Recovering the Lost World - Appendix C: Site Alignment Calculations

Recovering the Lost World -- Jno Cook
Appendix C: Mesoamerican Ceremonial Center Alignments.

This file is linked from Chapter 18 [Olmec Alignments],
part of the site [Recovering the Lost World].

[Table of Contents]
$Revision: 21.23 $
Contents of this appendix: [Expected Dates] [Izapa] [Edzná] Olmec sites: [San Lorenzo Tenochtitlan] [La Venta] [Tres Zapotes] [Laguna De Los Cerros] [Cerro De La Mesas] [Remojadas] [Zempoala] Valley of Mexico sites: [Teotihuacan] [Tlatilco] [Tizatlan] [Cuicuilco] [Tlapacoya] [Cholula] Other: [Monte Alban]
The following data is the results of an initial investigation. The latitudes and longitudes are from [www.geonames.org]. They are shown as {degrees north latitude} -- {degrees west longitude}. Truncation by Geonames. Locations of ceremonial centers and mountains are shown as "center:" and "marker:" below.
The angle between a site and a mountain can be found from the arctangent, arctangent({difference in latitude} / {difference in longitude})/rad using Unix BC notation. These are shown below. If the latitude and longitude of the site is used as the first term of the differences, then negative angles denote 'north of east' and 'south of west.'
The dates for various angles to the setting or rising Sun at the horizon are from the DOS QBasic program [sun.bas], available locally, which can be set for different axial inclinations and latitudes. The angles shown are for sunrise, even if listed for sunsets. Sunsets will differ from sunrise by about 0.25 degrees in the part of the year closer to the equinoxes, and virtually imperceptable as the Sun nears the solstices. Documentation of 'sun.bas' in the following endnote. [note 1]
The distance between two locations can be found approximately from the latitudes and longitudes also, using the Pythagorian theorem, and using 69 miles per degree of latitude and, for central Mexico at 20 degrees latitude, an average of 65 miles per degree of longitude, as sqrt((69 * {delta latitude})^2 + (65 * {delta longitude}) ^2). Distance between a center and a mountain is shown as "remove:" below.
The line of sight distance of a mountain can be found from sqrt(2 * 4000 * h), where 'h' is the height in miles. This can be closely approximated from sqrt(2 * 4000 * (3.25 * H) / 5280), where H is the height in meters. The figure '4000' is the radius of the Earth. The figure '3.25' is the number of feet per meter. Line of sight distances between a center and a mountain is shown as "viewed:" below. The line of sight is for sea level. Intervening hills and raised terrain might block the view.

Image: Antipodal alignment example. Plan view.

I am using the term antipodal to mean a reverse alignment to a horizon location. The equivalence of angles above and below the east-west cardinal direction could be implied, and would be correct as equivalent, but makes no sense. At a few locations this is used, however. Descriptions in italics are from [en.wikipedia.org/wiki/{}].
Expected Dates

To ease the task of reading the following data, let me propose the important dates (horizon locations) which we are looking for (or which have been discovered inadvertently). The angles shown below are for a sunrise or sunset, and thus so-many degrees north or south of an east-west axis. The angles shown in the list below are for a 'average' latitude of 19 degrees. The actual angles will vary with the latitude of individual sites. These are shown for an axial inclination of 30 degrees and 23.5 degrees, since many sites use either the horizon location for a 30 degree axis or for a 23.5 degree axis, irrespective of what the current axial inclination was at the time the site was founded. The overhead (zenithal) passage of the Sun is also listed below. The dates are all "equivalent Gregorian."

For an axial inclination of 30 degrees

Start of the era after 3114 BC, August 12 -- 19.9 degrees.
Start of the era after 2349 BC, September 8 -- 6.6 degrees.
Start of the era after 1492 BC, April 19 -- 15.3 degrees.
Start of the era after 747 BC, February 28 -- 11.0 degrees.
Solstice horizon location before 685 BC -- 32.0 degrees.

flareup of Jupiter, July 9, 685 BC -- 30.4 degrees.
start of Jupiter plasmoid, July 14, 685 BC -- 29.4 degrees.
end of Jupiter plasmoid, July 26, 685 BC -- 26.6 degrees.

Zenithal passages, August 9 to 14 -- 20.3 degrees.

For an axial inclination of 23.5 degrees

Start of the era after 3114 BC, August 12 -- 14.9 degrees.
Start of the era after 2349 BC, September 8 -- 5.2 degrees.
Start of the era after 1492 BC, April 19 -- 12.0 degrees.
Start of the era after 747 BC, February 28 -- 8.6 degrees.
Solstice horizon location after 685 BC -- 25.0 degrees.

flareup of Jupiter, July 9, 685 BC -- 23.7 degrees.
start of Jupiter plasmoid, July 14, 685 BC -- 23.0 degrees.
end of Jupiter plasmoid, July 26, 685 BC -- 20.7 degrees.

Zenithal passages, July 23 to Aug 1 -- 20.3 degrees.

In addition to sunsets, the setting angles for the Pleiades after culmination are suggested for some recurring alignment angles, as follows. These are additional to sunset alignments indicating the end of the era in 2349 BC on September 8. These are discussed in the text of Chapter 18, "Olmec Alignments."

Culmination 685 BC, Oct 8 Gregorian -- 13.0 degrees <-----
Culmination 600 BC, Oct 10 Gregorian -- 13.6 degrees <-----
Culmination 200 BC, Oct 14 Gregorian -- 15.8 degrees
Culmination AD 100, Oct 18 Gregorian -- 17.1 degrees
Culmination AD 200, Oct 20 Gregorian -- 18.1 degrees <-----
Culmination AD 400, Oct 21 Gregorian -- 18.7 degrees <-----

The angle of 13 to 14 degrees and the angle of 18 to 19 degrees, correspond to the setting locations for the Pleiades at the approximate dates shown above. These show up repeatedly.

Izapa

center: Izapa (Chiapas), 14.90 -- 92.18 axis 30 degrees axis 23.5 degrees event date angle date angle ------------ ------ ------ ------ ------ start 3114 BC era Aug 11 19.87 15.55*| start 2349 BC era Sep 8 6.52 5.11 start 1492 BC era Apr 19 15.01 11.75 start 747 BC era Feb 28 -10.82 -8.47 solstice Jun 21 31.16 24.36 ? Jup flareup Jul 9 29.66 23.20 Jup plasmoid Jul 14 28.73 22.48 Jup strike Jul 25 25.94 20.30 zenithal passage Aug 21 15.47* Aug 11 15.56* * -- alignment found, (*) -- antipodal, | -- site axis Note: August 11 is used as the start of creation.

Skip to [data].
"Izapa is a very large pre-Columbian archaeological site located in the Mexican state of Chiapas; it was occupied during the Late Formative period. The site is situated on the Izapa River near the base of the Tacaná volcano, the fourth largest mountain in Mexico."
"The settlement at Izapa extended over 1.4 miles, making it the largest site in Chiapas. The site reached its apogee between 600 BC and AD 100; several archaeologists have theorized that Izapa may have been settled as early as 1500 BC, making it as old as the Olmec sites of San Lorenzo Tenochtitlán and La Venta. Izapa remained occupied through the Late Classic period. The period of Izapa's height is still unknown due to little material for carbon dating, so the issue is still widely debated."
"Izapa is located on wet and hilly land made of volcanic soil, though it is still fertile for agriculture. The weather is very hot and very wet. The area around Izapa was a major cacao producing area known as the Soconusco region, which was used by the Aztecs."
"Izapa was a large site that included lots of monuments and architecture. The site had eight groups of mounds with between 80 and 130 total mounds, which roughly only half have been restored. Izapa's architecture makes up for roughly 250,000 cubic meters when combined. The site included pyramids, sculptured plazas and squares, and possibly two ballcourts. There are two long open areas that resemble ball courts found at other Mesoamerican sites, but it is unclear if these two courts were used for the ballgame. Mound 30A was where a stepped pyramid was built. This pyramid was around ten meters high and probably used for religious and ceremonial purposes."
"Like many Mesoamerican sites, Izapa is laid out just east of true north, It is aligned with the volcano Tacaná and also seems to be situated to the December solstice horizon."
"Michael Coe describes Izapa as being a connective link between the Olmec and the early Maya. He supports his argument with the large amount of Olmec style motifs used in Izapan art, including jaguar motifs, downturned human mouths, St. Andrew's Cross, flame eyebrows, scrolling skies and clouds, and baby-face figurines. Also used to support Coe's hypothesis are elements in Maya culture thought to be derived from the Izapans, including similarities in art and architecture styles, continuity between Maya and Izapan monuments, and shared deities."
"Other archaeologists argue that there not yet enough known to support Coe and that the term 'Izapan Style' should only be used when describing art from Izapa. Virginia Smith argues that Izapan art is too unique and different in style to be the result of Olmec influence or the precursor to Maya art. Smith says that Izapan art is very site specific and did not spread far from the site. Izapan art most likely did indirectly influence Maya art, though it would just be one of the many influences on the Maya."
"Izapa is also included in the debate of the origin of the 260-day calendar. The calendar was originally thought to be a Maya invention, but recently it has been hypothesized that calendar originated in Izapa. This hypothesis is supported by the fact that Izapa fits the geological and historical conditions better than the previous place thought to be the origin."
"Izapa gains its fame through its art style. The art found at the site includes sculptures of stelae and also altars that look like frogs. The stelae and frog altars generally went together, the toads symbolized rain. Much of the art of Izapa that features people includes large groups of people, not individuals. There are common characteristics of Izapan art, such as winged objects, long-lipped gods much like the Chaac of the Maya, Olmec-like swirling sky and clouds, feline mouth used as frame, representation of animals (crocodile, jaguar, frog, fish, birds), overlapping, and lack of dates."
"The sheer number of sculptures outweighs that [of] any contemporaneous site. Garth Norman has counted 89 stelae, 61 altars, 3 thrones, and 68 'miscellaneous monuments' at Izapa. In contrast to the ruler-oriented sculpture of the Epi-Olmec culture across the Isthmus of Tehuantepec, Izapan sculpture has a mythological and religious subject matter, and is ceremonial and frequently narrative in nature."
"Izapa Stela 1 features a long lipped deity, which Coe describes as the early version of Maya god of lightning and rain, Chaac. In Stela I, the god is walking on water while collecting fish into a basket and also wearing a basket of water on his back.
"Izapa Stela 2, like Stela 25, has been linked to the battle of the Maya Hero Twins against Vucub Caquix, a powerful ruling bird-demon of the Maya underworld, also known as Seven Macaw."
"Izapa Stela 3 shows a deity wielding a club. This deity's leg turns into a serpent while twisting around his body. This could be an early form of the Maya God K, who carried a staff."
"Izapa Stela 4 depicts a bird dance, which has a king being transformed into a bird. The scene is most likely connected with the Principle Bird Deity. This transformation could symbolize shamanism and ecstasy, meaning the shaman-ruler used hallucinogens to journey to another world. The type of political system that was in place at Izapa is still unknown, though Stela 4 could suggest that a shaman was in charge. This shaman-ruler would serve the role of both the political and religious leader."
"Izapa Stela 5 presents perhaps the most complex relief at Izapa. Central to the image is a large tree, which is surrounded by perhaps a dozen human figures and scores of other images. The complexity of the imagery has led some researchers, particularly Mormon and 'out of Africa' theorists, to view Stela 5 as support for their theories."
"Izapa Stela 8 shows a ruler seated on a throne. The scene shown on Stela 8 is often compared to Throne 1, which was located by the central pillar of Izapa. Stela 8 may be showing a ruler seated atop Throne 1."
"Izapa Stela 21 is a rare depiction of violence involving deities. The Stela illustrates a warrior holding the head of a decapitated god."
"Izapa Stela 25 possibly contains a scene from the Popol Vuh. The image depicted on Stela 25 is most likely the Maya Hero Twins shooting a perched Principle Bird Deity with a blowgun. This scene is also shown on the Maya pot called the "Blowgunner Pot". It is also suggested that Stela 25 could be seen as a map of the night sky, which was used to tell the story of the Hero Twins shooting the bird deity." --Wikipedia.org
I have added Volcán de Agua in Guatemala which is 3760 meters high, and can clearly be seen from Izapa. Izapa is located at the base of the volcano Tacaná. But the site axis (16 degrees e of n, thus 74 degrees n of e) does not point to Tacaná (69.67 degrees n of e) except as 'sort of.'
Additionally I have added an alignment corresponding to a site axis which falls 16 degrees east of north. At right angles this points to 16 degrees north of west.

Izapa (Chiapas), 14.90 -- 92.18 marker: Volcá Tajumulco, 15.034 -- 91.903, 4220 meter remove: sqrt((69*(14.9-15.034))^2+(65*(92.18-91.9))^2) = 20.4 mi a((14.90-15.034)/(92.18-91.9))/rad = -25.57 degrees n of e marker: Volcán Tacaná (Mexico), 15.116 -- 92.1 a((14.90-15.116)/(92.18-92.1))/rad = -69.67 degrees (out of limits) marker: Volcán de Agua (Guatemala), 14.466 -- 90.742, 5280 meters remove: sqrt((69*(14.9-14.466))^2+(65*(92.18-90.742))^2) = 98 mi viewed: sqrt(2*4000*(3.25*3760)/5280) = 136 mi a((14.90-14.466)/(92.18-90.742))/rad = 16.79 degrees s of e marker: site axis, 16 degrees e of n At right angle this equals 16 degrees n of w Note: 'a' is the arctangent, here and in following tables

Image: Izapa alignments. Plan view.
The Sun passes overhead on August 11 (89.87 degrees above the horizon), rising at 15.55 degrees north of east. Malmström uses a latitude of 14.8 degrees north. This results in an alignment corresponding to August 12, where I have August 11.
The alignment at right angles to the site axis points also to a sunset on August 11, at 16.0 degrees (15.56 n of w).
There is no solstitual alignment. The volcano Tajumulco is held to represent a solsticial alignment by Malmstrom (and others), but an alignment of 25.57 degrees n of e, is not close to the solstice sunrise which happens at 24.36 deggrees n of e. It is off by a degree, which at the time of a solstice, causes an error of 15 days.
I should note, however, that there is no reliable latitude and longitude for Izapa, and changes of a few percent will change the angles to some of the nearby mountains considerably. Malmstrom used a latitude of 14.8 which is seven miles south of my use of 14.9 degrees.

Edzná

center: Edzna (Campeche), 19.583 -- 90.25 The long axis of the site is aligned 15.5 degrees east of north. The Sun passes over the site on July 25th.

Image: Edzna alignments. Plan view.

The 15.5 degree alignment is identical to the alignment of the long axis of Teotihuacan in the valley of Mexico and results in sight line between three structures at a right angle to this, which represents a sunset on August 12, 3114 BC (15.6 degrees north of west).
The overhead passage of the Sun is elevated at an angle of 89.96 degrees on July 25th, setting at 20.85 degrees n of w. New Year's Day is July 26th.
Malmström lists an additional sightline made at 30 degrees north of west. He identifies this as the most northerly displacement of the Moon. This is correct, for at an 'axial inclination' of 28.5 degrees, consisting of 23.5 degrees for the Earth plus 5 degrees more for the Moon, this places the angle to a possible horizon location of the Moon at 30.42 degrees n of w.

San Lorenzo Tenochtitlan

San Lorenzo is an extensive site. I have checked data using the latitude/longitude for three included sites, shown below, but am only showing the results for the village of Tenochtitlan which seems to strike an average.
The first three sites are within 8.3 miles of each other; Potrero Nuevo is 10 miles further south. Tenochtitlan is a couple of miles north of the archaeological site, thus about 0.03 degrees of latitude different. The following only considers the location of Tenochtitlan.

center: San Lorenzo, 17.666 -- 94.833 Tenochtitlan, 17.758 -- 94.75 <--- El Azuzul, 17.733 -- 94.8 Potrero Nuevo, 17.783 -- 94.58 axis 30 degrees axis 23.5 degrees event date angle date angle ------------ ------ ------ ------ ------ start 3114 era Aug 12 19.75 15.46 start 2349 BC era Sep 8 6.62 5.18 start 1492 BC era Apr 19 15.23** 11.93 start 747 BC era Feb 28 -10.98 -8.60 solstice Jun 21 31.67 24.75 Jup flareup Jul 9 30.14 23.56 Jup plasmoid Jul 14 29.19 22.83 Jup strike Jul 25 26.35 20.16 zenithal passage Aug 15 18.45* Aug 2 18.54* * -- alignment found

Skip to [data]
"San Lorenzo Tenochtitlán (or San Lorenzo) is the collective name for three related archaeological sites -- San Lorenzo, Tenochtitlán, and Potrero Nuevo -- located in the southeast portion of the Mexican state of Veracruz. From 1200 BC to 900 BC, it was the major center of Olmec culture. San Lorenzo Tenochtitlán is best known today for the colossal stone heads unearthed there, the greatest of which weigh 20 tons or more and are 3 meters high."
"The earliest evidence for Olmec culture is found at nearby El Manati, a sacrificial bog with artifacts dating to 1600 BCE or earlier. Sedentary agriculturalists had lived in the area for centuries before San Lorenzo developed into a regional center."
"San Lorenzo was the largest city in Mesoamerica from roughly 1200 BC to 900 BC, at which time it had begun to be overtaken by the Olmec center of La Venta. By 800 BC, there was little or no population, although there was an important recolonization of the San Lorenzo plateau from 600 to 400 BC and again from circa AD 800 to 1000."
"In contrast to La Venta's swamp-like environs, San Lorenzo was situated in the midst of a large agricultural area. San Lorenzo seems to have been largely a ceremonial site, a town without city walls, centered in the midst of a widespread medium-to-large agricultural population. The ceremonial center and attendant buildings could have housed 5,500 while the entire area, including hinterlands, could have reached 13,000."
"Although the original site was at a higher elevation than the surrounding countryside, it was further modified through extensive filling and leveling; by one estimate half-a-million to 2 million cubic meters of earthen fill were needed, moved by the basketload."
"San Lorenzo also boasted an elaborate drainage system which used buried, covered, channeled stones as a type of 'pipe'. Some researchers have inferred that the purpose of this system was not only to provide drinking water for the population but for ritual purposes as well, and that the rulership was 'intimately linked to the figure of a patron water supernatural.'"
"Matthew Stirling was the first to begin excavations on the site after a visit in 1938. Between 1946 and 1970, four archaeological projects were undertaken, with a lull until 1990. The archaeology work recommenced in 1990, putting emphasis on the establishment pattern of community and regional levels."
"The original Olmec name of the area, like nearly all of the Olmec language, is unknown. The name San Lorenzo Tenochtitlán was coined by Stirling in 1955, taken from the nearby present-day villages, and refers to the entire complex of sites." --Wikipedia.org

San Lorenzo Tenochtitlan, 17.758 -- 94.75 valley mountains..... marker: Nauhcampatepetl, 19.483 -- 97.133, 4282 meters remove: sqrt((69*(17.758-19.483))^2+(65*(94.75-97.133))^2) = 195 mi viewed: sqrt(2*4000*(3.25*4282)/5280) = 145 mi a((17.758-19.483)/(94.75-97.133))/rad = 35.89 degrees (out of limits) marker: Popocatepetl, 19.033 -- 98.633, 5452 meters remove: sqrt((69*(17.758-19.033))^2+(65*(94.75-98.633))^2) = 267 mi viewed: sqrt(2*4000*(3.25*5452)/5280) = 163 mi a((17.758-19.033)/(94.75-98.633))/rad = 18.17 degrees n of w marker: Citlaltepetl (Pico de Orizaba), 19.016 -- 97.266, 5636 meters remove: sqrt((69*(17.758-19.016))^2+(65*(94.75-97.266))^2) = 185 mi viewed: sqrt(2*4000*(3.25*5636)/5280) = 166 mi a((17.758-19.016)/(94.75-97.266))/rad = 26.56 degrees n of w marker: Ixtaccihuatl, 19.183 -- 98.65, 5230 meters remove: sqrt((69*(17.758-19.183))^2+(65*(94.75-98.65))^2) = 271 mi viewed: sqrt(2*4000*(3.25*5230)/5280) = 160 miles a((17.758-19.183)/(94.75-98.65))/rad = 20.07 degrees marker: Volcan La Malinche, 19.233 -- 98.033, 4462 meters remove: sqrt((69*(17.758-19.233))^2+(65*(94.75-98.033))^2) = 236 mi viewed: sqrt(2*4000*(3.25*4462)/5280) = 148 mi a((17.758-19.233)/(94.75-98.033))/rad = 24.19 degrees coast mountains.... marker: Volcan San Martin Pajapan, 18.316 -- 94.8, 1219 meters remove: sqrt((69*(17.758-18.316))^2+(65*(94.75-94.8))^2) = 38 mi viewed: sqrt(2*4000*(3.25*1219)/5280) = 77 mi a((17.758-18.316)/(94.75-94.8))/rad = 84.8 degrees (out of limits) marker: Volcan San Martin Tuxtla, 18.55 -- 95.2, 1650 meters remove: sqrt((69*(17.758-18.55))^2+(65*(94.75-95.2))^2) = 62 mi viewed: sqrt(2*4000*(3.25*1659)/5280) = 90 mi a((17.758-18.55)/(94.75-95.2))/rad = 60.4 degrees (out of limits) marker: Cerro Santa Martha (Veracruz), 18.35 -- 94.855, 1680 meters remove: sqrt((69*(17.758-18.35))^2+(65*(94.75-94.855))^2) = 41 mi viewed: sqrt(2*4000*(3.25*1680)/5280) = 91 mi a((17.758-18.35)/(94.75-94.855))/rad = 79.9 degrees (out of limits) marker: Cerro San Martin (Queretaro), 20.745 -- 99.970 remove: sqrt((69*(17.758-20.745))^2+(65*(94.75-99.970))^2) = 397 mi viewed: ?? a((17.758-20.745)/(94.75-99.970))/rad = 29.78 degrees marker: El Chichon (Chiapas), 17.35 -- 93.233, 1060 meters remove: sqrt((69*(17.758-17.35))^2+(65*(94.75-93.233))^2) = 102 mi viewed: sqrt(2*4000*(3.25*1060)/5280) = 72 mi a((17.758-17.35)/(94.75-93.233))/rad = 15.05 degrees s of e marker: Cerro Zempoaltepec, 17.42 -- 95.98, 3396 meters remove: sqrt((69*(17.758-17.42))^2+(65*(94.75-95.98))^2) = 83 mi viewed: sqrt(2*4000*(3.25*3396)/5280) = 129 miles a((17.758-17.42)/(94.75-95.98))/rad = -15.36 degrees s of w

Image: San Lorenzo alignments. Plan view.

San Lorenzo site identity...

18.177 degrees n of w -- At 5452 meters, Popocatepetl is the 2nd highest mountain in Mexico, but cannot be seen from San Lorenzo, since it is 267 miles away. Under the condition of a 30 degree axial inclination of the polar axis, this mountain would signal the day (sunset) that the Sun passes directly overhead at San Lorenzo (Tenochtitlan), on August 15 (setting at 18.45 degrees n of w).
After 685 BC, the Sun would pass directly over San Lorenzo, on August 2, 13 days earlier, setting at 18.54 degrees north of west. The horizon location thus stayed nearly the same.
San Lorenzo era marker...

15.05 degrees s of e -- El Chichon is 1060 meters high. This mountain could not be seen. Before 685, with the Earth's axis at 30 degrees, this angle defined a sunrise in winter (sunrise at 15.23 degrees south of east), but in an antipodal direction it is a spring sunset on April 19th, the start of the era after 1492 BC.
15.36 degrees s of w -- At 3396 meters Cerro Zempoaltepec is the 11th highest mountain in Mexico. It can be seen from any of the San Lorenzo locations. With the Earth's axis at 30 degrees, the angle defined a winter sunset. In the antipodal direction it marked a spring sunrise, which matches the sunrise angle made by El Chichon, April 19.
Under the condition of having the axis of the Earth was at 30 degrees, the mountains El Chichon and Cerro Zempoaltepec would triangulate San Lorenzo to a Gregorian equivalent calendar date of April 19th (15.23 degrees).
San Lorenzo additional notes...

The two alignments of 15 degrees could suggested to represent alignments for a sunrise and sunset for August 12 in the current era. That is just unlikely.

La Venta

center: La Venta, 18.125 -- 93.99 The axis of the site is aligned 8.0 degrees west of north. axis 30 degrees axis 23.5 degrees event date angle date angle ------------ ------ ------ ------ ------ start 3114 BC era Aug 13 19.36* ? 15.49 start 2349 BC era Sep 8 6.63 5.20 start 1492 BC era Apr 19 15.27** 11.95 start 747 BC era Feb 28 -11.00(*) -8.61* solstice Jun 21 31.74 24.81 Jup flareup Jul 9 30.21 23.62* Jup plasmoid Jul 14 29.26 22.88 Jup strike Jul 25 26.41 20.66 zenithal passage Aug 14 18.93* Jul 31 19.13*(*) Pleiades setting (actual) -- Oct 8 12.79* 685 BC Oct 8 13.27* 685 BC * -- alignment found; (*) -- antipodal

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"La Venta is a pre-Columbian archaeological site of the Olmec civilization located in the present-day Mexican state of Tabasco."
"The Olmec civilization was the first civilization of the Americas. Rising from the sedentary agriculturalists of the Gulf Lowlands as early as 1600 BC, the Olmecs held sway in the Olmec heartland, an area on the southern Gulf of Mexico coastal plain, in Veracruz and Tabasco."
"Roughly 125 miles long and 50 miles wide (200 by 80 km), with the Coatzalcoalcos River system running through the middle, the heartland is home to the major Olmec sites of La Venta, San Lorenzo Tenochtitlán, Laguna de los Cerros, and Tres Zapotes."
"By no later than 1200 BC, San Lorenzo had emerged as the most prominent Olmec center. While a layer of occupation at La Venta dates to 1200 BC, La Venta did not reach its apogee until the decline of San Lorenzo, after 900 BC. After 500 years of pre-eminence, La Venta was all but abandoned by the beginning of the fourth century BC."
"Located on an island in a coastal swamp overlooking the then-active Río Palma, La Venta probably controlled a region between the Mezcalapa and Coatzacoalcos rivers. The site itself is about 16 km (10 miles) inland with the island consisting of slightly more than 2 square miles (5 sq km) of dry land. The main part of the site is a complex of clay constructions stretched out for 20 km (12 miles) in a north-south direction, although the site is oriented 8 degrees west of north. The urbanized zone may have covered an area as large of 2 sq km."
"Unlike later Maya or Aztec cities, La Venta was built from earth and clay -- there was little locally abundant stone for the construction. Large basalt stones were brought in from the Tuxtla mountains, but these were used nearly exclusively for monuments including the colossal heads, the 'altars', and various stelae. For example, the basalt columns that surround Complex A were quarried from Punta Roca Partida, on the Gulf coast north of the San Andres Tuxtla volcano."
"Today, the entire southern end of the site is covered by a petroleum refinery and has been largely demolished, making excavations difficult or impossible. Many of the site's monuments are now on display in the archaeological museum and park in the city of Villahermosa, Tabasco."
"(Archaeological site plan for La Venta.) Notice how the site is aligned slightly west -- 8 degrees west -- of north. Several Mesoamerican sites have this alignment, including San Jose Mogote."
"La Venta was a civic and ceremonial center. While it may have included as-yet-undiscovered royal residences, habitation for the non-regal elite and the commoners were located at outlying sites such as San Andrés."
"Instead of dwellings, La Venta is dominated by a royal/sacred area (Complex A), the Great Pyramid, and the large plaza to their south."
"As a ceremonial center, La Venta contains an elaborate series of buried offerings and tombs, as well as monumental sculptures. These stone monuments, stelae, and 'altars' were carefully distributed amongst the mounds and platforms. The mounds and platforms were built largely from local sands and clays. It is assumed that many of these platforms were once topped with wooden structures, which have long since disappeared."
"One of the earliest pyramids known in Mesoamerica, the Great Pyramid, is 110 ft (33 m) high and contains an estimated 100,000 cubic meters of earth fill. The current conical shape of the pyramid was once thought to represent nearby volcanoes or mountains, but recent work by Rebecca Gonzalez-Lauck has shown that the pyramid was in fact a rectangular pyramid with stepped sides and inset corners, and the current shape is most likely due to 2500 years of erosion. The pyramid itself has never been excavated, but a magnetometer survey in 1967 found an anomaly high on the south side of the pyramid. Speculation ranges from a section of burned clay to a cache of buried offerings to a tomb."
"Complex A is a mound and plaza group located just to the north of the Great Pyramid. Surrounded by a series of basalt columns, which likely restricted access to the elite, it was erected in a period of 4 construction phases that span over 4 centuries. Beneath the mounds and plazas were found a vast array of offerings and other buried objects, more than 50 separate caches by one count, including buried jade celts, polished mirrors made of iron-ores, and five large 'Massive Offerings' of serpentine blocks. It is estimated that Massive Offering 3 contains 50 tons of carefully finished serpentine blocks, covered by 4,000 tons of clay fill."
"Also unearthed in Complex A were 3 rectangular mosaics (also known as 'Pavements') each roughly 15 ft x 20 ft and each consisting of up to 485 blocks of serpentine. These blocks were arranged horizontally to form what has been variously interpreted as an ornate Olmec bar-and-four-dots motif, the Olmec Dragon, a very abstract jaguar mask, a cosmogram, or a symbolic map of La Venta and environs. Not intended for viewing, soon after completion these pavements were covered over with colored clay and then many feet of earth."
"Five formal tombs were discovered within Complex A. Diehl states that these tombs 'are so elaborate and so integrated to the architecture that it seems clear that Complex A really was a mortuary complex dedicated to the spirits of deceased rulers.'"
"Other notable artifacts within Complex A include:
Monument 19. This relief sculpture is the earliest known example of the feathered serpent in Mesoamerica.
Offering 4. Sixteen figurines and six celts form a strange tableau."
South of the Great Pyramid lies Complex B. Whereas Complex A was apparently restricted to the elite, the plaza of Complex B seems to be built specifically for large public gatherings. This plaza is just south of the Great Pyramid, east of the Complex B platforms, and west of the huge raised platform referred to as the Stirling Acropolis. This plaza is nearly 400 metres (yards) long and over 100 metres (yards) wide. A small platform is situated in the center of the plaza."
"This layout has led researchers to propose that the platforms surrounding the plaza functioned as stages where ritual drama was enacted for viewers within the plaza. These rituals may well have been related to the 'altars,' monuments, and the stelae surrounding and within the plaza. These monuments, including Colossal Head 1, were of such a large size and were placed in such a position that they could convey their messages to many viewers at once."
"The arrangement of the mounds, platforms, complexes, and monumental artifacts at La Venta created a unique civil and ceremonial center that, in the words of Rebecca Gonzalez-Lauck, constitutes 'one of the earliest examples of large-scale ideological communications through the interaction of architecture and sculpture.'"
"Certainly the most famous of the La Venta monumental artifacts are the four colossal heads. Seventeen colossal heads have been unearthed in the Olmec area, four of them at La Venta, officially named Monuments 1 through 4."
"Three of the heads -- Monuments 2, 3, & 4 -- were found roughly 150 meters north of Complex A, which is itself just north of the Great Pyramid. These heads were in a slightly irregular row, facing north. The other colossal head -- Monument 1 (shown at left) -- is a few dozen meters south of the Great Pyramid."
The La Venta heads are thought to have been carved by 700 BC, but possibly as early as 850 BCE, while the San Lorenzo heads are credited to an earlier period. The colossal heads can measure up to 9 ft 4 in. in height and weigh several tons. The sheer size of the stones causes a great deal of speculation on how the Olmecs were able to move them. The major basalt quarry for the colossal heads at La Venta was found at Cerro Cintepec in the Tuxtla Mountains, over 80 km away."
"Each of the heads wears headgear reminiscent of 1920s-style American football helmets, although each is unique in its decoration. These helmets probably served as protection in war and in the ceremonial Mesoamerican ballgame played throughout Mesoamerica. The consensus is that the heads likely represent mighty Olmec rulers."
"The flat-faced, thick-lipped characteristics of the heads have caused some debate due to their apparent resemblance to African facial characteristics. Based on this comparison, some have insisted that the Olmecs were Africans who had emigrated to the New World. However, archaeologists and other Mesoamerican scholars now reject this view, and offer other possible explanations for the facial features of the colossal heads. One of this is that the heads were carved this way due to the shallow space allowed on the basalt boulders, and do not represent the actual appearance of the Olmec people. Others note that in addition to the broad noses and thick lips, the heads have the Asian eye-fold, and that all these characteristics can still be found in modern Mesoamerican Indians. To support this, in the 1940s artist/art historian Miguel Covarrubias published a series of photos of Olmec artworks and of the faces of modern Mexican Indians with very similar facial characteristics."
"(Altar 4 at La Venta.) Note the rope that winds along the ground, held by the figure. Note also the eyes and the fangs on the cornice above the figure, implying that the figure is seated in that creature's mouth."
"Seven basalt 'altars' were found at La Venta, the most familiar being Altar 4 and Altar 5. These altars, roughly 2 meters high and twice as wide, both feature an elaborately dressed and sculpted figure on the center front."
"The figure on Altar 4 is sitting inside what appears to be a cave or the mouth of a fantastic creature, holding a rope which wraps around the base of the altar to his right and left. On the left side, the rope is connected to a seated bas-relief figure. The right side is eroded away but is thought to be similar to the scene on the right."
"The consensus today is that these 'altars' are thrones on which the Olmec rulers were seated during important rituals or ceremonies. This leads many researchers to interpret the figure at the front of Altar 4 as a ruler, who is contacting or being helped by his ancestors, the figures on either side of the altar. Alternatively, some believe the side figures to be bound captives. (Adams finds that, 'examined carefully, these two people seem to be male and female and therefore are the parents of the ruler, symbolically attached to him by umblical cords'.)"
"Altar 5 faces Altar 4 across Structure D-8 (one of the dozens of mounds at La Venta, the remains of platforms). Altar 5 is similar in design and size to Altar 4, except that the central figure holds an inert, perhaps dead, were-jaguar baby. The left side of Altar 5 features bas-reliefs of humans holding quite lively were-jaguar babies. Like the Altar 4, the right side of Altar 5 has been defaced."
"Some have seen child sacrifice echoed in the limp were-jaguar baby on the front of Altar 5. Others, however, view the tableau as a myth of human emergence or as story of a spiritual journey."
"Although less striking and displaying a lesser degree of craftmanship, Altars 2 and 3 are similar to Altars 4 and 5. They each show a central figure, one with a baby and one without, and they sit facing each other on the southern edge of the Great Pyramid."
"Little is known about the structure of La Venta society or about the Olmec state. From the size and diversity of La Venta, it is assumed that the society consisted of an elite class, a class of artisans, and a large pool of laborers and farmers who supported these classes."
"It has been estimated that La Venta would need to be supported by a population of at least 18,000 people during its principal occupation."
"Frans Blom and Oliver La Farge made the first detailed descriptions of La Venta during their 1925 expedition, sponsored by Tulane University."
"La Venta was first excavated by Matthew Stirling between 1941 and 1943, with several subsequent excavations following through the 1960s. Stirling is sometimes credited with identifying the Olmec civilization; although some Olmec sites and monuments had been known earlier, it was Stirling's work that put the Olmec culture into context."
"Rebecca Gonzalez-Lauck led an INAH (Instituto Nacional de Antropología e Historia) team on digs here in the 1980s." -- Wikipedia.org

La Venta, 18.125 -- 93.99 valley mountains..... marker: Nauhcampatepetl, 19.483 -- 97.133, 4282 meters remove: sqrt((69*(18.125-19.483))^2+(65*(93.99-97.133))^2) = 224 mi viewed: sqrt(2*4000*(3.25*4282)/5280) = 145 mi a((18.125-19.483)/(93.99-97.133))/rad = 23.36 degrees s of w marker: Popocatepetl, 19.033 -- 98.633, 5452 meters remove: sqrt((69*(18.125-19.033))^2+(65*(93.99-98.633))^2) = 308 mi viewed: sqrt(2*4000*(3.25*5452)/5280) = 163 mi a((18.125-19.033)/(93.99-98.633))/rad = 11.06 degrees s of w marker: Citlaltepetl (Pico de Orizaba), 19.0164 -- 97.2667, 5636 meters remove: sqrt((69*(18.125-19.0164))^2+(65*(93.99-97.2667))^2) = 221 mi viewed: sqrt(2*4000*(3.25*5636)/5280) = 166 mi a((18.125-19.0164)/(93.99-97.2667))/rad = 15.22 degrees n of w marker: Ixtaccihuatl, 19.183 -- 98.65, 5230 meters remove: sqrt((69*(18.125-19.183))^2+(65*(93.99-98.65))^2) = 311 mi viewed: sqrt(2*4000*(3.25*5230)/5280) = 160 miles a((18.125-19.183)/(93.99-98.65))/rad = 12.79 degrees marker: Volcan La Malinche, 19.233 -- 98.033, 4462 meters remove: sqrt((69*(18.125-19.233))^2+(65*(93.99-98.033))^2) = 273 mi viewed: sqrt(2*4000*(3.25*4462)/5280) = 148 mi a((18.125-19.233)/(93.99-98.033))/rad = 15.32 degrees n of w coast mountains..... marker: Volcan San Martin Pajapan, 18.316 -- 94.8, 1219 meters remove: sqrt((69*(18.125-18.316))^2+(65*(93.99-94.8))^2) = 54 mi viewed: sqrt(2*4000*(3.25*1219)/5280) = 77 mi a((18.125-18.316)/(93.99-94.8))/rad = 13.27 degrees n of w marker: Volcan San Martin Tuxtla, 18.55 -- 95.2, 1650 meters remove: sqrt((69*(18.125-18.55))^2+(65*(93.99-95.2))^2) = 84 mi viewed: sqrt(2*4000*(3.25*1650)/5280) = 90 mi a((18.125-18.55)/(93.99-95.2))/rad = 19.35 degrees n of w marker: Cerro Santa Martha (Veracruz), 18.35 -- 94.855, 1680 meter remove: sqrt((69*(18.125-18.35))^2+(65*(93.99-94.855))^2) = 58 mi viewed: sqrt(2*4000*(3.25*1680)/5280) = 91 mi a((18.125-18.35)/(93.99-94.855))/rad = 14.58 degrees n of w marker: Cerro San Martin (Queretaro), 20.745 -- 99.970 remove: sqrt((69*(18.125-20.745))^2+(65*(93.99-99.970))^2) = 428 mi viewed: ?? - a((18.125-20.745)/(93.99-99.970))/rad = 23.65 degrees n of w marker: El Chichon (Chiapas), 17.35 -- 93.233, 1060 meters remove: sqrt((69*(18.125-17.35))^2+(65*(93.99-93.233))^2) = 72 mi viewed: sqrt(2*4000*(3.25*1060)/5280) = 72 mi a((18.125-17.35)/(93.99-93.233))/rad = 45.67 degrees (out of limit) marker: Cerro Zempoaltepec, 17.419 -- 95.983, 3396 meter remove: sqrt((69*(18.125-17.419))^2+(65*(93.99-95.983))^2) = 138 mi viewed: sqrt(2*4000*(3.25*3396)/5280) = 129 miles a((18.125-17.419)/(93.99-95.983))/rad = 19.50 degrees s of w

Image: La Venta alignments. Plan view.

La Venta site identity...

19.35 degrees north of west -- The alignment with Volcan San Martin Tuxtla defines the sunset after the overhead passage of the Sun at La Venta on August 14 (18.93 degrees), when the axial inclination was 30 degrees, and on July 31 (19.13 degrees), in the current era with a 23.5 degree axial inclination.
19.50 degrees s of w -- This angle to Cerro Zempoaltepec defines the same day as above, but as an antipodal sunrise.
La Venta era marker...

Both of the angles shown above locate a sunset on August 13 before 685 BC (19.36 degrees n of w). Thus at this site an era ending marker is combined with a zenithal passage of the Sun. The site of Izapa will accomplish the same, but for the date of August 11, and conformed to the current axial inclination of the Earth.
15.22 degrees n of w -- This angle to Citlaltepetl defines a sunset on April 19 (15.27 degrees), for a 30 degree axial inclination. Citlaltepetl is the highest peak in Mexico. (See notes, below.)
15.32 degrees n of w -- This angle to Volcan La Malinche defines the same sunset on April 19 as above, for a 30 degree axial inclination. Volcan La Malinche in direct line with Citlaltepetl. (See notes, below.)
11.06 degrees s of w -- The angle to Popocatepetl defines a sunrise for the day of February 28 (11.00 degrees), as the start of the era after 747 BC, but selected while the axial inclination was still at 30 degrees, that is, before 685 BC.
Site axis at 8 degrees w of n -- The central axis of the present monuments at La Venta determine an orientation for the date of February 28th (8.61 degrees), based on the current axial inclination of 23.5 degrees. Actually, the following day, March 1 might be a better fit (8.21 degrees).
23.65 degrees north of west -- The angle with Cerro San Martin (Queretaro) defines a summer sunset on July 9th (23.62 degrees) in the current era. This may be a coincidence.
Setting of the Pleiades -- There are two coaxial alignments for the setting of the Pleiades in 685 to 600 BC to the mountains Ixtaccihuatl (12.79 degrees) and Volcan San Martin Pajapan (13.27 degrees).
La Venta notes...

The site location was likely established after 747 BC, as shown by the fact that there is an alignment for February 28. This was selected while the axial inclination was still at 30 degrees. This suggests that the 15.22 degree alignment (a sunset n of w) with Citlaltepetl (and Volcan La Malinche), defines an antipodal sunrise (s of e) for the date of April 19 (of 1492 BC).
Thus the 1492 BC 'era ending' date of San Lorenzo was duplicated at La Venta, and the era ending date for 3114 BC and 747 BC were added. These are site location alignments which could not be altered. When the Earth's axis changed in 685 BC, a new alignment for the just previous era ending was established by selecting a reconstruction site axis as 8 degrees west of north.
Coincidentally, the two prior alignments at approximately 15.27 degrees, which had pointed to the 1492 BC era ending date of April 19th, now could be assigned to point to the 3147 BC era ending date of August 13th at 15.49 degrees north of west.
Malmström, in "Archaeoastronomy in the Americas" (Ray Williamson, ed 1981), shows the "Stirling compound," located adjacent (east) to the main structures (Compounds A, B, and C) at La Venta as aligned 15 degrees east of north. I do not know the date on the Stirling compound, but the alignment could point directly to a northwest sunset (15.49 degrees) for August 12 of the current era. Malmström wanted to use this to establish a "August 13" alignment. This is unlikely because the "Stirling Compound" is older that the remainder of the site, and thus built before 747 BC and before the invention of the Long Count. From site plans I have seen, the Stirling compound looks to have one edge aligned at about 20 degrees west of north, and another at 28 degrees east of north.

Tres Zapotes

center: Tres Zapotes, 18.4667 -- 95.4333 axis 30 degrees axis 23.5 degrees event date angle date angle ------------ ------ ------ ------ ------ start 3114 BC era Aug 12 19.83* 15.52 start 2349 BC era Sep 8 6.65 5.21 start 1492 BC era Apr 19 15.30 11.98 ? start 747 BC era Feb 28 -11.02(*) -8.63 solstice Jun 21 31.81 24.86 Jup flareup Jul 9 30.28* 23.67 Jup plasmoid Jul 14 29.32 22.92 Jup strike Jul 25 26.47*(*) 20.70 zenithal passage Aug 13 19.40* Jul 30 19.44* Pleiades setting (actual) -- Oct 8 12.56* 685 BC Oct 8 13.39(*) 685 BC Oct 16 16.68* 100 BC Oct 16 16.43* 100 BC * -- alignment found; (*) -- antipodal

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Tres Zapotes was founded some time in the centuries well before 1000 BC, Tres Zapotes became a regional center in 900 BC to 800 BC, coinciding with the decline of San Lorenzo Tenochtitlan. Abandoned by AD 900.
"Tres Zapotes is located in the south-central Gulf Lowlands of Mexico in the Papaloapan river plain. Tres Zapotes is sometimes referred to as the third major Olmec capital."
"The 2000-year existence of Tres Zapotes as a cultural center is unusual, if not unique, in Mesoamerica. The nearby small site of Rancho la Cobata may have functioned as a monument workshop -- most of the basalt stonework at Tres Zapotes was crafted from the colossal spheroid smooth-faced boulders. Some of these boulders are more than 3 meters in diameter."
"It is thought that the two colossal heads date from this period, plus one at Rancho la Cobata. The colossal heads are of local style of dress and sculpture, differing from that of San Lorenzo and La Venta. Most of the monumental sculpture at Tres Zapotes is post-Olmec, dating from after 400 BC." -- Wikipedia.org .

Tres Zapotes, 18.4667 -- 95.4333 ... valley mountains marker: Nauhcampatepetl, 19.483 -- 97.133, 4282 meters remove: sqrt((69*(18.4667-19.483))^2+(65*(95.433-97.133))^2) = 130 mi viewed: sqrt(2*4000*(3.25*4282)/5280) = 145 mi a((18.4667-19.483)/(95.433-97.133))/rad = 30.87 degrees n of w marker: Popocatepetl, 19.033 -- 98.633, 5452 meters remove: sqrt((69*(18.4667-19.033))^2+(65*(95.433-98.633))^2) = 211 mi viewed: sqrt(2*4000*(3.25*5452)/5280) = 163 mi a((18.4667-19.033)/(95.433-98.633))/rad = 10.03 degrees s of w marker: Citlaltepetl (Pico de Orizaba), 19.0164 -- 97.2667, 5636 meters remove: sqrt((69*(18.4667-19.0164))^2+(65*(95.433-97.2667))^2) = 125 mi viewed: sqrt(2*4000*(3.25*5636)/5280) = 166 mi a((18.4667-19.0164)/(95.433-97.2667))/rad = 16.68 degrees n of w marker: Ixtaccihuatl, 19.183 -- 98.65, 5230 meters * remove: sqrt((69*(18.466-19.183))^2+(65*(95.433-98.65))^2) = 214 mi viewed: sqrt(2*4000*(3.25*5230)/5280) = 160 miles a((18.466-19.183)/(95.433-98.65))/rad = 12.56 degrees marker: Volcan La Malinche, 19.233 -- 98.033, 4462 meters * remove: sqrt((69*(18.466-19.233))^2+(65*(95.433-98.033))^2) = 177 mi viewed: sqrt(2*4000*(3.25*4462)/5280) = 148 mi a((18.466-19.233)/(95.433-98.033))/rad = 16.43 degrees n of w coast mountains.... marker: Volcan San Martin Pajapan, 18.316 -- 94.8, 1219 meters remove: sqrt((69*(18.4667-18.316))^2+(65*(95.433-94.8))^2) = 42 mi viewed: sqrt(2*4000*(3.25*1219)/5280) = 77 mi a((18.4667-18.316)/(95.433-94.8))/rad = 13.39 degrees s of e marker: Volcan San Martin Tuxtla, 18.55 -- 95.2, 1650 meters remove: sqrt((69*(18.4667-18.55))^2+(65*(95.433-95.2))^2) = 16 mi viewed: sqrt(2*4000*(3.25*1650)/5280) = 90 mi a((18.4667-18.55)/(95.433-95.2))/rad = -19.67 degrees n of e marker: Cerro Santa Martha (Veracruz), 18.35 -- 94.855, 1680 meter remove: sqrt((69*(18.4667-18.35))^2+(65*(95.433-94.855))^2) = 38 mi viewed: sqrt(2*4000*(3.25*1680)/5280) = 91 mi a((18.4667-18.35)/(95.433-94.855))/rad = 11.41 degrees s of e marker: Cerro San Martin (Queretaro), 20.745 -- 99.970 remove: sqrt((69*(18.4667-20.745))^2+(65*(95.433-99.970))^2) = 334 mi viewed: ?? - a((18.4667-20.745)/(95.433-99.970))/rad = 26.66 degrees n of w marker: El Chichon (Chiapas), 17.35 -- 93.233, 1060 meters remove: sqrt((69*(18.4667-17.35))^2+(65*(95.433-93.233))^2) = 162 mi viewed: sqrt(2*4000*(3.25*1060)/5280) = 72 mi a((18.4667-17.35)/(95.433-93.233))/rad = 26.91 degrees s of e marker: Cerro Zempoaltepec, 17.419 -- 95.983, 3396 meter remove: sqrt((69*(18.4667-17.419))^2+(65*(95.433-95.983))^2) = 80 mi viewed: sqrt(2*4000*(3.25*3396)/5280) = 129 miles a((18.4667-17.419)/(95.433-95.983))/rad = -62.30 degrees (out of limits)

Tres Zapotes site identity...

19.67 degrees n of e -- The alignment with Volcan San Martin Tuxtla represents the day the Sun passes directly overhead on August 13 in the previous era, rising at 19.40 degrees n of e.
Tres Zapotes era markers...

The above 19.67 degree angle is also an alignment for August 12th, 3114 BC (19.83 degrees), for the era before 685 BC.
11.41 degrees s of e -- This angle with Cerro Santa Martha (Veracruz), is an antipodal alignment for a sunrise on April 19th, 1492 BC (11.98 degrees), conformed to the current axial inclination of 23.5 degrees. But this is unlikely since all the other alignments are conformed to the era before 685 BC. Thus this more likely represents the era-ending for 747 BC (11.02 degrees s of w), conformed to the previous axial inclination. The antipodal alignment here reflects across the north south axis.
30.87 degrees n of w -- This angle with Nauhcampatepetl for a summer sunset defines July 9th (30.28 degrees), but in the era of an axial inclination of 30 degrees, before 685 BC.
26.66 degrees n of w -- The alignment with Cerro San Martin (Queretaro) defines a sunset for the date of July 25th (26.47 degrees), but for the era where the axis is still 30 degrees.
26.91 degrees s of e -- The angle with El Chichon also defines a sunset for the day of July 25, but in antipodal fashion, and also for the era where the axis is still 30 degrees.
Pleiades setting: -- There are two alignments for the setting of the Pleiades in the era of 685 BC or earlier, to Ixtaccihuatl (12.56 degrees) and Volcan San Martin Pajapan (13.39 degrees).
Pleiades setting: -- There are two additional alignments for the setting of the Pleiades in about 100 BC, at 16.68 degrees n of w to Citlaltepetl and 16.43 degrees to Volcan La Malinche also n of w.
Tres Zapotes notes...

It is really strange to see the current era ending alignments of July 9 and July 25 cast in terms of the previous axial alignment, and to find the much older alignment with April 19th -- of 1492 BC -- presented in terms of the current axial inclination. It is more likely, however, that this last is an era-ending for 747 BC, conformed, like the other alignments, to a 30 degree axial inclination.
Tres Zapotes is an old site, and it has been suggested that it became important when San Lorenzo was abandoned. This is likely, but because of the August 13th zenithal, and the existence of a August 12 alignment for 3114 BC, I think the site was not developed and located until after 747 BC. Before that time it would have been impossible to retrocalculate the era ending date for 3114 BC.

Laguna De Los Cerros

center: Laguna De Los Cerros, 18.1167 -- 95.1 axis 30 degrees axis 23.5 degrees event date angle date angle ------------ ------ ------ ------ ------ start 3114 BC era Aug 12 19.79 15.49 start 2349 BC era Sep 8 6.63 5.20 start 1492 BC era Apr 19 15.26 11.95 start 747 BC era Feb 28 -11.00 -8.61 solstice Jun 21 31.74 24.80 Jup flareup Jul 9 30.21 26.62 Jup plasmoid Jul 14 29.26 22.87*(*) Jup strike Jul 25 26.41 20.66 zenithal passage Aug 14 18.93 Jul 31 19.13 Pleiades setting (actual) -- Oct 16 16.71* 100 BC * -- alignment found; (*) -- antipodal

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"Laguna De Los Cerros is a Classical period archaeological site in the highlands of the Mexican state of Veracruz, in the southern foothills of the Tuxtla Mountains. Laguna de los Cerros ("lake of the hills") was so named because of the nearly 100 mounds dotting the landscape. Long parallel mounds, terminated by conical mounds at each edge, flank large rectangular plazas."
"Laguna De Los Cerros is a little-excavated Olmec site in Veracruz, in the foothills of the Tuxtla Mountains. Laguna de los Cerros is considered one of the four major Olmec centers. Settled between 1400 -- 1200 BC. By 1200 BC it had become a regional center. A nearby workshop for monumental sculptures used at San Lorenzo Tenochtitlán and the site of Laguna de los Cerros, was abandoned sometime after 1000 BC, as was most of the main site. The extensive house mounds and parallel berms date to AD 250 through AD 900." -- Wikipedia.org .

Laguna De Los Cerros, 18.1167 -- 95.1 .... valley mountains marker: Nauhcampatepetl, 19.483 -- 97.133, 4282 meters remove: sqrt((69*(18.1167-19.483))^2+(65*(95.1-97.133))^2) = 162 mi viewed: sqrt(2*4000*(3.25*4282)/5280) = 145 mi a((18.1167-19.483)/(95.1-97.133))/rad = 33.9 degrees (out of limits) marker: Popocatepetl, 19.033 -- 98.633, 5452 meters remove: sqrt((69*(18.1167-19.033))^2+(65*(95.1-98.633))^2) = 238 mi viewed: sqrt(2*4000*(3.25*5452)/5280) = 163 mi a((18.1167-19.033)/(95.1-98.633))/rad = 14.54 degrees marker: Citlaltepetl (Pico de Orizaba), 19.0164 -- 97.2667, 5636 meters remove: sqrt((69*(18.1167-19.0164))^2+(65*(95.1-97.2667))^2) = 154 mi viewed: sqrt(2*4000*(3.25*5636)/5280) = 166 mi a((18.1167-19.0164)/(95.1-97.2667))/rad = 22.55 degrees n of w marker: Ixtaccihuatl, 19.183 -- 98.65, 5230 meters remove: sqrt((69*(18.1167-19.183))^2+(65*(95.1-98.65))^2) = 242 mi viewed: sqrt(2*4000*(3.25*5230)/5280) = 160 miles a((18.1167-19.183)/(95.1-98.65))/rad = 16.71 degrees marker: Volcan La Malinche, 19.233 -- 98.033, 4462 meters remove: sqrt((69*(18.1167-19.233))^2+(65*(95.1-98.033))^2) = 205 mi viewed: sqrt(2*4000*(3.25*4462)/5280) = 148 mi a((18.1167-19.233)/(95.1-98.033))/rad = 20.83 degrees ... coast mountains marker: Volcan San Martin Pajapan, 18.316 -- 94.8, 1219 meters remove: sqrt((69*(18.1167-18.316))^2+(65*(95.1-94.8))^2) = 24 mi viewed: sqrt(2*4000*(3.25*1219)/5280) = 77 mi a((18.1167-18.316)/(95.1-94.8))/rad = -33.59 degrees (out of limits) marker: Volcan San Martin Tuxtla, 18.55 -- 95.2, 1650 meters remove: sqrt((69*(18.1167-18.55))^2+(65*(95.1-95.2))^2) = 30 mi viewed: sqrt(2*4000*(3.25*1650)/5280) = 90 mi a((18.1167-18.55)/(95.1-95.2))/rad = 77.00 degrees (out of limits) marker: Cerro Santa Martha (Veracruz), 18.35 -- 94.855, 1680 meter remove: sqrt((69*(18.1167-18.35))^2+(65*(95.1-94.855))^2) = 23 mi viewed: sqrt(2*4000*(3.25*1680)/5280) = 91 mi a((18.1167-18.35)/(95.1-94.855))/rad = -43.59 degrees (out of limits) marker: Cerro San Martin (Queretaro), 20.745 -- 99.970 remove: sqrt((69*(18.1167-20.745))^2+(65*(95.1-99.970))^2) = 364 mi viewed: ?? - a((18.1167-20.745)/(95.1-99.970))/rad = 28.35 degrees marker: El Chichon (Chiapas), 17.35 -- 93.233, 1060 meters remove: sqrt((69*(18.1167-17.35))^2+(65*(95.1-93.233))^2) = 132 mi viewed: sqrt(2*4000*(3.25*1060)/5280) = 72 mi a((18.1167-17.35)/(95.1-93.233))/rad = 22.32 degrees s of e marker: Cerro Zempoaltepec, 17.419 -- 95.983, 3396 meter remove: sqrt((69*(18.1167-17.419))^2+(65*(95.1-95.983))^2) = 75 mi viewed: sqrt(2*4000*(3.25*3396)/5280) = 129 miles a((18.1167-17.419)/(95.1-95.983))/rad = -38.3 degrees (out of limits)

22.55 degrees n of w -- The angle made with Citlaltepetl in the northwest defines a summer sunset on July 14th (22.87 degrees).
22.32 degrees s of e -- The angle with El Chichon in the southeast defines an antipodal summer sunset on July 14th (22.87 degrees).
The alignment of 16.71 degrees may define the setting of the Pleiades after culmination in about 100 BC.

Cerro De La Mesas

center: Cerro De La Mesas, 18.7167 -- 96.15 axis 30 degrees axis 23.5 degrees event date angle date angle ------------ ------ ------ ------ ------ start 3114 BC era Aug 12 19.86* 15.55 start 2349 BC era Sep 8 6.66 5.21 start 1492 BC era Apr 19 15.32*(*) 11.99 start 747 BC era Feb 28 -11.04(*) -8.65 solstice Jun 21 31.86 24.90(*)? Jup flareup Jul 9 30.33 23.70 Jup plasmoid Jul 14 29.37 22.96 Jup strike Jul 25 26.51 20.73 zenithal passage Aug 12 19.86* Jul 29 19.74* * -- alignment found; (*) -- antipodal

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Cerro De La Mesas ("hill of the altars"), is an archaeological site in Veracruz, Mexico. It was a prominent regional center from 600 BC to AD 900, and a regional capital from perhaps AD 300 to AD 600.
"Cerro de las Mesas (Spanish, "hill of the altars") is an archaeological site in the Mexican state of Veracruz, in the Mixtequilla area of the Papaloapan River basin. It was a prominent regional center from 600 BC to AD 900, and a regional capital from perhaps AD 300 to AD 600."
"Located some 50 km (30 miles) due south of the city of Veracruz, Cerro de las Mesas is on the west edge of what had been the Olmec heartland. Rising to prominence after the decline of the Olmec culture, some researchers consider Cerro de las Mesas, along with similar sites like La Mojarra and Tres Zapotes, to be a center of the epi-Olmec culture, a successor culture to the Olmecs, and one that itself gave way to Classic Veracruz culture in the 3rd century AD."
"The site contains a man-made lagoon as well as hundreds of artificial mounds, usually in groups, often clustered with a long and a conical mound. These mound groups were likely built during the epi-Olmec period, 400 BC to AD 300. It was also during this period that the influence of Teotihuacan appears in the archaeological record."
"Sometime later, during the Classic period, a cache of some 800 jade items, some dating from Olmec times hundreds of years earlier, were buried at the base of the large mound of the central group."
"Cerro de las Mesas is home to many stelae, several of which contain portraits. Four of these stelae -- 5, 6, 8, and 15 -- contain what are likely to be instances of Epi-Olmec script." -- Wikipedia.org

Cerro De La Mesas, 18.7167 -- 96.15 .... valley mountains marker: Nauhcampatepetl, 19.483 -- 97.133, 4282 meters remove: sqrt((69*(18.7167-19.483))^2+(65*(96.15-97.133))^2) = 83 mi viewed: sqrt(2*4000*(3.25*4282)/5280) = 145 mi a((18.7167-19.483)/(96.15-97.133))/rad = 37.9 degrees (out of limits) marker: Popocatepetl, 19.033 -- 98.633, 5452 meters remove: sqrt((69*(18.7167-19.033))^2+(65*(96.15-98.633))^2) = 163 mi viewed: sqrt(2*4000*(3.25*5452)/5280) = 163 mi a((18.7167-19.033)/(96.15-98.633))/rad = 7.25 degrees marker: Citlaltepetl (Pico de Orizaba), 19.0164 -- 97.2667, 5636 meters remove: sqrt((69*(18.7167-19.0164))^2+(65*(96.15-97.2667))^2) = 75 mi viewed: sqrt(2*4000*(3.25*5636)/5280) = 166 mi a((18.7167-19.0164)/(96.15-97.2667))/rad = 15.02 degrees n of w marker: Ixtaccihuatl, 19.183 -- 98.65, 5230 meters remove: sqrt((69*(18.716-19.183))^2+(65*(96.15-98.65))^2) = 165 mi viewed: sqrt(2*4000*(3.25*5230)/5280) = 160 miles a((18.716-19.183)/(96.15-98.65))/rad = 10.58 degrees n of w marker: Volcan La Malinche, 19.233 -- 98.033, 4462 meters remove: sqrt((69*(18.716-19.233))^2+(65*(96.15-98.033))^2) = 127 mi viewed: sqrt(2*4000*(3.25*4462)/5280) = 148 mi a((18.716-19.233)/(96.15-98.033))/rad = 15.35 degrees n of w coast mountains.... marker: Volcan San Martin Pajapan, 18.316 -- 94.8, 1219 meters remove: sqrt((69*(18.7167-18.316))^2+(65*(96.15-94.8))^2) = 92 mi viewed: sqrt(2*4000*(3.25*1219)/5280) = 77 mi a((18.7167-18.316)/(96.15-94.8))/rad = 16.53 degrees marker: Volcan San Martin Tuxtla, 18.55 -- 95.2, 1650 meters remove: sqrt((69*(18.7167-18.55))^2+(65*(96.15-95.2))^2) = 62 mi viewed: sqrt(2*4000*(3.25*1650)/5280) = 90 mi a((18.7167-18.55)/(96.15-95.2))/rad = 9.95 degrees marker: Cerro Santa Martha (Veracruz), 18.35 -- 94.855, 1680 meter remove: sqrt((69*(18.7167-18.35))^2+(65*(96.15-94.855))^2) = 88 mi viewed: sqrt(2*4000*(3.25*1680)/5280) = 91 mi a((18.7167-18.35)/(96.15-94.855))/rad = 15.81 degrees s of e marker: Cerro San Martin (Queretaro), 20.745 -- 99.970 remove: sqrt((69*(18.7167-20.745))^2+(65*(96.15-99.970))^2) = 285 mi viewed: ?? - a((18.7167-20.745)/(96.15-99.970))/rad = 27.96 degrees marker: El Chichon (Chiapas), 17.35 -- 93.233, 1060 meters remove: sqrt((69*(18.7167-17.35))^2+(65*(96.15-93.233))^2) = 211 mi viewed: sqrt(2*4000*(3.25*1060)/5280) = 72 mi a((18.7167-17.35)/(96.15-93.233))/rad = 25.10 degrees s of e marker: Cerro Zempoaltepec, 17.419 -- 95.983, 3396 meter remove: sqrt((69*(18.7167-17.419))^2+(65*(96.15-95.983))^2) = 90 mi viewed: sqrt(2*4000*(3.25*3396)/5280) = 129 miles a((18.7167-17.419)/(96.15-95.983))/rad = 82.6 degrees (out of limits)

Cerro De La Mesas site identity...

Interestingly, the Sun passes overhead on August 12th, but their is no mountain at 19.73 degrees for an alignment. This is also the era-ending marker for 3114 BC.
25.10 degrees s of e -- The alignment with El Chichon (Chiapas) is a winter solstitual alignment (24.90 degrees) or an antipodal alignment for a summer solstice sunset, for the current era. I think this is in error, that is, it is a coincidence, for all the other alignments are for the previous era.
Cerro De La Mesas era marker...

The zenithal passage of the Sun on August 12 also signals the era-ending of 3114 BC.
15.35 degrees n of w -- The alignment with Volcan La Malinche defines a sunset on April 19 (15.32 degrees) in the era with the axis at 30 degrees.
15.81 degrees s of e -- The angle with Cerro Santa Martha (Veracruz) marks an antipodal sunset on April 19 (15.55 degrees), in the era with the axis at 30 degrees.
10.58 degrees n of w -- This is a summer sunset over Ixtaccihuatl but defines an antipodal winter sunrise for February 28th (11.04 degrees), for an axial inclination of 30 degrees.
Cerro De La Mesas discussion...

At this site, dated to after 600 BC, we see the first solstitual alignment, although it might be coincidental.

Remojadas

center: Remojadas, 18.9833 -- 96.3167 axis 30 degrees axis 23.5 degrees event date angle date angle ------------ ------ ------ ------ ------ start 3114 BC era Aug 12 19.90 15.57 start 2349 BC era Sep 8 6.67 5.22* start 1492 BC era Apr 19 15.34 12.01 start 747 BC era Feb 28 -11.06 -8.66(*) solstice Jun 21 31.92* 24.94 Jup flareup Jul 9 30.38 23.74(*) Jup plasmoid Jul 14 29.42 23.00(*) Jup strike Jul 25 26.56 20.77(*) zenithal passage Aug 11 20.32 Jul 28 20.03 * -- alignment found

Remojadas is an archaeological site that flourished on Mexico's Veracruz Gulf Coast from perhaps 100 BC to AD 800. The Remojadas culture is considered part of the large Classic Veracruz culture. The site has remained largely unexplored since the initial investigations by A. Medellin Zenil in 1949 and 1950. (wikipedia)

Remojadas, 18.9833 -- 96.3167 .... valley mountains marker: Nauhcampatepetl, 19.483 -- 97.133, 4282 meters remove: sqrt((69*(18.9833-19.483))^2+(65*(96.3167-97.133))^2) = 63 mi viewed: sqrt(2*4000*(3.25*4282)/5280) = 145 mi a((18.9833-19.483)/(96.3167-97.133))/rad = 31.47 degrees n of w marker: Popocatepetl, 19.033 -- 98.633, 5452 meters remove: sqrt((69*(18.9833-19.033))^2+(65*(96.3167-98.633))^2) = 150 mi viewed: sqrt(2*4000*(3.25*5452)/5280) = 163 mi a((18.9833-19.033)/(96.3167-98.633))/rad = 1.23 degrees n of w marker: Citlaltepetl (Pico de Orizaba), 19.0164 -- 97.2667, 5636 meters remove: sqrt((69*(18.9833-19.0164))^2+(65*(96.3167-97.2667))^2) = 61 mi viewed: sqrt(2*4000*(3.25*5636)/5280) = 166 mi a((18.9833-19.0164)/(96.3167-97.2667))/rad = 1.99 degrees n of w marker: Ixtaccihuatl, 19.183 -- 98.65, 5230 meters * remove: sqrt((69*(18.9833-19.183))^2+(65*(96.3167-98.65))^2) = 152 mi viewed: sqrt(2*4000*(3.25*5230)/5280) = 160 miles a((18.9833-19.183)/(96.3167-98.65))/rad = 4.89 degrees n of w marker: Volcan La Malinche, 19.233 -- 98.033, 4462 meters * remove: sqrt((69*(18.9833-19.233))^2+(65*(96.3167-98.033))^2) = 112 mi viewed: sqrt(2*4000*(3.25*4462)/5280) = 148 mi a((18.9833-19.233)/(96.3167-98.033))/rad = 8.27 degrees n of w coast mountains.... marker: Volcan San Martin Pajapan, 18.316 -- 94.8, 1219 meters remove: sqrt((69*(18.9833-18.316))^2+(65*(96.3167-94.8))^2) = 108 mi viewed: sqrt(2*4000*(3.25*1219)/5280) = 77 mi a((18.9833-18.316)/(96.3167-94.8))/rad = 23.74 degrees s of e marker: Volcan San Martin Tuxtla, 18.55 -- 95.2, 1650 meters remove: sqrt((69*(18.9833-18.55))^2+(65*(96.3167-95.2))^2) = 78 mi viewed: sqrt(2*4000*(3.25*1650)/5280) = 90 mi a((18.9833-18.55)/(96.3167-95.2))/rad = 21.20 degrees s of e marker: Cerro Santa Martha (Veracruz), 18.35 -- 94.855, 1680 meter remove: sqrt((69*(18.9833-18.35))^2+(65*(96.3167-94.855))^2) = 104 mi viewed: sqrt(2*4000*(3.25*1680)/5280) = 91 mi a((18.9833-18.35)/(96.3167-94.855))/rad = 23.42 degrees s of e marker: Cerro San Martin (Queretaro), 20.745 -- 99.970 remove: sqrt((69*(18.9833-20.745))^2+(65*(96.3167-99.970))^2) = 266 mi viewed: ?? - a((18.9833-20.745)/(96.3167-99.970))/rad = 25.74 degrees n of w marker: El Chichon (Chiapas), 17.35 -- 93.233, 1060 meters remove: sqrt((69*(18.9833-17.35))^2+(65*(96.3167-93.233))^2) = 229 mi viewed: sqrt(2*4000*(3.25*1060)/5280) = 72 mi a((18.9833-17.35)/(96.3167-93.233))/rad = 27.908 degrees marker: Cerro Zempoaltepec, 17.419 -- 95.983, 3396 meter remove: sqrt((69*(18.9833-17.419))^2+(65*(96.3167-95.983))^2) = 110 mi viewed: sqrt(2*4000*(3.25*3396)/5280) = 129 miles a((18.9833-17.419)/(96.3167-95.983))/rad = 77.95 degrees (out of limits)

Remojadas site identity...

31.47 degrees n of w -- This angle with Nauhcampatepetl defines a summer solstice in the previous era, with an axial inclination of 30 degrees (31.92 degrees).
Remojadas era markers...

4.89 degrees n of w -- The angle with Ixtaccihuatl marks the ending of the era on September 8, 2349 BC before 685 BC (5.22 degrees), but conformed to the current axial inclination, as are all the other alignments at this site (except the possible solstice, above).
8.27 degrees n of w -- The angle with Volcan La Malinche marks an antipodal sunrise of date of February 28th (8.66 degrees), conformed to the current era.
23.74 degrees s of e -- The angle with Volcan San Martin Pajapan defines an antipodal summer sunset on July 9th (23.74 degrees), conformed to the current era.
23.42 degrees s of e -- The angle with Cerro Santa Martha (Veracruz) marks the antipodal day of the release of the plasmoid, July 14, 586 BC (23.00 degrees), conformed to the current era.
21.20 degrees s of e -- The angle with Volcan San Martin Tuxtla marks the antipodal day of the delivery of the plasmoid, July 25, 586 BC (20.77 degrees), conformed to the current era.
Remojadas notes...

The complete array of era markers which are presented, September 8, 2349 BC, February 28, 747 BC, April 2, 685 BC, and July 9th, 14th, and 25th, is amazing. All of these are presented under the current condition of a 23.5 degree axial inclination.
The solstice alignment is conformed to the previous 30 degree axial inclination, and is probably in error.

Zempoala

center: Zempoala, 19.447 -- 96.408 axis 30 degrees axis 23.5 degrees event date angle date angle ------------ ------ ------ ------ ------ start 3114 BC era Aug 12 19.96 15.62 start 2349 BC era Sep 8 6.69(*) 5.24 start 1492 BC era Apr 19 15.39 12.05 start 747 BC era Feb 28 -11.09* -8.68 solstice Jun 21 32.02 25.01 Jup flareup Jul 9 30.48 23.81 Jup plasmoid Jul 14 29.51 23.07 Jup strike Jul 25 26.64* 20.83 zenithal passage Aug 10 20.80* Jul 26 20.59* * -- alignment found

"Cempoala (or Zempoala) was an important Mesoamerican city. It was the largest city on the Gulf of Mexico and the capital of the kingdom of Totonicapan occupied by the Totonac people. At its peak, it had a population of between 25,000 and 30,000. The name means "place of the twenty waters" due to several rivers meeting near the site and is eight kilometes from the current city of Veracruz, Veracruz, one kilometer from the banks of the Río Actopan and six kilometres from the Gulf. The city was an important staging post in the conquest of Mexico by Hernán Cortés."
"The city was populated at least 1,500 years before the arrival of the Spanish and there are signs of an Olmec influence. Although not much is known about the Preclassic and Classic Era, the Preclassic town was built on mounds to protect it from floods."
"The bulk of the buildings on the current archaeological site date from the 14th and 15th century. The archaeological sites of interest include the Great Temple which resembles the Temple of the Sun in Tenochtitlan [Teotihuacan ?] where human sacrifices also took place. The site also features other temples including the Temple of the Little Faces covered by stuccoed faces and writing, the Temple of Quetzalcoatl and the Temple of Ehecatl, the god of the wind." -- Wikipedia.org

Zempoala, 19.447 -- 96.408 valley mountains..... marker: Nauhcampatepetl, 19.483 -- 97.133, 4282 meters remove: sqrt((69*(19.447-19.483))^2+(65*(96.408-97.133))^2) = 47 mi viewed: sqrt(2*4000*(3.25*4282)/5280) = 145 mi a((19.447-19.483)/(96.408-97.133))/rad = 2.84 degrees marker: Popocatepetl, 19.033 -- 98.633, 5452 meters remove: sqrt((69*(19.447-19.033))^2+(65*(96.408-98.633))^2) = 147 mi viewed: sqrt(2*4000*(3.25*5452)/5280) = 163 mi a((19.447-19.033)/(96.408-98.633))/rad = -10.54 degrees s of w marker: Citlaltepetl (Pico de Orizaba), 19.0164 -- 97.2667, 5636 meters remove: sqrt((69*(19.447-19.0164))^2+(65*(96.408-97.2667))^2) = 63 mi viewed: sqrt(2*4000*(3.25*5636)/5280) = 166 mi a((19.447-19.0164)/(96.408-97.2667))/rad = -26.6 degrees s of w marker: Ixtaccihuatl, 19.183 -- 98.65, 5230 meters remove: sqrt((69*(19.447-19.183))^2+(65*(96.408-98.65))^2) = 146 mi viewed: sqrt(2*4000*(3.25*5230)/5280) = 160 miles a((19.447-19.183)/(96.408-98.65))/rad = -6.71 degrees s of w marker: Volcan La Malinche, 19.233 -- 98.033, 4462 meters remove: sqrt((69*(19.447-19.233))^2+(65*(96.408-98.033))^2) = 106 mi viewed: sqrt(2*4000*(3.25*4462)/5280) = 148 mi a((19.447-19.233)/(96.408-98.033))/rad = -7.50 degrees s of w coast mountains.... marker: Volcan San Martin Pajapan, 18.316 -- 94.8, 1219 meters remove: sqrt((69*(19.447-18.316))^2+(65*(96.408-94.8))^2) = 130 mi viewed: sqrt(2*4000*(3.25*1219)/5280) = 77 mi a((19.447-18.316)/(96.408-94.8))/rad = 35.12 degrees (out of limits) marker: Volcan San Martin Tuxtla, 18.55 -- 95.2, 1650 meters remove: sqrt((69*(19.447-18.55))^2+(65*(96.408-95.2))^2) = 100 mi viewed: sqrt(2*4000*(3.25*1650)/5280) = 90 mi a((19.447-18.55)/(96.408-95.2))/rad = 36.59 degrees (out of limits) marker: Cerro Santa Martha (Veracruz), 18.35 -- 94.855, 1680 meter remove: sqrt((69*(19.447-18.35))^2+(65*(96.408-94.855))^2) = 126 mi viewed: sqrt(2*4000*(3.25*1680)/5280) = 91 mi a((19.447-18.35)/(96.408-94.855))/rad = 35.23 degrees (out of limits) marker: Cerro San Martin (Queretaro), 20.745 -- 99.970 remove: sqrt((69*(19.447-20.745))^2+(65*(96.408-99.970))^2) = 248 mi viewed: ?? - a((19.447-20.745)/(96.408-99.970))/rad = 20.02 degrees n of w marker: El Chichon (Chiapas), 17.35 -- 93.233, 1060 meters remove: sqrt((69*(19.447-17.35))^2+(65*(96.408-93.233))^2) = 252 mi viewed: sqrt(2*4000*(3.25*1060)/5280) = 72 mi a((19.447-17.35)/(96.408-93.233))/rad = 33.44 degrees (out of limits) marker: Cerro Zempoaltepec, 17.419 -- 95.983, 3396 meter remove: sqrt((69*(19.447-17.419))^2+(65*(96.408-95.983))^2) = 142 mi viewed: sqrt(2*4000*(3.25*3396)/5280) = 129 miles a((19.447-17.419)/(96.408-95.983))/rad = 78.16 degrees (out of limits)

Zempoala site identity...

20.02 degrees n of w -- The angle with Cerro San Martin (Queretaro) defines the summer sunset for the zenithal passage of the Sun (at 89.92 elevation) on July 26th (20.59 degrees) conformed to the era after 685 BC. In the prior era the zenithal passage would have fallen on August 10.
Zempoala era markers...

10.54 degrees s of w -- The angle with Popocatepetl marks a sunset for the date of February 28th (11.09 degrees), but for the condition of a 30 degree axis. 6.71 degrees s of w -- The angle with Ixtaccihuatl marks a antipodal rise of the Pleiades for September 8, 2349 BC (6.69 degrees), for the condition of a 30 degree axis.
26.6 degrees s of w -- The angle with Citlaltepetl defines the day of the plasmoid strike on July 25th (26.64 degrees), but for the condition of a 30 degree axis.
Zempoala notes...

Again, era markers are presented as alignments only valid for the previous axial inclination. The site identification alignment could also be grouped with these. Interestingly, the site identity alignment became important after 685 BC because it fell on July 26 -- new year's day as established by Teotihuacan.

Teotihuacan

center: Teotihuacan; 19.683 -- 98.85 The axis of the site is aligned 15.5 degrees east of north. axis 30 degrees axis 23.5 degrees event date angle date angle ------------ ------ ------ ------ ------ start 3114 BC era Aug 12 19.99 15.64* start 2349 BC era Sep 8 6.70 5.24 start 1492 BC era Apr 19 15.41 12.06 start 747 BC era Feb 28 -11.11 -8.70 solstice Jun 21 32.07 25.05 Jup flareup Jul 9 30.52 23.85 Jup plasmoid Jul 14 29.56 23.10(*) Jup strike Jul 25 26.68 20.86# zenithal passage Aug 10 20.83* Jul 25 20.86* Pleiades setting (actual) -- Oct 22 18.65(*) AD 200 Oct 22 18.45(*) AD 200 * -- alignment found, (*) -- antipodal, # -- implied

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"Teotihuacan was, at its height in the first half of the 1st millennium AD, the largest pre-Columbian city in the Americas. The civilization and cultural complex associated with the site is also referred to as Teotihuacán. Its influence spread throughout Mesoamerica; evidence of Teotihuacano presence, if not outright political and economic control, can be seen at numerous sites in Veracruz and the Maya region."
"The early history of Teotihuacan is quite mysterious, and the origin of its founders is debated. There is evidence that at least some of the people living in Teotihuacan came from areas influenced by the Teotihuacano civilization, including the Zapotec, Mixtec and Maya peoples. The culture and architecture of Teotihuacan was influenced by the Olmec people. The earliest buildings at Teotihuacan date to about 200 BC, and the largest pyramid, the Pyramid of the Sun, was completed by 100 AD."
"The city reached its zenith between 150 and 450, when it was the center of a powerful culture whose influence extended through much of the Mesoamerican region. At its height the city covered over 30 sq km (over 11.5 square miles), and probably housed a population of over 150,000 people, possibly as many as 250,000. Various districts in the city housed people from across the Teotihuacano region of influence that spread south as far as Guatemala. Notably absent from the city are fortifications and military structures."
"The nature of political and cultural interactions between Teotihuacan and the centers of the Maya region (as well as elsewhere in Mesoamerica) has been a long-standing and significant area for debate in Mesoamerican scholarship. It is clearly established that substantial exchange and interaction occurred over the centuries from the Terminal Preclassic to the Mid Classic period, and that 'Teotihuacan-inspired ideologies' and motifs persisted at Maya centers into the Late Classic long after Teotihuacan itself had declined."
"Architectural styles prominent at Teotihuacan are also found widely dispersed at a number of distant Mesoamerican sites, which some researchers have interpreted as evidence for Teotihuacan's far-reaching interactions and political or militaristic dominance. A style that has been particularly associated with Teotihuacan is known as talud-tablero, in which an inwards-sloping external side of a structure (talud) is surmounted by a rectangular panel (tablero). Variants of the generic style are found in a number of Maya region sites, including Tikal, Kaminaljuyu, Copan, Becan, and Oxkintok, and particularly in the Petén Basin and the central Guatemalan highlands."
"However, it has been established that the talud-tablero style pre-dates its earliest appearance at Teotihuacan in the Early Classic period, and instead seems to have first originated in the Tlaxcala-Puebla region during the Preclassic. Analyses have also been able to trace the development into local variants of the talud-tablero style at sites such as Tikal, where its use precedes the 5th-century appearance of iconographic motifs shared with Teotihuacan. Thus it appears that the talud-tablero style disseminated through Mesoamerica generally from the end of the Preclassic and not specifically or only via Teotihuacano influence. It is unclear how or from where the style spread into the Maya region."
"The city was a center of industry, home to many potters, jewelers and craftsmen. Teotihuacan is known for producing a great number of obsidian artifacts. Unfortunately no ancient Teotihuacano non-ideographic texts are known to exist (or known to have existed), but mentions of the city in inscriptions from Maya cities show that Teotihuacan nobility travelled to and perhaps conquered local rulers as far away as Honduras. Maya inscriptions mention an individual nicknamed by scholars as "Spearthrower Owl", apparently ruler of Teotihuacan, who reigned for over 60 years and installed his relatives as rulers of Tikal and Uaxactún in Guatemala."
"Most of what we infer about the culture at Teotihuacan comes from the murals that adorn the site (and others, like the Wagner Murals, found in private collections) and from hieroglyphic inscriptions made by the Maya describing their encounters with Teotihuacan conquerors. The creation of murals, perhaps tens of thousands of murals, reached its height between 450 and 650 AD."
"It was previously believed that sometime during the 7th or 8th centuries, the city was sacked and burned by invaders, possibly the Toltecs. More recent evidence, however, seems to indicate that the burning was limited to the structures and dwellings associated primarily with the elite class. Some see this as evidence that the burning was from an internal uprising and that the invasion theory is flawed due to the fact that early archaeological work on the city was focused exclusively on the palaces and temples, places used by the elites, and because all of these sites showed burning, archaeologists concluded that the whole city was burned. Instead, it is now known that the destruction in the city was focused on major civic structures along the Avenue of the Dead. Some statues seem to have been destroyed in a methodical way, their fragments dispersed."
"Evidence for population decline beginning around the 6th century lends some support to the internal unrest hypothesis. The decline of Teotihuacan has been correlated with the droughts related to the climate changes of 535-536 AD. This theory is supported by the archaeological remains that show a rise in the percentage of juvenile skeletons with evidence of malnutrition during the 6th century. This does not conflict with either of the above theories however since both increased warfare and internal unrest can also be effects of a general period of drought and famine. Other nearby centers such as Cholula, Xochicalco, and Cacaxtla attempted to fill the powerful vacuum left by Teotihuacan's decline. They may have aligned themselves against Teotihuacan in an attempt to reduce its influence and power. The art and architecture at these sites shows an interest in emulating Teotihuacan forms, but also a more eclectic mix of motifs and iconography from other parts of Mesoamerica, particularly the Maya region."
"The religion of Teotihuacan is similar to those of other Mesoamerican cultures. Many of the same gods were worshiped, including the Feathered Serpent and The Rain god. Teotihuacan was a major religious center, and the priests probably had a great deal of political power. As with other Mesoamerican cultures, Teotihuacanos practiced human sacrifice. Human bodies and animal sacrifices have been found during excavations of the pyramids at Teotihuacán; it is believed that when the buildings were expanded, sacrifices were made to dedicate the new building. The victims were probably enemy warriors captured in battle and then brought to the city to be ritually sacrificed so the city could prosper. Some were decapitated, some had their hearts removed, others were killed by being hit several times over the head and some were even buried alive. Animals that were considered sacred and represented mythical powers and military might were also buried alive but imprisoned in cages: cougars, a wolf, eagles, a falcon, an owl, and even venomous snakes."
"The city's broad central avenue, called "Avenue of the Dead" (a translation from its Nahuatl name Miccaotli), is flanked by impressive ceremonial architecture, including the immense Pyramid of the Sun (second largest in the New World after the Great Pyramid of Cholula) and the Pyramid of the Moon. Along the Avenue of the Dead are many smaller talud-tablero platforms. The Aztecs believed they were tombs, inspiring the name of the avenue. Now they are known to be ceremonial platforms that were topped with temples. Further down the Avenue of the Dead is the area known as the Citadel, containing the ruined Temple of the Feathered Serpent. This area was a large plaza surrounded by temples that formed the religious and political center of the city. The name "Citadel" was given to it by the Spanish, who believed it was a fort. Many of the rich and powerful Teotihuacanos lived in Palaces near the temples, the largest of these covering more than 3300 sq m. Most of the common people lived in large apartment buildings spread across the city. Many of the buildings contained workshops that produced pottery and other goods." -- Wikipedia.org

Teotihuacan; 19.683 -- 98.85 valley mountains..... marker: Nauhcampatepetl, 19.483 -- 97.133, 4282 meters remove: sqrt((69*(19.683-19.483))^2+(65*(98.85-97.133))^2) = 112 mi viewed: sqrt(2*4000*(3.25*4282)/5280) = 145 mi a((19.683-19.483)/(98.85-97.133))/rad = 6.64 degrees s of e marker: Popocatepetl, 19.033 -- 98.633, 5452 meters remove: sqrt((69*(19.683-19.033))^2+(65*(98.85-98.633))^2) = 47 mi viewed: sqrt(2*4000*(3.25*5452)/5280) = 164 mi a((19.683-19.033)/(98.85-98.633))/rad = 71.5 degrees (out of limits) marker: Citlaltepetl (Pico de Orizaba), 19.0164 -- 97.2667, 5636 meters remove: sqrt((69*(19.683-19.0164))^2+(65*(98.85-97.2667))^2) = 113 mi viewed: sqrt(2*4000*(3.25*5636)/5280) = 166 mi a((19.683-19.0164)/(98.85-97.2667))/rad = 22.83 degrees s of e marker: Ixtaccihuatl, 19.183 -- 98.65, 5230 meters remove: sqrt((69*(19.683-19.183))^2+(65*(98.85-98.65))^2) = 36 mi viewed: sqrt(2*4000*(3.25*5230)/5280) = 160 miles a((19.683-19.183)/(98.85-98.65))/rad = 68.1 degrees (out of limits) marker: Volcan La Malinche, 19.233 -- 98.033, 4462 meters remove: sqrt((69*(19.683-19.233))^2+(65*(98.85-98.033))^2) = 61 mi viewed: sqrt(2*4000*(3.25*4462)/5280) = 148 mi a((19.683-19.233)/(98.85-98.033))/rad = 28.84 degrees coast mountains.... marker: Volcan San Martin Pajapan, 18.316 -- 94.8, 1219 meters remove: sqrt((69*(19.683-18.316))^2+(65*(98.85-94.8))^2) = 279 mi viewed: sqrt(2*4000*(3.25*1219)/5280) = 77 mi a((19.683-18.316)/(98.85-94.8))/rad = 18.65 degrees s of e marker: Volcan San Martin Tuxtla, 18.55 -- 95.2, 1650 meters remove: sqrt((69*(19.683-18.55))^2+(65*(98.85-95.2))^2) = 249 mi viewed: sqrt(2*4000*(3.25*1659)/5280) = 90 mi a((19.683-18.55)/(98.85-95.2))/rad = 17.24 degrees marker: Cerro Santa Martha (Veracruz), 18.35 -- 94.855, 1680 meters remove: sqrt((69*(19.683-18.35))^2+(65*(98.85-94.855))^2) = 275 mi viewed: sqrt(2*4000*(3.25*1680)/5280) = 91 mi a((19.683-18.35)/(98.85-94.855))/rad = 18.45 degrees s of e marker: Cerro San Martin (Queretaro), 20.745 -- 99.970 remove: sqrt((69*(19.683-20.745))^2+(65*(98.85-99.970))^2) = 103 mi viewed: ?? a((19.683-20.745)/(98.85-99.970))/rad = 43.47 degrees (out of limits) marker: El Chichon (Chiapas), 17.35 -- 93.233, 1060 meters remove: sqrt((69*(19.683-17.35))^2+(65*(98.85-93.233))^2) = 399 mi viewed: sqrt(2*4000*(3.25*1060)/5280) = 72 mi a((19.683-17.35)/(98.85-93.233))/rad = 22.55 degrees s of e marker: Cerro Zempoaltepec, 17.42 -- 95.98, 3396 meters remove: sqrt((69*(19.683-17.42))^2+(65*(98.85-95.98))^2) = 243 mi viewed: sqrt(2*4000*(3.25*3396)/5280) = 129 mi a((19.683-17.42)/(98.85-95.98))/rad = 38.25 degrees (out of limits)

Image: Teotihuacan alignments. Plan view.

Teotihuacan site identity...

The Sun passes overhead at 89.86 degrees on July 25th. This also marks the delivery of Jupiter's plasmoid at the Sun in 685 BC.
Teotihuacan era marker...

The axis of the site defines the setting of Sun at 15.60 degrees north of west for August 12, 3114 BC (15.64 degrees n of w) -- at right angle to the long axis of the site.
22.83 degrees s of e -- This angle with Citlaltepetl, the highest mountain in Mexico, suggests an antipodal sunset on July 15th (22.93 degrees), the day after July 14th (23.10 degrees).
The zenithal passage of the Sun on July 25 also marks the era-ending of 685 BC.
Pleiades setting: -- There are two antipodal alignments to Volcan San Martin Pajapan (18.65 degrees) and Cerro Santa Martha (Veracruz) (18.45 degrees). Both of these are correct for the era of AD 200 to 400.
The overhead passage of the Sun is a also a marker for the current era.

Tlatilco

center: Tlatilco, 19.466 -- 99.166 axis 30 degrees axis 23.5 degrees event date angle date angle ------------ ------ ------ ------ ------ start 3114 BC era Aug 12 19.96* 15.62 start 2349 BC era Sep 8 6.69 5.24 start 1492 BC era Apr 19 15.39** 12.05 start 747 BC era Feb 28 -11.09* -8.68 solstice Jun 21 32.02 25.02 Jup flareup Jul 9 30.48 23.81 Jup plasmoid Jul 14 29.51 23.07 Jup strike Jul 25 26.64 20.83 zenithal passage Aug 10 20.80 Jul 26 20.59* Pleiades setting (actual) -- Oct 8 13.31(*) 685 BC Oct 8 13.00(*) 685 BC * -- alignment found; (*) -- antipodal

"It was one of the first chiefdom centers to arise in the Valley, flourishing on the western shore of Lake Texcoco during the Middle Pre-Classic period, between the years of 1500 BCE and 500 BC. It gives its name to the "Tlatilco culture", which also included the town of Tlapacoya, on the eastern shore of Lake Chalco. It is believed that Tlatilco was significantly influenced by the Olmecs" -- Wikipedia.org

Tlatilco, 19.466 -- 99.166 .... valley mountains marker: Nauhcampatepetl, 19.483 -- 97.133, 4282 meters * remove: sqrt((69*(19.466-19.483))^2+(65*(99.166-97.133))^2) = 132 mi viewed: sqrt(2*4000*(3.25*4282)/5280) = 145 mi a((19.466-19.483)/(99.166-97.133))/rad = -.479 degrees n of e marker: Popocatepetl, 19.033 -- 98.633, 5452 meters remove: sqrt((69*(19.466-19.033))^2+(65*(99.166-98.633))^2) = 45 mi viewed: sqrt(2*4000*(3.25*5452)/5280) = 163 mi a((19.466-19.033)/(99.166-98.633))/rad = 39.09 degrees (out of limits) marker: Citlaltepetl (Pico de Orizaba), 19.0164 -- 97.2667, 5636 meters remove: sqrt((69*(19.466-19.0164))^2+(65*(99.166-97.2667))^2) = 127 mi viewed: sqrt(2*4000*(3.25*5636)/5280) = 166 mi a((19.466-19.0164)/(99.166-97.2667))/rad = 13.31 degrees marker: Ixtaccihuatl, 19.183 -- 98.65, 5230 meters remove: sqrt((69*(19.466-19.183))^2+(65*(99.166-98.65))^2) = 38 mi viewed: sqrt(2*4000*(3.25*5230)/5280) = 160 miles a((19.466-19.183)/(99.166-98.65))/rad = 28.74 degrees marker: Volcan La Malinche, 19.233 -- 98.033, 4462 meters remove: sqrt((69*(19.466-19.233))^2+(65*(99.166-98.033))^2) = 75 mi viewed: sqrt(2*4000*(3.25*4462)/5280) = 148 mi a((19.466-19.233)/(99.166-98.033))/rad = 11.62 degrees s of e coast mountains.... marker: Volcan San Martin Pajapan, 18.316 -- 94.8, 1219 meters remove: sqrt((69*(19.466-18.316))^2+(65*(99.166-94.8))^2) = 294 mi viewed: sqrt(2*4000*(3.25*1219)/5280) = 77 mi a((19.466-18.316)/(99.166-94.8))/rad = 14.75 degrees s of w marker: Volcan San Martin Tuxtla, 18.55 -- 95.2, 1650 meters remove: sqrt((69*(19.466-18.55))^2+(65*(99.166-95.2))^2) = 264 mi viewed: sqrt(2*4000*(3.25*1650)/5280) = 90 mi a((19.466-18.55)/(99.166-95.2))/rad = 13.00 degrees marker: Cerro Santa Martha (Veracruz), 18.35 -- 94.855, 1680 meter remove: sqrt((69*(19.466-18.35))^2+(65*(99.166-94.855))^2) = 290 mi viewed: sqrt(2*4000*(3.25*1680)/5280) = 91 mi a((19.466-18.35)/(99.166-94.855))/rad = 14.51 degrees s of w marker: Cerro San Martin (Queretaro), 20.745 -- 99.970 remove: sqrt((69*(19.466-20.745))^2+(65*(99.166-99.970))^2) = 102 mi viewed: ?? - a((19.466-20.745)/(99.166-99.970))/rad = 57.84 degrees (out of limits) marker: El Chichon (Chiapas), 17.35 -- 93.233, 1060 meters remove: sqrt((69*(19.466-17.35))^2+(65*(99.166-93.233))^2) = 412 mi viewed: sqrt(2*4000*(3.25*1060)/5280) = 72 mi a((19.466-17.35)/(99.166-93.233))/rad = 19.62 degrees s of e marker: Cerro Zempoaltepec, 17.419 -- 95.983, 3396 meter remove: sqrt((69*(19.466-17.419))^2+(65*(99.166-95.983))^2) = 250 mi viewed: sqrt(2*4000*(3.25*3396)/5280) = 129 miles a((19.466-17.419)/(99.166-95.983))/rad = 32.74 degrees (out of limits)

Tlatilco site identity...

In the era after 685 BC, the zenithal sun passed over the site on July 26, a significant day, but there is no mountain associated with this.
0.479 degrees n of e -- This is an vernal equinox sunrise over the mountain Nauhcampatepetl, a very unusual alignment.
Tlatilco era markers...

19.62 degrees s of e -- The angle with El Chichon (Chiapas) marks a sunset for August 12, under the condition of a 30 degree axis.
14.75 degrees s of w -- The angle with Volcan San Martin Pajapan marks a sunset for the date of April 19th, 1492 BC (15.39 degrees), under the condition of a 30 degree axis.
14.51 degrees s of w -- The angle with Cerro Santa Martha (Veracruz) also marks a sunset for the date of April 19th (15.39 degrees), under a 30 degree axis, lining up with Volcan San Martin Pajapan.
11.62 degrees s of e -- The angle with Volcan La Malinche marks a sunrise for the date of February 28, 747 BC (11.09 degrees) for the era before 685 BC.
Pleiades setting: -- There are two antipodal alignment to Citlaltepetl (Pico de Orizaba) (13.31 degrees) and Volcan San Martin Tuxtla (13.00 degrees). These alignments were in effect directly after 685 BC.
Tlatilco notes...

The era markers, and the curious equinoxial site identity, suggest that this is a fairly old site, but established after 747 BC.

Tizatlan

center: Tizatlan, 19.338 -- 98.219 axis 30 degrees axis 23.5 degrees event date angle date angle ------------ ------ ------ ------ ------ start 3114 BC era Aug 12 19.94 ? 15.61 start 2349 BC era Sep 8 6.68 5.23 start 1492 BC era Apr 19 15.38(*) 12.04 start 747 BC era Feb 28 -11.08 -8.68 solstice Jun 21 32.00 25.00 Jup flareup Jul 9 30.45 23.80 Jup plasmoid Jul 14 29.49* 23.05 Jup strike Jul 25 26.62 20.81 zenithal passage Aug 11 20.37* Jul 26 20.57* Pleiades setting (actual) -- Oct 16 16.64(*) 100 BC Oct 16 16.36(*) 100 BC Oct 22 18.66(*) AD 200 * -- alignment found; (*) -- antipodal

An archaeological site in the valley of Mexico.

Tizatlan, 19.338 -- 98.219 .... valley mountains marker: Nauhcampatepetl, 19.483 -- 97.133, 4282 meters * remove: sqrt((69*(19.338-19.483))^2+(65*(98.219-97.133))^2) = 71 mi viewed: sqrt(2*4000*(3.25*4282)/5280) = 145 mi a((19.338-19.483)/(98.219-97.133))/rad = -7.60 degrees marker: Popocatepetl, 19.033 -- 98.633, 5452 meters remove: sqrt((69*(19.338-19.033))^2+(65*(98.219-98.633))^2) = 34 mi viewed: sqrt(2*4000*(3.25*5452)/5280) = 163 mi a((19.338-19.033)/(98.219-98.633))/rad = -36.37 degrees (out of limits) marker: Citlaltepetl (Pico de Orizaba), 19.0164 -- 97.2667, 5636 meters remove: sqrt((69*(19.338-19.0164))^2+(65*(98.219-97.2667))^2) = 65 mi viewed: sqrt(2*4000*(3.25*5636)/5280) = 166 mi a((19.338-19.0164)/(98.219-97.2667))/rad = 18.66 degrees marker: Ixtaccihuatl, 19.183 -- 98.65, 5230 meters remove: sqrt((69*(19.338-19.183))^2+(65*(98.219-98.65))^2) = 30 mi viewed: sqrt(2*4000*(3.25*5230)/5280) = 160 miles a((19.338-19.183)/(98.219-98.65))/rad = -19.78 degrees s of w marker: Volcan La Malinche, 19.233 -- 98.033, 4462 meters remove: sqrt((69*(19.338-19.233))^2+(65*(98.219-98.033))^2) = 14 mi viewed: sqrt(2*4000*(3.25*4462)/5280) = 148 mi a((19.338-19.233)/(98.219-98.033))/rad = 29.44 degrees s of e coast mountains.... marker: Volcan San Martin Pajapan, 18.316 -- 94.8, 1219 meters remove: sqrt((69*(19.338-18.316))^2+(65*(98.219-94.8))^2) = 233 mi viewed: sqrt(2*4000*(3.25*1219)/5280) = 77 mi a((19.338-18.316)/(98.219-94.8))/rad = 16.64 degrees marker: Volcan San Martin Tuxtla, 18.55 -- 95.2, 1650 meters remove: sqrt((69*(19.338-18.55))^2+(65*(98.219-95.2))^2) = 203 mi viewed: sqrt(2*4000*(3.25*1650)/5280) = 90 mi a((19.338-18.55)/(98.219-95.2))/rad = 14.62 degrees s of e marker: Cerro Santa Martha (Veracruz), 18.35 -- 94.855, 1680 meter remove: sqrt((69*(19.338-18.35))^2+(65*(98.219-94.855))^2) = 229 mi viewed: sqrt(2*4000*(3.25*1680)/5280) = 91 mi a((19.338-18.35)/(98.219-94.855))/rad = 16.36 degrees marker: Cerro San Martin (Queretaro), 20.745 -- 99.970 remove: sqrt((69*(19.338-20.745))^2+(65*(98.219-99.970))^2) = 149 mi viewed: ?? - a((19.338-20.745)/(98.219-99.970))/rad = 38.78 degrees (out of limits) marker: El Chichon (Chiapas), 17.35 -- 93.233, 1060 meters remove: sqrt((69*(19.338-17.35))^2+(65*(98.219-93.233))^2) = 352 mi viewed: sqrt(2*4000*(3.25*1060)/5280) = 72 mi a((19.338-17.35)/(98.219-93.233))/rad = 21.73 degrees marker: Cerro Zempoaltepec, 17.419 -- 95.983, 3396 meter remove: sqrt((69*(19.338-17.419))^2+(65*(98.219-95.983))^2) = 196 mi viewed: sqrt(2*4000*(3.25*3396)/5280) = 129 miles a((19.338-17.419)/(98.219-95.983))/rad = 40.63 degrees (out of limits)

Tizatlan site identity...

19.78 degrees s of w -- The angle with Ixtaccihuatl marks the antipodal zenithal sunrise for July 26 for current era (20.57 degrees) or August 11 of the previous era (20.37 degrees).
Tizatlan era markers...

The zenithal passage is so close to the angle required to denote August 12, 3114 BC (19.94) before 685 BC, that it may as well be used as such. This is yet another case of the setting angle of the zenithal Sun being used also for an era-ending marker. However, see below.
14.62 degrees s of e -- The angle with Volcan San Martin Tuxtla marks an antipodal sunset for April 19, 1492 BC (15.38 degrees) under the previous 30 degree axial alignment.
29.44 degrees s of e -- The angle with Volcan La Malinche defines the date of July 14 (29.49 degrees), but in the era before 685 BC, with an axial inclination at 30 degrees.
Pleiades setting: -- There is an antipodal alignment with Citlaltepetl (Pico de Orizaba) (18.66 degrees) representing a date of AD 200.
Pleiades setting: -- There is an alignment with Volcan San Martin Pajapan at 16.64 degrees, and an alignment with Cerro Santa Martha at 16.36 degrees. Both point southeast and are thus antipodal. The horizon locations represent the setting of the Pleiades after culmination in about 100 BC.

Cuicuilco

center: Cuicuilco, 19.301 -- 99.181, from 700 BC axis 30 degrees axis 23.5 degrees event date angle date angle ------------ ------ ------ ------ ------ start 3114 BC era Aug 12 19.94 ? 16.60 start 2349 BC era Sep 8 6.68 5.23* start 1492 BC era Apr 19 15.37 12.03(*)(*) start 747 BC era Feb 28 -11.08(*) -8.67(*) solstice Jun 21 31.99 24.99 Jup flareup Jul 9 30.44(*) 24.62 Jup plasmoid Jul 14 29.48 22.04 Jup strike Jul 25 26.62(*) 20.81 zenithal passage Aug 11 20.36 ? Jul 26 20.57 Pleiades setting (actual) -- Oct 22 18.15(*) AD 200 * -- alignment found; (*) -- antipodal; ? -- suspected

"Cuicuilco was an ancient city in the central Mexican highlands, on the southern shore of the Lake Texcoco in the southeastern Valley of Mexico. Today, it is a significant archaeological site that was occupied during the Mesoamerican Middle and Late Formative (ca. 700 BC to AD 150). Based on its date of occupation, Cuicuilco may be the oldest city in the Valley of Mexico and was roughly contemporary with, and possibly interacting with the Olmec of the Gulf Coast of lowland Veracruz and Tabasco."
"Archaeologists conclude that Cuicuilco was a prominent community prior to the emergence of Teotihuacan as an urban center, noting that the six small communities which eventually combined to become Teotihuacan were founded and showing evidence of modest growth during the time Cuicuilco was building pyramids and public monuments. The city seems to have been abandoned around AD 150 to 200 after the eruption of a nearby volcano, Xitle, although the territory was reoccupied at a much later date. Pottery, and other evidence, suggest that refugees from the volcanic disaster migrated north and became part of the population pool of Teotihuacan, near the northern shore of the Lake Texcoco." -- Wikipedia.org

Cuicuilco, 19.301 -- 99.181 .... valley mountains marker: Nauhcampatepetl, 19.483 -- 97.133, 4282 meters * remove: sqrt((69*(19.301-19.483))^2+(65*(99.181-97.133))^2) = 133 mi viewed: sqrt(2*4000*(3.25*4282)/5280) = 145 mi a((19.301-19.483)/(99.181-97.133))/rad = -5.07 degrees n of e marker: Popocatepetl, 19.033 -- 98.633, 5452 meters remove: sqrt((69*(19.301-19.033))^2+(65*(99.181-98.633))^2) = 40 mi viewed: sqrt(2*4000*(3.25*5452)/5280) = 163 mi a((19.301-19.033)/(99.181-98.633))/rad = 26.06 degrees s of w marker: Citlaltepetl (Pico de Orizaba), 19.0164 -- 97.2667, 5636 meters remove: sqrt((69*(19.301-19.0164))^2+(65*(99.181-97.2667))^2) = 126 mi viewed: sqrt(2*4000*(3.25*5636)/5280) = 166 mi a((19.301-19.0164)/(99.181-97.2667))/rad = 8.45 degrees s of e marker: Volcan La Malinche, 19.233 -- 98.033, 4462 meters remove: sqrt((69*(19.301-19.233))^2+(65*(99.181-98.033))^2) = 74 mi viewed: sqrt(2*4000*(3.25*4462)/5280) = 148 mi a((19.301-19.233)/(99.181-98.033))/rad = 3.38 degrees coast mountains.... marker: Volcan San Martin Pajapan, 18.316 -- 94.8, 1219 meters remove: sqrt((69*(19.301-18.316))^2+(65*(99.181-94.8))^2) = 292 mi viewed: sqrt(2*4000*(3.25*1219)/5280) = 77 mi a((19.301-18.316)/(99.181-94.8))/rad = 12.67 degrees s of e marker: Volcan San Martin Tuxtla, 18.55 -- 95.2, 1650 meters remove: sqrt((69*(19.301-18.55))^2+(65*(99.181-95.2))^2) = 263 mi viewed: sqrt(2*4000*(3.25*1650)/5280) = 90 mi a((19.301-18.55)/(99.181-95.2))/rad = 10.68 degrees s of e marker: Cerro Santa Martha (Veracruz), 18.35 -- 94.855, 1680 meter remove: sqrt((69*(19.301-18.35))^2+(65*(99.181-94.855))^2) = 288 mi viewed: sqrt(2*4000*(3.25*1680)/5280) = 91 mi a((19.301-18.35)/(99.181-94.855))/rad = 12.39 degrees s of e marker: Cerro San Martin (Queretaro), 20.745 -- 99.970 remove: sqrt((69*(19.301-20.745))^2+(65*(99.181-99.970))^2) = 112 mi viewed: ?? - a((19.301-20.745)/(99.181-99.970))/rad = 61.34 degrees (out of limits) marker: El Chichon (Chiapas), 17.35 -- 93.233, 1060 meters remove: sqrt((69*(19.301-17.35))^2+(65*(99.181-93.233))^2) = 409 mi viewed: sqrt(2*4000*(3.25*1060)/5280) = 72 mi a((19.301-17.35)/(99.181-93.233))/rad = 18.15 degrees marker: Cerro Zempoaltepec, 17.419 -- 95.983, 3396 meter remove: sqrt((69*(19.301-17.419))^2+(65*(99.181-95.983))^2) = 245 mi viewed: sqrt(2*4000*(3.25*3396)/5280) = 129 miles a((19.301-17.419)/(99.181-95.983))/rad = 30.47 degrees s of e

Cuicuilco site identity...

There seem to be no site identity alignments. The zenithal Sun passes over on August 11, setting at an angle nearly identical to the angle needed to mark the era-ending of August 12, 3114 BC. There are no mountains associated with these.
Cuicuilco era markers...

prior era...

A possible dual use of the zenithal passage of the Sun is noted above.
10.68 degrees s of e -- The angle with Volcan San Martin Tuxtla defines an antipodal sunset for the date of February 28 (11.08 degrees), under the condition of a 30 degree axial inclination.
30.47 degrees s of e -- The angle with Cerro Zempoaltepec defines (surprisingly) an antipodal sunset date of the suspected initial flareup of Jupiter on July 9 (30.44 degrees), and under the condition of a 30 degree axial inclination.
26.06 degrees s of w -- The angle with Popocatepetl likewise defines the antipodal sunrise date of the suspected delivery of the plasmoid by Jupiter on July 26 (26.91 degrees), under the condition of a 30 degree axial inclination.
current era...

12.67 degrees s of e -- The angle with Volcan San Martin Pajapan defines an antipodal sunset for the date of April 19, 1492 BC (12.03 degrees), for a 23.5 degree axis.
12.39 degrees s of e -- The angle with Cerro Santa Martha (Veracruz) additionally marks the date of April 19th. The mountain is almost the same distance from the site as Volcan San Martin Pajapan.
8.45 degrees s of e -- The angle to Citlaltepetl defines an antipodal sunset for the date of February 28th (8.67 degrees), under the present conditions of the sky. This duplicates the 10.68 degree alignment.
5.07 degrees n of e -- The angle with Nauhcampatepetl marks September 8, 2349 BC (5.23 degrees) for the current era.
Pleiades setting: -- In addition to a sunset for September 8 in the era before 685 BC, there is an antipodal alignment for the setting of the Pleiades to El Chichon (Chiapas) (18.15 degrees).
Cuicuilco notes...

Many era markers, but no site identification.

Tlapacoya

center: Tlapacoya, 19.3 -- 98.916 axis 30 degrees axis 23.5 degrees event date angle date angle ------------ ------ ------ ------ ------ start 3114 BC era Aug 12 19.94? 15.60 start 2349 BC era Sep 8 6.68 5.23(*) start 1492 BC era Apr 19 15.37 12.03 start 747 BC era Feb 28 -11.08* -8.67 solstice Jun 21 31.99 24.99 Jup flareup Jul 9 30.44 23.79(*) Jup plasmoid Jul 14 29.48 23.04 Jup strike Jul 25 26.61 20.81 zenithal passage Aug 11 20.36? Jul 26 20.57 Pleiades setting (actual) -- Oct 8 13.44(*) 685 BC Oct 8 13.16(*) 685 BC Oct 22 18.93(*) AD 200 * -- alignment found; (*) -- antipodal

"Tlapacoya is an important archaeological site in Mexico, located at the foot of the Tlapacoya volcano, southeast of Mexico City, on the former shore of Lake Chalco. Tlapacoya was a major site for the Tlatilco culture."
"Tlapacoya is known in particular for Tlapacoya figurines. These sophisticated earthware figurines were generally created between 1500 and 300 BCE and are representative of the Preclassic Period."
"Tlapacoya was also a manufacturing center for so-called "Dragon Pots". These flat-bottomed cylindrical bowls have white or buff surfaces incised with almost abstract Olmec-style drawings, generally of were-jaguars." -- wikipedia.org

Tlapacoya, 19.3 -- 98.916 .... valley mountains marker: Nauhcampatepetl, 19.483 -- 97.133, 4282 meters remove: sqrt((69*(19.3-19.483))^2+(65*(98.916-97.133))^2) = 116 mi viewed: sqrt(2*4000*(3.25*4282)/5280) = 145 mi a((19.3-19.483)/(98.916-97.133))/rad = -5.86 degrees n of e marker: Popocatepetl, 19.033 -- 98.633, 5452 meters remove: sqrt((69*(19.3-19.033))^2+(65*(98.916-98.633))^2) = 26 mi viewed: sqrt(2*4000*(3.25*5452)/5280) = 163 mi a((19.3-19.033)/(98.916-98.633))/rad = 43.3 degrees (out of limits) marker: Citlaltepetl (Pico de Orizaba), 19.0164 -- 97.2667, 5636 meters remove: sqrt((69*(19.3-19.0164))^2+(65*(98.916-97.2667))^2) = 109 mi viewed: sqrt(2*4000*(3.25*5636)/5280) = 166 mi a((19.3-19.0164)/(98.916-97.2667))/rad = 9.75 degrees marker: Ixtaccihuatl, 19.183 -- 98.65, 5230 meters remove: sqrt((69*(19.3-19.183))^2+(65*(98.916-98.65))^2) = 19 mi viewed: sqrt(2*4000*(3.25*5230)/5230) = 161 miles a((19.3-19.183)/(98.916-98.65))/rad = 23.74 degrees s of e marker: Volcan La Malinche, 19.233 -- 98.033, 4462 meters remove: sqrt((69*(19.3-19.233))^2+(65*(98.916-98.033))^2) = 57 mi viewed: sqrt(2*4000*(3.25*4462)/5280) = 148 mi a((19.3-19.233)/(98.916-98.033))/rad = 4.33 degrees coast mountains.... marker: Volcan San Martin Pajapan, 18.316 -- 94.8, 1219 meters remove: sqrt((69*(19.3-18.316))^2+(65*(98.916-94.8))^2) = 276 mi viewed: sqrt(2*4000*(3.25*1219)/5280) = 77 mi a((19.3-18.316)/(98.916-94.8))/rad = 13.44 degrees marker: Volcan San Martin Tuxtla, 18.55 -- 95.2, 1650 meters remove: sqrt((69*(19.3-18.55))^2+(65*(98.916-95.2))^2) = 247 mi viewed: sqrt(2*4000*(3.25*1650)/5280) = 90 mi a((19.3-18.55)/(98.916-95.2))/rad = 11.41 degrees s of e marker: Cerro Santa Martha (Veracruz), 18.35 -- 94.855, 1680 meter remove: sqrt((69*(19.3-18.35))^2+(65*(98.916-94.855))^2) = 271 mi viewed: sqrt(2*4000*(3.25*1680)/5280) = 91 mi a((19.3-18.35)/(98.916-94.855))/rad = 13.16 degrees marker: Cerro San Martin (Queretaro), 20.745 -- 99.970 remove: sqrt((69*(19.3-20.745))^2+(65*(98.916-99.970))^2) = 121 mi viewed: ?? - a((19.3-20.745)/(98.916-99.970))/rad = 53.89 degrees (out of limits) marker: El Chichon (Chiapas), 17.35 -- 93.233, 1060 meters remove: sqrt((69*(19.3-17.35))^2+(65*(98.916-93.233))^2) = 393 mi viewed: sqrt(2*4000*(3.25*1060)/5280) = 72 mi a((19.3-17.35)/(98.916-93.233))/rad = 18.93 degrees marker: Cerro Zempoaltepec, 17.419 -- 95.983, 3396 meter remove: sqrt((69*(19.3-17.419))^2+(65*(98.916-95.983))^2) = 230 mi viewed: sqrt(2*4000*(3.25*3396)/5280) = 129 miles a((19.3-17.419)/(98.916-95.983))/rad = 32.67 degrees (out of limits)

Tlapacoya site identification...

There seem to be no site identity alignments. The sun passes over on August 11.
Tlapacoya site identification...

There seem to be no site identity alignments, although it could be held that the zenithal sun would mark the era-ending of August 12, 3114 BC. But there are no mountains associated with this.
11.41 degrees s of e -- The angle to Volcan San Martin Tuxtla marks the winter sunrise for the date of February 28th (11.08 degrees), but for the condition of having the inclination of the Earth's axis at 30 degrees.
5.86 degrees n of e -- The angle with Nauhcampatepetl marks an antipodal sunset for September 8, 2349 BC (5.23 degrees).
23.74 degrees s of e -- The angle to Ixtaccihuatl marks an antipodal sunset for the date of July 9th (23.79 degrees).
Setting of the Pleiades -- In addition to the sunset alignment for September 8, 2349 BC, there are two alignments for the setting of the Pleiades in 685 to 600 BC to Volcan San Martin Pajapan (13.44 degrees) and Cerro Santa Martha (Veracruz) (13.16 degrees) and one for the era of AD 200 to 400 to El Chichon (Chiapas) (18.93 degrees).

Cholula

center: Cholula, 19.066 -- 98.3 axis 30 degrees axis 23.5 degrees event date angle date angle ------------ ------ ------ ------ ------ start 3114 BC era Aug 12 19.91 14.94 start 2349 BC era Sep 8 6.67 5.22* start 1492 BC era Apr 19 15.35 12.02(*)(*) start 747 BC era Feb 28 -11.06 -8.66 solstice Jun 21 31.94* 24.95 Jup flareup Jul 9 30.40 23.75 Jup plasmoid Jul 14 29.44 23.01 Jup strike Jul 25 26.57 20.78 zenithal passage Aug 11 20.33* Jul 27 20.29* Pleiades setting (actual) -- Oct 22 18.48(*) AD 200 Oct 22 18.71* AD 200 * -- alignment found; (*) antipodal

"Cholula, or, Acholollan in Nahuatl, was an important city of pre-Columbian Mesoamerica, dating back to at least the 2nd century BC, with settlement as a village going back at least some thousand years earlier."
"Cholula was a major center contemporary with Teotihuacan and seems to have avoided, at least partially, that city's fate of violent destruction at the end of the Mesoamerican Classic period. Cholula thus remained a regional center of importance, enough so that, at the time of the fall of the Aztec empire, Aztec princes were still formally anointed by a Cholulan priest in a manner reminiscent, and perhaps even analogous, to the way some Mayan princes appear to have come to Teotihuacan in search of some sort of formalization of their rulership."
"At the time of the arrival of Hernán Cortés Cholula was second only to the Aztec capital Tenochtitlan (modern Mexico City) as the largest city in central Mexico, possibly with a population of up to 100,000 people. In addition to the great temple of Quetzalcoatl and various palaces, the city had 365 temples."
"Cholula is most famous as the site of the Great Pyramid of Cholula, the largest man-made structure by volume in the world."

Cholula, 19.066 -- 98.3 .... valley mountains marker: Nauhcampatepetl, 19.483 -- 97.133, 4282 meters remove: sqrt((69*(19.066-19.483))^2+(65*(98.3-97.133))^2) = 81 mi viewed: sqrt(2*4000*(3.25*4282)/5280) = 145 mi a((19.066-19.483)/(98.3-97.133))/rad = -19.66 degrees n of e marker: Popocatepetl, 19.033 -- 98.633, 5452 meters remove: sqrt((69*(19.066-19.033))^2+(65*(98.3-98.633))^2) = 21 mi viewed: sqrt(2*4000*(3.25*5452)/5280) = 163 mi a((19.066-19.033)/(98.3-98.633))/rad = -5.66 degrees s of e marker: Citlaltepetl (Pico de Orizaba), 19.0164 -- 97.2667, 5636 meters remove: sqrt((69*(19.066-19.0164))^2+(65*(98.3-97.2667))^2) = 67 mi viewed: sqrt(2*4000*(3.25*5636)/5280) = 166 mi a((19.066-19.0164)/(98.3-97.2667))/rad = 2.74 degrees marker: Ixtaccihuatl, 19.183 -- 98.65, 5230 meters remove: sqrt((69*(19.066-19.183))^2+(65*(98.3-98.65))^2) = 24 mi viewed: sqrt(2*4000*(3.25*5230)/5280) = 160 miles a((19.066-19.183)/(98.3-98.65))/rad = 18.48 degrees marker: Volcan La Malinche, 19.233 -- 98.033, 4462 meters remove: sqrt((69*(19.066-19.233))^2+(65*(98.3-98.033))^2) = 20 mi viewed: sqrt(2*4000*(3.25*4462)/5280) = 148 mi a((19.066-19.233)/(98.3-98.033))/rad = -32.02 degrees n of e coast mountains.... marker: Volcan San Martin Pajapan, 18.316 -- 94.8, 1219 meters remove: sqrt((69*(19.066-18.316))^2+(65*(98.3-94.8))^2) = 233 mi viewed: sqrt(2*4000*(3.25*1219)/5280) = 77 mi a((19.066-18.316)/(98.3-94.8))/rad = 12.09 degrees s of e marker: Volcan San Martin Tuxtla, 18.55 -- 95.2, 1650 meters remove: sqrt((69*(19.066-18.55))^2+(65*(98.3-95.2))^2) = 204 mi viewed: sqrt(2*4000*(3.25*1650)/5280) = 90 mi a((19.066-18.55)/(98.3-95.2))/rad = 9.45 degrees marker: Cerro Santa Martha (Veracruz), 18.35 -- 94.855, 1680 meter remove: sqrt((69*(19.066-18.35))^2+(65*(98.3-94.855))^2) = 229 mi viewed: sqrt(2*4000*(3.25*1680)/5280) = 91 mi a((19.066-18.35)/(98.3-94.855))/rad = 11.74 degrees s of e marker: Cerro San Martin (Queretaro), 20.745 -- 99.970 remove: sqrt((69*(19.066-20.745))^2+(65*(98.3-99.970))^2) = 158 mi viewed: ?? - a((19.066-20.745)/(98.3-99.970))/rad = 45.15 degrees (out of limits) marker: El Chichon (Chiapas), 17.35 -- 93.233, 1060 meters remove: sqrt((69*(19.066-17.35))^2+(65*(98.3-93.233))^2) = 350 mi viewed: sqrt(2*4000*(3.25*1060)/5280) = 72 mi a((19.066-17.35)/(98.3-93.233))/rad = 18.71 degrees marker: Cerro Zempoaltepec, 17.419 -- 95.983, 3396 meter remove: sqrt((69*(19.066-17.419))^2+(65*(98.3-95.983))^2) = 188 mi viewed: sqrt(2*4000*(3.25*3396)/5280) = 129 miles a((19.066-17.419)/(98.3-95.983))/rad = 35.40 degrees (out of limits)

Cholula site identification...

19.66 degrees n of e -- The angle with Nauhcampatepetl defines a zenithal sunrise for July 27th (20.29 degrees).
32.02 degrees n of e -- The angle with Volcan La Malinche is the summer solstice sunrise of June 21 (31.94 degrees), for the condition of having the inclination of the Earth's axis at 30 degrees. I doubt the validity of this alignment, since all the other alignments are conformed to the current era.
Cholula era markers...

12.09 degrees s of e -- The angle with Volcan San Martin Pajapan defines an antipodal sunset for the start of a previous era, on April 19, 1492 BC (12.02 degrees), but under the current axial inclination.
11.74 degrees s of e -- The angle with Cerro Santa Martha (Veracruz) also defines an antipodal sunset for the date of the start of the previous era, on April 19, 1492 BC (and under the current axial inclination). Cerro Santa Martha is almost the same distance from the site as Volcan San Martin Pajapan
5.66 degrees s of e -- The angle with Popocatepetl defines September 8, 2349 BC (5.22 degrees).
Setting of the Pleiades -- In addition to the sunset alignment for September 8, 2349 BC, there are two alignments for the setting of the Pleiades in AD 200 -- 400 Ixtaccihuatl (18.48 degrees) and El Chichon (Chiapas) (18.71 degrees).
Cholula notes...

Except for the possible solstice marker under the condition of a 30 degree axis, all the alignments are conformed to the current axial inclination.

Monte Alban

center: Monte Alban, 17.033 -- 96.766 axis 30 degrees axis 23.5 degrees event date angle date angle ------------ ------ ------ ------ ------ start 3114 BC era Aug 12 19.67 15.40 start 2349 BC era Sep 8 6.59 5.17 start 1492 BC era Apr 19 15.18 11.88 start 747 BC era Feb 28 -10.94 -8.56 solstice Jun 21 31.53 24.65 Jup flareup Jul 9 30.01 23.47 Jup plasmoid Jul 14 29.07 22.73 Jup strike Jul 25 26.25 20.53 zenithal passage Aug 16 17.93 Aug 4 17.89

I am including Monte Alban as a matter of reference. I have not checked this site against the mountains of Veracruz and the Valley of Mexico because it is too far south. Monte Alban is discussed in Chapter 18, "Olmec Alignments."

Endnotes

Note 1 --
The short QBasic (DOS) program below will list the location (in degrees from east) and time of sunrise and sunset for any axial inclination and latitude. Originally written to predict the angle of shadows for outdoor filming at various locations and dates. "Qbasic.exe" is found in the directory "olddos" under "windows" in Windows-95 or Windows-98 OS.
As shown below, the program is not usable because the < and > angle brackets have been altered (shown here as HTML "entities") as required for inclusion between PRE tags. However, the program can be obtained as a text file from SaturnianCosmology.Org as [sun.bas].

10 CLS : PRINT , , "Sun.bas -- SUNRISE and SUNSET": PRINT 11 'sun.bas,v 1.4 2008/01/05 23:27:10 jno Exp 20 PI = 3.14159: KEY OFF 30 RAD = 2 * PI / 360 'factor converts degrees to rads 40 DEG = 1 / RAD 'factor converts radians to degrees 50 DEF FNASIN (A) = ATN(A / ((1 - A * A) ^ .5)) 60 DEF FNACOS (A) = -ATN(A / SQR(-A * A + 1)) + PI / 2 80 '.........................inputs......................................... 90 PRINT , 100 INPUT ; "For location"; Locat$: PRINT : PRINT , 101 INPUT ; "For axial inclination"; INC: PRINT : PRINT , 102 INPUT ; "North latitude of location"; LAT: PRINT : PRINT , 200 ' ..............dom.....month.............................. 111 INPUT ; "For Month (Nnn)"; Month$: INPUT ; " DOM"; DOM: PRINT 601 IF Month$ = "Jun" THEN Days = ABS(DOM - 21) 602 IF Month$ = "Jul" THEN Days = DOM + 9 603 IF Month$ = "Aug" THEN Days = DOM + 9 + 31 604 IF Month$ = "Sep" THEN Days = DOM + 9 + 31 + 31 605 IF Month$ = "Oct" THEN Days = DOM + 9 + 31 + 31 + 30 606 IF Month$ = "Nov" THEN Days = DOM + 9 + 31 + 31 + 30 + 31 607 IF Month$ = "Dec" THEN Days = DOM + 9 + 31 + 31 + 30 + 31 + 30 608 IF Month$ = "Jan" THEN Days = 31 - DOM + 20 + 31 + 30 + 31 + 28 609 IF Month$ = "Feb" THEN Days = 28 - DOM + 20 + 31 + 30 + 31 610 IF Month$ = "Mar" THEN Days = 31 - DOM + 20 + 31 + 30 611 IF Month$ = "Apr" THEN Days = 30 - DOM + 20 + 31 612 IF Month$ = "May" THEN Days = 31 - DOM + 20 613 IF Days >= 182 THEN Days = 182 - ABS(Days - 182) 621 PRINT 120 'PRINT , : PRINT ; " -- Solstice is on June 21--" 131 'PRINT ; " Dec Jan Feb Mar Apr May Jun | Jun Jul Aug Sep Oct Nov Dec" 132 'PRINT ; " 9 31 28 31 30 31 20 - 9 31 31 30 31 30 21" 133 'PRINT ; " 171 140 112 81 51 20 9 40 71 101 132 162" 134 'PRINT 622 PRINT ; Month$; DOM; "(days after/before solstice:)"; Days 180 '........................declination............................. 190 DEC = INC * (COS(RAD * Days * 360 / 365.25)) 220 '...............latitude - elevation of noon sun............. 240 IF LAT >= 90 OR LAT <= 0 THEN PRINT ; "LAT OUT OF LIMITS": GOTO 699 250 ELE = 90 - LAT + DEC 260 IF ELE <= 0 THEN PRINT , "Arctic Circle; no sun": GOTO 699 270 IF ELE > 90 THEN ELE = 180 - ELE 280 PRINT ; "Noon elevation of sun is"; ELE; "degrees." 350 '...................sunset /sunrise.................... 380 LAT = RAD * LAT 381 DEC = RAD * DEC: SSAZICOS = SIN(DEC) / COS(LAT) 410 SSAZI = PI - FNACOS(SSAZICOS) 412 SUMAZI = DEG * SSAZI - 90 471 PRINT ; "sunrise at "; SUMAZI; "degrees No or So of East" 500 '...........times and day length ............. 520 SINHR = SIN(SSAZI) / COS(DEC): TIME = FNASIN(SINHR) * DEG 540 IF DEC > 0 THEN TIME = 180 - TIME 550 DHR = TIME / 15: WHR = INT(DHR): EHR = 11 - WHR 560 M = INT(60 * (DHR - WHR)): LM = 60 - M 561 PRINT ; "Sunrise at approximately "; EHR; ":"; LM; "am," 562 PRINT ; "Sunset at approximately "; WHR; ":"; M; "pm LMT" 563 HOURS = 2 * WHR: MIN = 2 * M 564 IF MIN >= 60 THEN MIN = MIN - 60: HOURS = HOURS + 1 577 PRINT ; "Length of the day "; HOURS; "hours"; MIN; "minutes" 699 END

Documentation: The program uses spherical geometry to determine the location of the Sun. The year is divided up into two halves of 182 days each with the solstice of June 21 as day zero. Thus the quarter day is neglected. The actual calendar days of the equinoxes and solstices move over two or three days in the year, because our calendar varies between 365 and 366 days. In this program the leap days are neglected, summer solstice is set to 'day zero' and the remainder of the year is divided up into two 182 day segments.
Since the Sun travels a little over one degree on the ecliptic each day, sunset will differ from sunrise by about a half degree per day on average. Except for these, the program should be fairly acurate. Small differences in latitude or axial inclination will not significantly effect the results.
The angles are for sunrises. To find the equivalent sunset angle, find the difference between the current sunrise and the next one. One half of this difference, when added to a sunrise angle, will give a good approximation for the corresponding sunset angle.
The program will on occasion crash at the equinox (a divide by zero problem). Live with it, or change the axial inclination from 23.5 to 23.4 degrees (the actual value being 23.45 degrees). You can print results with the "PrintScreen" button of a 101 keyboard under Windows OS.
[return to text]

Return to [Olmec Alignments] chapter.
Return to [table] of contents.

Calculations are in Unix bc notation, where ^ denotes exponentiation; the functions (a)rctangent, (s)ine, and (c)osine use radians; angle conversions to radians or degrees by the divisors rad=.017+ and deg=57.2+; other functions are shown as f( );
units: million == 1,000,000; billion == 1,000,000,000;
one AU == 93,000,000 miles.

URL of this page: http://saturniancosmology.org/align.php
This page last updated: Wednesday, February 24th, 2010
Size of this page: 22149 words.

Feel free to email me with any comments or corrections. Find an email [address] here.
Copyright © 2010 Jno Cook
Permission is granted to copy, distribute and/or modify this document under the terms and licence of Creative Commons. A copy of the license is included on the page entitled
Creative Commons Deed 2.5

Recovering the Lost World -- Jno Cook Appendix C: Mesoamerican Ceremonial Center Alignments.

Expected Dates

Izapa

Edzná

San Lorenzo Tenochtitlan

San Lorenzo site identity...

San Lorenzo era marker...

San Lorenzo additional notes...

La Venta

La Venta site identity...

La Venta era marker...

La Venta notes...

Tres Zapotes

Tres Zapotes site identity...

Tres Zapotes era markers...

Tres Zapotes notes...

Laguna De Los Cerros

Cerro De La Mesas

Cerro De La Mesas site identity...

Cerro De La Mesas era marker...

Cerro De La Mesas discussion...

Remojadas

Remojadas site identity...

Remojadas era markers...

Remojadas notes...

Zempoala

Zempoala site identity...

Zempoala era markers...

Zempoala notes...

Teotihuacan

Teotihuacan site identity...

Teotihuacan era marker...

Tlatilco

Tlatilco site identity...

Tlatilco era markers...

Tlatilco notes...

Tizatlan

Tizatlan site identity...

Tizatlan era markers...

Cuicuilco

Cuicuilco site identity...

Cuicuilco era markers...

prior era...

current era...

Cuicuilco notes...

Tlapacoya

Tlapacoya site identification...

Tlapacoya site identification...

Cholula

Cholula site identification...

Cholula era markers...

Cholula notes...

Monte Alban

Endnotes

Recovering the Lost World -- Jno Cook
Appendix C: Mesoamerican Ceremonial Center Alignments.