century A.D., apparently as part of an ingeniously designed
astronomical matrix.
The sight-line between Temple I and Temple IV (the highest of the
pyramids) marks the sunset position on August 13, whereas the
sunrise position at the winter solstice is perpetuated in the
sight-tine between Temple IV and Temple III. Because Temple I and
Temple III are sited due east-west of each other, they mark sunrise
and sunset alignments at the equinoxes. Although there was no star
located directly above the earth's pole of rotation in Maya times, a
sight-line from Temple V to Temple II appears to have marked the
most westerly position of the Maya's equivalent to a polestar, Kochab.


The western horizon at Tikal as
seen from Temple I. The low, squat structure in the middle
foreground is Temple II, which serves not only as an architectural
counterweight to Temple I as seen across the plaza of Tikal but also
as a horizon marker for the enigmatic "8º west of north" orientation
when viewed from Temple V. The latter orientation was present at La
Venta about 1000 B.C., but also shows up at the Maya capital about
A.D. 800. Farther to the left, Temple III defines the equinoctial
sunset position as seen from Temple I, while the highest of the
skyscraper pyramids -- Temple IV, on the right -- fixes the sunset
position on August 13 as seen from Temple I.
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Photos of Tikal:

Location: Latitude 20°40'N Longitude 88°32'W
"El Caracol" at
Chichén Itzá has long been recognized as an astronomical observatory
whose foundations are Maya and whose subsequent embellishments are
Toltec. Perhaps the most significant alignments of this structure
are those of its front door and its principal window, located just
above it, both of which look out at the western horizon toward the
sunset position on August 13.
The Maya were expert sky-watchers, careful observers of the
motions of the celestial bodies. Proof of the Mayan fascination with
astronomy is literally carved in stone in the grand architecture at
sites such as Chichén Itzá, Uxmal, Uaxactun, Edzna, and dozens more.
At many of these sites, hieroglyphic carvings refer to celestial
bodies and cycles. Often, the buildings they adorn have been built
to align with significant cyclical astronomical events—solstices,
equinoxes, the shifting moon, or the rise of planets.
At Chichén Itzá, two structures bear witness to Mayan astronomy:
El Castillo and El Caracol. Every year, tens of thousands of
visitors flock to Chichén Itzá to see “the snake,” an apparition
made of shadows that descends the stairs at El Castillo during the
solar equinoxes each spring and fall. At El Caracol, dubbed “the
observatory,” narrow shaftlike windows frame important astronomical
events. One such window marks an appearance of Venus at a particular
point on the horizon that takes place—like clockwork—once every
eight years.

Chichén Itzá - Layout

Chichén Itzá - El Castillo (pyramid of Kukulkan)

"El Caracol"
and El Castillo at Chichén Itzá

"El Caracol" at
Chichén Itzá
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Location: 19°55' N, 98°40' W
Research by Vincent H. Malmström of Dartmouth College describes
an interesting astronomical relationship that exists between the
Three Ceremonial Rings Of Zempoala:
In the central plaza of Zempoala, just beneath the massive
pyramids that frame its northeastern corner, are three intriguing
rings of stone, each fashioned of rounded beach cobbles cemented
together to form a series of small, stepped pillars.
The largest of
the rings contains 43 of the stepped pillars, the middle- sized ring
has 28 such features, and the smallest ring numbers 13 stepped
pillars around its circumference. It would appear that the three
rings were used to calibrate different astronomical cycles, possibly
by moving a marker or an idol from one stepped pillar to the next
with each passing day (in somewhat the same way that has been
suggested for recording the passage of time at the Pyramid of the
Niches at El Tajín).

The largest ring is the most enigmatic, for no cycle based on 43
is known from Mesoamerica. However, the manner in which the ring is
constructed differs from the two smaller rings in that it is divided
at the cardinal points into quarters -- on its north side by a door
or gate opening into the circle, and on the east, south, and west by
a composite pillar having a step on each side of it. Thus, each of
the respective quarters contains 10 single-stepped pillars, all of
whose steps face in the same direction -- clockwise in the
northeasterly and southwesterly quadrants and counter-clockwise in
the southeasterly and northwesterly quadrants. (To describe it in
another way it may be said that all steps in the southern half of
the circle face north while all those in the northern half face
south.) While it is obvious that a conscious effort had been made to
distinguish the four cardinal points or quadrants through the
architectural device of alternating the orientation of their steps,
what is not so clear is whether only the single-stepped pillars in
each quadrant were meant to be counted -- yielding a total of 40 --
or whether one or more of the three composite pillars marking the
cardinal points were to have been counted as well -- yielding a
total of 43. (Naturally, if it were the steps which were being
counted, the total would be 46 instead, i.e., 40 pillars with
single-steps and three with double-steps). Lacking any indigenous
explanation for how the circle was actually employed, we can only
conclude that its Totonac builders were attempting to calibrate some
celestial cycle which lay in the range of 40 to 46 days, but what
might this have been?

The three stone rings of Zempoala [the Totonac capital, situated near the coast
of the Gulf of Mexico, about 40 km (25 mi) north of present-day Veracruz].
Inasmuch as the three rings are surmounted by 13, 28, and 40 steplike pillars,
respectively, it appears that they were used by the Totonac priests as counting
devices to keep track of eclipse cycles.

Source:
http://www.inaoep.mx/~sole/turismo/Veracruz/Zempoala.html
Of course, if it is argued that the three composite pillars, each
with their double steps, served merely as architectural markers
which set off the cardinal points, then the number that was being
reckoned was 40 rather than either 43 or 46. However, no count of 40
days is known from Mesoamerica, although it obviously could have
served to define two cycles of 20. Naturally, if it had been used as
one component in defining a "year," then we might have expected to
find some means of recording nine full circuits of the ring -- i.e.
9 x 40 = 360 -- but no such "device" is present.
If it had been used
in conjunction with the middle-sized ring, it would, of course,
define an interval of 1120 days (40 x 28), which bears no
relationship to either the sacred or secular calendar. However, had
it been used together with the smallest ring of 13 pillars, it could
have calibrated two full cycles of the sacred almanac, or 40 x 13 =
520 days. The latter, known as a double tzolkin in Mayan
terminology, equates to three eclipse half-years, and thereby
provides a useful interval in predicting eclipses. (An eclipse year
is the length of time it takes for the sun to move from one of its
intersections with the path of the moon, or node, until it returns
to the same intersection, or node. It measures 346.62 days in
length. Hence, an eclipse half-year totals 173.31 days, and three
eclipse half years add up to 519.93 days. In Mesoamerican terms,
this value would be rounded to 520 days, or the equivalent of two
rounds of the 260-day sacred almanac.)

The Largest Of "The Three Ceremonial Rings Of
Zempoala"
Image Source:
http://www.delange.org/Zempoala/Zempoala.htm

The Smaller Two Of "The Three Ceremonial Rings Of Zempoala"
The Three Rings Are In The North East Corner Of The Pyramid Complex
Image Source:
http://www.delange.org/Zempoala/Zempoala.htm
If we are correct in suggesting a lunar association for the two
smaller rings, namely 13 full moons per year with approximately 28
days between each of them, then what observable movement of the moon
has a periodicity in the range of 40 to 46 days?.
For anyone practicing a horizon-based astronomy, as did the
Mesoamericans, it would soon become apparent that the average
interval between extreme rising positions of the moon was about 13
days, although it varies in fact between 12 and 15 days. Were they
to have defined the interval between two consecutive risings at
either the moon's northern or southern extreme positions, they would
have found that it averaged between 27 and 28 days -- in other
words, one sidereal month (27.32 days). But for a people with no
appreciation of fractions, neither of these cycles was accurate
enough to pinpoint the possible occurrence of an eclipse. On the
other hand, a cycle which embraces an interval of one and a half
sidereal months (which is the length of time it would take the moon
to move, for example, between two consecutive risings at its
northern extreme and its next rising at its southern extreme)
averages out at almost exactly 41 days (27.32 + 13.66 = 40.98). To
have used such a cycle, of course, would have meant ignoring two of
the pillars in the ring -- most likely, I would imagine, the two
composite pillars marking the east and west extremes of the circle
-- while counting only the southernmost one.
How might this cycle have been useful in warning of eclipses?
Naturally, the 41-day cycle can be tested anywhere in the world, but
for this study an analysis was made of all the eclipses which were
visible at Zempoala during the years 1992 through 1997. Not too
surprisingly, the most common intervals between eclipses were found
to be 162-163 days (3 occurrences), 177-178 days (3 occurrences),
and 191-192 days (3 occurrences), and/or combinations of these
values.
To approximate the lowest of these values would obviously require
four rounds of counting, perhaps each round being calibrated by a
mneomic device which designated one of the four quadrants of the
circle. Thus, as a given count neared the end of the fourth round of
the ring, the priest would be aware that an eclipse might take
place, although he could never be entirely sure whether it actually
would take place (in the sense of being visible to him). If the
fourth round was completed without an eclipse being observed, i.e.,
taking him up through day 164, he would initiate both a second count
using the 13-pillar ring and a third count using the 28-pillar ring.
If the second count likewise was completed without an eclipse being
observed, i.e., with day 177 having been passed, he had a fall-back
position by utilizing the 28-pillar ring to bring him up to day 192.
Of course, if an eclipse did take place near the end of a 13-day
cycle, it was also quite possible that another eclipse would occur
by the time the 28-day cycle ended, in effect building an additional
15-day cycle into the equation as well. On the other hand, if day
192 also came and went without an eclipse being observed, he could
quite confidently start his initial 41-day count over again.
It is, therefore, quite possible that by using the three rings in
the manner described, the Totonac priests were able to calibrate the
movements of the moon closely enough so as to know when it might
next be "devoured" by the sun. In any event, there is every reason
to believe that the three stone rings of Zempoala afford yet another
bit of evidence testifying to the intellectual curiosity and
architectural ingenuity of the early Mesoamericans.
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