PowerPoint

The Marriage of Heaven and Earth:
Images and Representations of the Sky in Sacred Space
2014 Sophia Centre Conference, Bath Royal Literary and Scientific Institution, 28-29 June 2014, Bath, England
“Zenith Sun as Organizing Principle in the Constructed Sacred Space
and Calendrics of Central Mexico”
Harold H. Green
Maya Exploration Center Research Associate
Fundamental Differences between
Tropical and Temperate Zone Astronomy
75º
105º
285º
Tropical systems of ancient astronomy embody
a “reference system consisting of zenith and
nadir as poles and the horizon as a fundamental
reference circle.”
255º
“Zenith [is] the fundamental reference pole.”
This is “in remarkable contrast to the celestial
pole-equator (or ecliptic) systems ... of the
temperate zone.”
Image courtesy of Alonso Mendez
Aveni, Tropical Archaeastronomy, Science 213(4504)(1981)
Orientation of the Pyramid of the Sun, Teotihuacán, Mexico
Street Grid at Teotihuacán
Sunset on
Apr 30, Aug 13
Pyramid of the Sun
After Millon, René, The Teotihuacan Map, Map 1 (1973)
Latitude 19º41’N, Longitude 98º51’W
Photo by Hal Green 2007
Teotihuacán in relation to the 260-day band at ~15º N
Teotihuacán at ~20º N
260-day latitudinal band at ~15º N
Propositions of Johanna Broda relating
to zenith observations in Mesoamerica
1. “Conspicuous Calendrical Properties”
Solar events in the 260-day band have “conspicuous calendrical properties,”
being separated by multiples of 13 and 20 days, the factors of the 260-day
calendar of Central Mexico, the tonalpohualli.
2. “Shared Knowledge” of these “Calendrical Properties”
Awareness of these calendrical properties was likely widely shared
throughout Mesoamerica.
3. “Horizon Reference System”
Central Mexicans used a horizon reference system by which the most
important dates - the precise days of the solar cycle – were tracked
on the local horizon.
Lake Atitlán
Chocolá
Antigua
“Calendrical Properties”
of the 260-day Band
Illustrated with horizon images
from the Preclassic site of
Chocolá, Guatemala
Cerro “2665”
Cerro Paquisís
Volcan Atitlán Volcan Fuego
Photo by Hal Green 2006
Photo by Byron Lemus 2006
Cerro “2665”
Zenith passage
sunrise at Chocolá
April 30, 2006
Zenith Passage
Apr 30, Aug 13
Cerro “2665”
Cerro Paquisís
Photo by Hal Green 2006
Photo by Byron Lemus 2006
Cerro “2665”
Zenith passage
sunrise at Chocolá
April 30, 2006
Zenith Passage
Apr 30, Aug 13
Cerro “2665”
Cerro Paquisís
Nadir Passage
Feb 9, Nov 1
Volcan Fuego
Photo by Hal Green 2006
Photo by Byron Lemus 2006
Cerro “2665”
Zenith passage
sunrise at Chocolá
April 30, 2006
Zenith Passage
Apr 30, Aug 13
Nadir Passage
Feb 9, Nov 1
80 days
Cerro “2665”
Cerro Paquisís
Volcan Fuego
Photo by Hal Green 2006
Photo by Hal Green 2006
Zenith Passage
Apr 30, Aug 13
Nadir Passage
Feb 9, Nov 1
Equinox
Mar 21, Sep 22
40 days
Cerro Paquisís
40 days
Volcan Atitlán
Photo by Hal Green 2006
Stelae 12-10 Baseline at Copán
Stela 10
Equinox
Mar 21, Sep 22
Stela
12
Zenith/Equinox
Midpoint
Apr 10, Sep 2
Photo by Hal Green 2006
Zenith Passage
Apr 30, Aug 13
20 d
Nadir Passage
Feb 9, Nov 1
20 d
Cerro Paquisís
40 d
Volcan Atitlán
Photo by Hal Green 2006
Photo by Hal Green 2006
Stelae 12-10 Baseline at Copán
Stela 10
Equinox
Mar 21, Sep 22
Zenith/Equinox
Midpoint
Apr 10, Sep 2
Nadir/Equinox
Midpoint
Mar 1, Oct 12
Zenith Passage
Apr 30, Aug 13
20 d
Stela
12
Photo by Hal Green 2006
Nadir Passage
Feb 9, Nov 1
20 d
Cerro Paquisís
20 d
20 d
Volcan Atitlán
Photo by Hal Green 2006
Photo by Hal Green 2006
13-day (Trecena) Marker
May 13 is 13 days after the April 30 zenith
passage and 39 (3x13) days before the summer
solstice.
July 31 is 13 days before the August 13
zenith passage that begins a new 260-day
cycle to the winter solstice and back to the
April 30 zenith passage.
Photo by Byron Lemus 2006
13-day Marker
Zenith ±13 days
May 13, July 31
Zenith Passage
Apr 30, Aug 13
13 d
Winter Solstice
Dec 21
260 d
Cerro “2665”
Photo by Hal Green 2006
“Calendrical Properties” of the 260-day Latitudinal Band
Zenith/Equinox
Midpoint
Apr 10, Sep 2
13-day Marker
Zenith ±13d
May 13, July 31
Zenith
Apr 30, Aug 13
13 d
Nadir/Equinox
Midpoint
Mar 1, Oct 12
Equinox
Mar 21, Sep 22
20 d
20 d
Nadir
Feb 9, Nov 1
20 d
40 d
20 d
40 d
80 d
130 d
130 d
= 260 days
Winter Solstice
Jun 21, Dec 21
“Calendrical Properties” of the 260-day Latitudinal Band
Zenith/Equinox
Midpoint
13-day Marker
Zenith
Reference Pole
13 d
Nadir/Equinox
Midpoint
Nadir
Reference Pole
Equinox
20 d
20 d
20 d
40 d
20 d
40 d
80 d
130 d
130 d
= 260 days
Winter Solstice
Jun 21, Dec 21
The “Horizon Reference System”
Orientations systematically documented by
Ivan Šprajc (2001) at 37 Central Mexico sites:
8 Preclassic,
9 Classic and
20 Postclassic sites.
These Central Mexico orientation data establish
that the “horizon reference system” proposed by
Broda is defined by the “calendrical properties”
of the 260-day band.
Photo © wordlessTech 2011
Pyramid of the Sun
Architectural Orientations of the Pyramid of the Sun, Teotihuacán
(reported by Šprajc 2001)
Structure
Azimuth, A
Pyramid of the Sun
105º45'±1º
285º45'±1º
Height, h Declination, δ
2º01'±5'
0º22'±10'
Dates in bold exactly match dates of 260-day band events
-14º11'±1º
14º48'±1º
Dates
Feb 10, Oct 30±3d
Apr 30, Aug 13±3d
Analysis of Reported Dates
(consistent with criteria established by Šprajc)
1. Architectural orientations: mean azimuth values of east-west lines of structures.
Dates of calendrically significant 260-day band events within the stated
margin of error for reported dates are assumed to be the dates intended
to be marked by the orientation.
Reported dates
Feb 10, Oct 30 ±3d
Dates within
Margin of error
Feb 9, Nov 1
2. All dates: architectural and horizon orientations.
“... [A] tolerance of ± 1 day should be considered for all dates”
due to the intercalation of leap days in the Gregorian calendar system.
(Šprajc 2001: 159 Note 1)
Photo © wordlessTech 2011
Pyramid of the Sun
Architectural Orientations of the Pyramid of the Sun, Teotihuacán
(within reported margin of error)
Structure
Azimuth, A
Pyramid of the Sun
105º45'±1º
285º45'±1º
Height, h Declination, δ
2º01'±5'
0º22'±10'
Dates in bold exactly match dates of 260-day band events
-14º11'±1º
14º48'±1º
Dates
Feb 9, Nov 1
Apr 30, Aug
Postclassic site architectural orientations marking dates separated by 20 days (or multiple)
Site
Structure
Reported dates marked
by Orientation
260-day Band
Dates within
Margin of Error
Dates within
Solar Event
±1 day Tolerance within the 260-day Band
El Corral
Feb 27, Oct 14±1d
Feb 28, Oct 13
Structure C
Apr 30, Aug 13±2d
Apr 30, Aug 13
Zenith
Tenayuca
Pyramid and altars
Feb 8, Nov 2±1d
Feb 9, Nov 1
Nadir
Huexotla
El Circular II (Ehecatl)
Feb 10, Nov 1±2d
Feb 9, Nov 1
Nadir
Santa Maria I (Str. A)
Feb 8, Nov 2±1d
Feb 9, Nov 1
Nadir
C. Tlaloc
C. La Malinche
Feb 9, Nov 2
Feb 9, Nov 2
Calixtlahuaca
Templo de Ehecatl
Mar 19, Sep 24±2d
Mar 22, Sep 20±2d
Mar 21, Sep 22
Mar 21, Sep 22
Equinoxes
Equinoxes
Yautepec
Palace, early
Feb 8, Nov 2±2d
Feb 9, Nov 1
Nadir
C. de los Idoles
Str. II
Feb 12, Oct 30±2d
Feb 10, Nov 1
Malinalco
Str. II
Apr 13, Aug 29±?
Apr 10, Sep 2
Str. IV
Feb 7, Nov 3±1d
Feb 8, Nov 2
El Tepozteco
Templo
Feb 10, Oct 31±3d
Feb 9, Nov 1
Tecoaque
Templo de Ehecatl
Feb 12, Oct 30±2d
May 1, Aug 11±2d
Feb 10, Nov 1
Apr 30, Aug 13
Texcotzingo
Area D
Mar 1, Oct 13±1d
Mar 1, Oct 12
Nadir/Equinox Midpoint
Area F
Apr 10, Sep 3±?
Mar 3, Oct 10±?
Apr 10, Sep 2
Mar 1, Oct 12
Zenith/Equinox Midpoint
Nadir/Equinox Midpoint
T. Mayor
Mar 1, Oct 12±1d
Mar 1, Oct 12
Nadir/Equinox Midpoint
Templo Calendarico
Mar 4, Oct 9±2d
Apr 8, Sep 2±2d
Mar 2, Oct 11
Apr 10, Sep 2
Mar 1, Oct 12
Nadir/Equinox Midpoint
Zenith/Equinox Midpoint
Templo Mayor, Stage II
Mar 3, Oct 10±1d
Apr 9, Sep 1±1d
Mar 2, Oct 11
Apr 10, Sep 2
Mar 1, Oct 12
Nadir/Equinox Midpoint
Zenith/Equinox Midpoint
Tula
Tlatelolco
Templo Mayor,
Tenochtitlan
Dates in bold exactly match dates of 260-day band events
Mar 1, Oct 12
Feb 9, Nov 1
Feb 9, Nov 1
Nadir/Equinox Midpoint
Nadir
Nadir
Zenith/Equinox Midpoint
Feb 9, Nov 1
Nadir
Nadir
Feb 9, Nov 1
Nadir
Zenith
Tecoaque, Tlaxcala -- Temple of Ehécatl (Postclassic)
Temple of Ehécatl
Tecoaque (Postclassic) -- Temple of Ehécatl -- East Horizon
T. Ehécatl 105º00’±30’
Nadir
Feb 9, Nov 1
C. San Nicolás S
Temple of Ehécatl
Tecoaque (Postclassic) -- Temple of Ehécatl -- West Horizon
T. Ehécatl 285º00’±30’
Zenith
Apr 30, Aug 13
C. Chame
Temple of Ehécatl
Tecoaque (Postclassic) -- Temple of Ehécatl -- West Horizon
C. la Cantera 277º03’
Zenith/Equinox Midpoint
Apr 10, Sep 2
T. Ehécatl 285º00’±30’
Zenith
Apr 30, Aug 13
C. Chame
Temple of Ehécatl
Tx-TF-10 (Parsons) -- Mound 119 (Preclassic) -- East horizon
C. Tlamacas 99º14’
Nadir/Equinox Midpoint
Mar 1, Oct 12
Mound 119
7.9º
14.7º
Zenith
Apr 30
Aug 13
14
Zenith
Reference Pole
Zenith/Equinox
Midpoint
Apr 10
Sep 2
20 d
20 d
8
Z/E Midpoint
Reference Pole
-7.5º
Nadir/Equinox
-14.5º
Equinox
Nadir
Midpoint
Mar 21
Feb 9
Mar 1
Sep 22
Nov 1
Oct 12
20 d
20 d
0º
7
11
20
N/E Midpoint
Nadir
Reference Pole Reference Pole
Frequency of orientations marking dates of 260-day band events
at 20-day intervals between the zenith and nadir reference poles
60
Teotenango, Mexico -- Structure 1A (Postclassic)
Str. 1A
Str. 1B
Teotenango, Mexico (Postclassic) -- East Horizon
C. Zempoala 105º46’
Nadir Passage
Feb 9, Nov 1
Str. 1 B
Str. 1A
Teotenango, Mexico (Postclassic) -- East Horizon
C. Mateo 70º56’
Zenith ±13d
May 13, Jul 31
Cerro ? 95º42’
Nadir ±26d
Mar 7, Oct 6
C. Zempoala 105º46’
Nadir Passage
Feb 9, Nov 1
Str. 1 B
Str. 1A
C. Mateo 70º56’
Zenith ±13d
May 13, Jul 31
Cerro ? 95º42’
Nadir ±26d
Mar 7, Oct 6
Str. 1 B
Str. 1A
Apr 30
Aug 13
May 13
Jul 31
13 d
Zenith
Reference Pole
Mar 21
Sep 22
Feb 9
Nov 1
Mar 7
Oct 6
26 d
Nadir
Reference Pole
Cerro de la Estrella (Postclassic), Mexico
C. Telapón 85º32’
Zenith ±26d
Apr 4, Sep 8
C. Papayo 95º32’
Nadir ±26d
Mar 7, Oct 6
C. Guadalupe 101º50’±15’
Nadir ±13d
Feb 22, Oct 19
C. Tláloc 79º09’
Zenith ±13d
Apr 17, Aug 26
Apr 30
Aug 13
Mar 21
Sep 22
Apr 17
Aug 26
Apr 4
Sep 8
Feb 9
Nov 1
Mar 7
Oct 6
Feb 22
Oct 19
13 d
13 d
26 d
Zenith
Reference Pole
26 d
Nadir
Reference Pole
7.9º
-7.5º
Zenith
Zenith/Equinox
Midpoint
Equinox
Nadir/Equinox
Midpoint
Apr 30
Aug 13
Apr 10
Sep 2
Mar 21
Sep 22
Mar 1
Oct 12
14.7º
20 d
20 d
18.3º
21.1º
May 26 May 13
Jul 18 Jul 31
1
0º
20 d
-14.5º
Nadir
Feb 9
Nov 1
20 d
10.4º
5.7º
-5.2º
-10.1º
-18.3º
Apr 17
Aug 26
Apr 4
Sep 8
Mar 7
Oct 6
Feb 22
Oct 19
Jan 27 Jan 14
Nov 14 Nov 27
13 d
13 d
13 d
13 d
26 d
26 d
26 d
26 d
7
12
Zenith
Reference Pole
9
9
12
1
Nadir
Reference Pole
Frequency of orientations that mark dates matching
dates of 260-day band events at 13- and 26-day intervals
from the zenith and nadir reference poles
-21.2º
0
51
“Mirror opposite” orientations
at Teotenango and Xochitécatl
Zenith/Equinox
Midpoint
Apr 10
Sep 2
Nadir/Equinox
Midpoint
Mar 1
Oct 12
Str. 1A
Postclassic Structure 1A at Teotenango oriented to sunsets
on Mar 28, Sep 15 behind V. Nevado de Toluca on W horizon
Sunset
orientation
of Str. 1A,
Teotenango
Mar 28
Sep 15
13 d
Str. E1
Preclassic Structure E1 at Xochitécatl oriented to sunrises
on Mar 14, Sep 29 behind V. La Malinche on E horizon
Sunrise
orientation
of Str. E1,
Xochitécatl
Mar 14
Sep 29
13 d
7.9º
-7.5º
Zenith
Zenith/Equinox
Midpoint
Equinox
Nadir/Equinox
Midpoint
Apr 30
Aug 13
Apr 10
Sep 2
Mar 21
Sep 22
Mar 1
Oct 12
14.7º
0º
20 d
20 d
20 d
-14.5º
Nadir
Feb 9
Nov 1
20 d
21.1º
18.3º
10.4º
5.7º
-5.2º
-10.1º
-18.3º
-21.2º
May 26
Jul 18
May 13
Jul 31
Apr 17
Aug 26
Apr 4
Sep 8
Mar 7
Oct 6
Feb 22
Oct 19
Jan 27
Nov 14
Jan 14
Nov 27
13 d
13 d
13 d
13 d
26 d
26 d
26 d
26 d
16.6º
12.4º
2.9º
-2.4º
-12.3º
-16.2º
May 6
Aug 7
Apr 23
Aug 20
Mar 28
Sep 15
Mar 14
Sep 29
Feb 16
Oct 25
Feb 3
Nov 7
13 d
13 d
13 d
26 d
26 d
5
9
Z/E Midpoint 13
Reference Pole
13 d
7
N/E Midpoint 1
Reference Pole
3
Frequency of orientations that mark dates matching dates of 260-day band events at
13- and 26-day intervals from the zenith/equinox and nadir/equinox midpoint reference poles
38
Additional Adjustment to Šprajc Orientation Data
Teotenango
Str. 1A
Structure or
Horizon Marker
Declination,
δ
Reported Dates
Dates within
Dates within
Margin of Error ±1d Tolerance
18º20’±1º
May 12, Jul 31±4d
May 13, Jul 31
May 13, Jul 31
13d after NZP/before SZP
C. Mateo (1A&1B) 18º33’
May 14, Jul 31
May 14, Jul 31
May 13, Jul 31
13d after NZP/before SZP
18º03’
May 12, Aug 2
May 12, Aug 2
May 13, Aug 1(+1)
13d after NZP/before SZP(+1d)
Dates within
Margin of Error
Dates within
±1d Tolerance
Str. 1B
C. Mateo (Str 2D)
Structure or
Declination,
Horizon Marker
δ
Reported Dates
Structure 1A
-10º15’±35’
12º02’±35’
Feb 22, Oct 19±2d Feb 22, Oct 19
Apr 21, Aug 21±2d Apr 23, Aug 20
Structure 2D
-11º09’±10’
12º56’±15’
Feb 19, Oct 22±1d Feb 20, Oct 21
Apr 24, Aug 19±1d Apr 23, Aug 20
Dates in bold exactly match dates of 260-day band events
Feb 22, Oct 19
Apr 23, Aug 20
Solar Event
within 260-day Band
Solar Event
within 260-day Band
13d after NNP/before SNP
13d after NZP/E/before SZP/E MPs
Feb 21(-1), Oct 20(+1) 13d after NNP/before SZP (±1d)
13d after NZP/E/before SZP/E MPs
Apr 23, Aug 20
Percentage of Dates Marked by Central Mexico Orientations
Exactly Matching Dates of 260-day Band Events
60
+
Dates of reference
poles, separated
by 20 days
51
+
38
Dates separated by Dates separated by
13 or 26 days from 13 or 26 days from
Zenith and Nadir
Midpoint
reference poles
reference poles
+
39
= 188/231* = 81.4%
Dates within ±1 day
of dates that exactly
match dates of 260day band events
* Not counting solstices (16), local zenith passages (6) or non-solar (4)
Central Mexico Horizon Reference System
14.7º
Sun Direction
N
S
7.9º
Apr 30
Aug 13
0º
Apr 10
Sep 2
Mar 21
Sep 22
20 d
21.1º
18.3º
May 26 May 13
Jul 18 Jul 31
20 d
-7.5º
-14.5º
Mar 1
Oct 12
Feb 9
Nov 1
20 d
20 d
10.6º
5.7º
-5.2º
-10.1º
Apr 17
Aug 26
Apr 4
Sep 8
Mar 7
Oct 6
Feb 22
Oct 19
-18.3º
Jan 27 Jan 14
Nov 14 Nov 27
13 d
13 d
13 d
13 d
26 d
26 d
26 d
26 d
Nadir
Reference Pole
Zenith
Reference Pole
16.6º
12.4º
2.9º
-2.4º
-12.3º
-16.2º
May 6
Aug 7
Apr 23
Aug 20
Mar 28
Sep 15
Mar 14
Sep 29
Feb 16
Oct 25
Feb 3
Nov 7
13 d
13 d
26 d
Zenith/Equinox Midpoint
Reference Pole
13 d
13 d
26 d
Nadir/Equinox Midpoint
Reference Pole
-21.2º
Central Mexico Horizon Reference System
Apr 30
Aug 13
20 d
20 d
20 d
20 d
13 d
13 d
13 d
13 d
26 d
26 d
26 d
26 d
Nadir
Reference Pole
Zenith
Reference Pole
13 d
13 d
26 d
Zenith/Equinox Midpoint
Reference Pole
13 d
13 d
26 d
Nadir/Equinox Midpoint
Reference Pole
Astronomical Chamber 1 at Teotihuacán
May 18, Jul 24
First direct sunlight enters: April 30
Last direct sunlight enters: August 13
(260-day band zenith passages)
Morante (1996)
The chamber also marks dates of:
February 9 and November 1
(260-day band nadir passages)
Soruco Sáenz (1991)
The stela enables determination of the days
of local zenith passage, May 18, July 24
From Broda 2006:191; Morante 1996; 2001:50
Zenith Tube at Xochicalco, Morelos
Construction enables precise determination of the
260-day band zenith passages and local zenith passages.
First direct sunlight enters: April 30
Last direct sunlight enters: August 13
Dates of the 260-day band zenith passages (red arrow).
On the dates of local zenith passage, direct sunlight
enters vertically (blue arrow).
Aveni and Hartung, Archaeoastronomy No. 3 (1981); diagram by H. Hartung
Pyramid of the Niches, El Tajín, Veracruz, Mexico
First direct sunlight enters: April 30
Last direct sunlight enters: August 13
© MorGwenn 2013-2014
Morante, La Pirámide de los Nichos de Tajín, Fig. 52,
based on diagram by J. Sanchez and J. Brüggemann
Direction of solar rays
Conclusions: Zenith sun as organizing principle
Constructed sacred space:
1. Sites were located, and structures within sites were oriented, according to a horizon
reference system;
2. That system was defined by the unique “calendrical properties” of the ~15º latitude;
3. The zenith passages comprised the “fundamental reference pole” of that system;
4. The zenith sun was thus an organizing principle of sacred space in Central Mexico.
Calendrics:
1. Subterranean chambers and other devices were capable of precise measurement of the
actual dates of the ~15º zenith passages;
2. This, in conjunction with the horizon reference system, enabled astronomers to maintain
concordance of the 260-day sacred count with the tropical year.
3. The zenith sun was thus also an organizing principle of calendrics in Central Mexico.
Acknowledgments
I wish to thank each of the following:
Nicholas Campion and the staff of the Sophia Centre for inviting me to
participate in the 2014 conference “The Marriage of Heaven and Earth;”
Johanna Broda for the inspiration to dig deeper into the importance of
zenith passage in Mesoamerica;
Ivan Šprajc for the extensive and systematically documented corpus of
orientation data that made this study possible;
Gerardo Aldana, Edwin L. Barnhart and Christopher Powell for helpful
comments on early versions of this presentation.