![[logo]](eyecon.jpg)
Recovering the Lost World,
A Saturnian Cosmology -- Jno Cook
Appendix C: Site Alignments.
![[previous]](bp.gif)
![[table of contents]](bc.gif)
![[next]](bn.gif)
$Revision: 1.48 $ (align.php)
Contents of this appendix:
[Expected Dates]
[Izapa]
[Edzna]
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]
[Endnotes]
This file is linked from the chapter ["Olmec Alignments"];
it is primarily data, and well worth skipping.
No metric equivalents in this Appendix.
Site Alignments
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}). 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 a javascript program, [saturniancosmology.org/sun.html], 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, with a virtually imperceptible difference as the Sun nears the solstices. Documentation of "sun.html" in the following endnote. [note 1]
The distance between two locations can be found approximately from the latitudes and longitudes also, using the Pythagorean 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.
![[image:
sun.html output example]](bin/cap1.jpg)
[Image: sun.html output example. Kees Cook.]
![[image: Antipodal alignment example]](bin/align-antipodal.jpg)
[Image: Antipodal alignment example; plan view.]
The line of sight distance of a mountain can be found from sqrt(2 * 4000 * h), where "h" is the height in miles. The value of h is derived from 3.25 * H / 5280, where H is the height in meters. The figure "4000" is the radius of the Earth in miles. The figure "3.25" is the number of feet per meter. Line of sight distance 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. [note 2]
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 little sense. At a few locations this is used, however.
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 an "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."
Sunset in Degrees North of West for Various Dates For an axial inclination of ... 30 degrees 23.5 degrees End of era 3114 BC, August 12 19.9 degrees 14.9 degrees End of era 2349 BC, September 8 6.6 degrees 5.2 degrees End of era 1492 BC, April 19 15.3 degrees 12.0 degrees End of era 747 BC, February 28 11.0 degrees 8.6 degrees Solstice before 685 BC 32.0 degrees 25.0 degrees Plasmoid start, July 9, 685 BC 30.4 degrees 23.7 degrees Jupiter plasmoid, July 14 29.4 degrees 23.0 degrees Delivery of plasmoid, July 26 26.6 degrees 20.7 degrees Zenithal, August 9 - 14 20.3 degrees * July 23 - Aug 1 20.3 degrees * * varies with latitude
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 the chapter "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 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 flare-up 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.
I have added Volcan 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 Tacana. But the site axis (16 degrees e of n, thus 74 degrees n of e) does not point to Tacana (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.
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]](bin/align-izapa.jpg)
[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. Malmstrom 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 solstitial alignment. The volcano Tajumulco is held to represent a solstitial 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 degrees n of e. It is off by more than 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.
Edzna
![[image: Edzna alignments]](bin/align-edzna.jpg)
[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.
Malmstrom 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 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 flare-up 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
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]](bin/align-sanlorenzo.jpg)
[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 be 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 flare-up 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
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]](bin/align-laventa.jpg)
[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 site identity angles shown above (19.36 and 19.50 degrees n of w) also locate a sunset on August 13 before 685 BC. 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 dates of April 19th, now could be assigned to point to the 3114 BC era-ending date of August 13th at 15.49 degrees north of west.
Malmstrom, 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 of the Stirling compound, but the alignment could point directly to a northwest sunset (15.49 degrees) for August 12 of the current era. Malmstrom wanted to use this to establish an "August 13" alignment. This is unlikely to be so because the "Stirling Compound" is older than 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 flare-up 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
Tres Zapotes was founded sometime 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, 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 an 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 flare-up 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
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 flare-up 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
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 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 there 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 solstitial 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 solstitial 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 flare-up 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, 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), 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 flare-up 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
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 an 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 flare-up 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
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]](bin/align-teotihuacan.jpg)
[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 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 flare-up 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
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 a 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 alignments 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 equinoctial site identity, suggest that this is a fairly old site, but established after 747 BC.
Tizatlan
An archaeological site in the valley of Mexico.
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 flare-up 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
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 flare-up 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, 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 flare-up 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 flare-up 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, 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, 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 flare-up 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, 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 flare-up 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 the chapter "Olmec Alignments."
Endnotes
The short javascript program is available on line which can be used to find 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. At [saturniancosmology.org/sun.html].
Documentation: The program uses elements of 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 two 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, a sunset will differ from sunrise by about a half degree at most (but considerably less near the solstices). Except for this, the program should be fairly accurate. Small differences in latitude or axial inclination will not significantly affect the results.
The angles are for sunrises. To find the equivalent sunset angle, find the difference between the current sunrise and the next day. One half of this difference, when added to a sunrise angle, will give a good approximation for the corresponding sunset angle in the tropics.
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 23.45
degrees (the actual value).
[return to text]
The line of sight distance is at a right angle to the radius of the Earth. Thus we have from the pythagorian:
hypotenuse squared = leg1 squared + leg2 squared
(r + h)^2 = r^2 + d^2
r^2 + 2rh + h^2 = r^2 + d^2
solving for d, d^2 = r^2 + 2rh + h^2 - r^2.
Since h is a fractional mile, h^2 is very small compared to 2rh,
and can be neglected.
[return to text]
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( );
tan( )=s( )/c( )
units: million == 1,000,000; billion
== 1,000,000,000;
AU == 93,000,000 miles.
URL of this page: http://saturniancosmology.org/align.php
This page last updated: Tuesday, May 2nd, 2017
Size of this page: 15212 words.
Feel free to email me with any comments or corrections. Find an email [address] here.
Copyright © 2001 - 2024 Jno Cook
Permission to reprint in whole or in part is granted,
provided full credit is given.