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Hans Jelitto

Institute of Advanced Ceramics

Institute Meeting, TUHH, March 3, 2020

1. Introduction

2. Planetary correlation

3. Quantitative analysis

4. Including the Sun

5. Temple of Quetzalcoatl

6. Geographical alignment

7. Discussion

8. Summary

Outline 2

(After the talk at the TUHH, the presenta-

tion has been slightly updated, extended,

and an explanatory text has been added.

2nd Ed., July 2022)

(Figures on front page: Quetzalcoatl, God of Wind and Wisdom, as depicted in the Codex Borbonicus,

taken from Wikipedia. For more information concerning licenses, see the Appendix on the last slide.)

Conference in Cancun in 2005 (IMRC-2005) with

subsequent visit of some archaeological sites in Mexico

4

Pyramid site of Teotihuacán

1. Introduction Display board: INAH, Instituto Nacional

de Antropología e Historia, México (see next slide)

Viewpoint (on the Adosada platform) and

viewing direction of the photo to the left

The Moon Pyramid is not quadratic but

elongated. Why? – This will be answered.

(SECRETARIA DE CULTURA.-INAH.-MEX. Reproduction Authorized by the Instituto Nacional de Antropología e Historia, México)

Pyramid of the Sun

Pyramid of the Moon

Remark: It seems that several structures and pyramid-like platforms are hidden under the grass and trees.

1. Introduction 8

Feathered Serpent Pyramid Adosada platform

Solid barriers on the

Avenue of the Dead

View to the Southwest from the Pyramid of the Sun

A closer look on four

of the solid barriers

Satellite images:

© 2017 HERE, 2014

DigitalGlobe, INEGI.

a) The six barriers on

the Avenue of the Dead

and the Pyramid of the

Sun.

b) Simplified drawing

of the barriers.

c) The Citadel including

the Feathered Serpent

Pyramid and the Adosa-

da platform – also called

Temple of Quetzalcoatl.

According to modern

research, the whole site

was built in the first two

centuries after Christ.

1. Introduction

12

The six barriers with heights of

around one to three meters are a

strange phenomenon. They are

obstacles that people must climb

over when walking along the

fantastic avenue. They appear to

not make any sense. – But now,

a question to the audience:

What does the whole site look

like?

To us, it looks like an axis or

a scale with the barriers being

markers along the scale. The

barriers are highlighted in red

(Fig. b).

2. Planetary correlation

Satellite image from Google

Maps: © 2014 Cnes/Spot Image,

DigitalGlobe

2. Planetary correlation

When considering the planets,

we have a problem in that we

have six barriers and eight

planets.

13

Satellite image from Google

Maps: © 2014 Cnes/Spot Image,

DigitalGlobe

American civil engineer

Hugh Harleston Jr.

(1925 – 2013):

“Teotihuacan represents

relations concerning the

Earth and our solar

system.”

2. Planetary correlation

When considering the planets,

we have a problem in that we

have six barriers and eight

planets.

However, the Rio San Juan

and the Pyramid of the Sun

provide two additional posi-

tions on the main axis.

13

Satellite image from Google

Maps: © 2014 Cnes/Spot Image,

DigitalGlobe

American civil engineer

Hugh Harleston Jr.

(1925 – 2013):

“Teotihuacan represents

relations concerning the

Earth and our solar

system.”

14

2. Planetary correlation The approach to explain the positions of the barriers

The positions are localized mainly on the east side of the Avenue of the Dead defining the

main axis. Otherwise, the position of the planet Earth on the scale would not be correct.

* Pyramid or temple position (off-axis)

† Sum or difference of two distances

15

3. Quantitative analysis Positions in Teotihuacán

The distances in meters were calculated

using GPS coordinates. (The correspond-

ing equations can be found in [1] on

pages 58–59. Concerning Teotihuacán, its

altitude of about 2300 m above mean sea

level must be taken into account.)

The lengths in millimeters in the last

column were precisely measured with

a ruler on a computer monitor showing

a satellite image. These are called “map

data.”

Geographical coordinates are

taken from Google Maps and

HERE WeGo.

[1] Jelitto, H.: Planetary Correlation of the Giza Pyramids – P4 Program

Description. ResearchGate (2015), DOI: 10.13140/RG.2.1.5135.2164

b=a⋅

√

1−e

2

Some orbital elements

●semi-major axis a

●eccentricity e

●semi-minor axis

●perihelion distance

●aphelion distance

16

q=a⋅(1−e)

Q=a⋅(1+e)

3. Quantitative analysis Astronomical data

17

French planetary theory VSOP: Variations

Séculaires des Orbites Planétaires

VSOP82 [3]

P. Bretagnon

VSOP87

[4]

orbital

elements [5]

P. Bretagnon,

G. Francou J. Meeus

[2] Lang, K. R.: Astrophysical Data: Planets and Stars. Springer New York, … (1992)

[3] Bretagnon, P.: Théorie du mouvement … – VSOP82. Astron. Astroph. 114 (1982) 278

[4] Bretagnon, P., Francou, G.: Planetary Theories … – VSOP87, Astron. Astroph. 202 (1988) 309

[5] Meeus, J.: Astronomical Algorithms. 1st Ed., Willmann-Bell Inc., Richmond, Virginia (1991) 197

[6] Brown, T. M., Christensen-Dalsgaard, J.: Accurate D. …, Astrophys. J. 500, L195-L198 (1988)

(last 4 columns of table)

Semi-major axes a and eccentricities e (three alternatives)

3. Quantitative analysis Astronomical data

Aphelion distances Q

18

Position on the avenue [m]

The distances of the planets from

the Sun (AD 200) do not fit be-

cause they increase exponentially

when moving towards the outer

planets.

Instead, their logarithms work

very well. The blue trend line

represents a linear regression fit.

3. Quantitative analysis Correlation between planets and barriers

Mercury

Venus

Earth

Mars

Jupiter

Saturn

Uranus

Neptune

log (Q/km)

It seems reasonable to place the origin of the horizontal axis at the Pyramid of the Moon.

Semi-major axes a

19

Position on the avenue [m]

The fit becomes better.

3. Quantitative analysis Correlation between planets and barriers

Mercury

Venus

Earth

Mars

Jupiter

Saturn

Uranus

Neptune

log (a/km)

It seems reasonable to place the origin of the horizontal axis at the Pyramid of the Moon.

Perihelion distances q

20

Position on the avenue [m]

The fit is almost perfect and the

coefficient of determination is

close to 1 when the perihelion

distances are used.

Note that the coefficient of

determination is a measure that

means the correlation is not a co-

incidence. So, if R approaches 1,

the probability that we have an

accidental correlation is close to

zero.

2

3. Quantitative analysis Correlation between planets and barriers

Mercury

Venus

Earth

Mars

Jupiter

Saturn

Uranus

Neptune

log (q/km)

It seems reasonable to place the origin of the horizontal axis at the Pyramid of the Moon.

R=n

∑

d

i

p

i

−

∑

d

i

⋅

∑

p

i

√

n

∑

d

i

2

−

(

∑

d

i

)

2

⋅

√

n

∑

p

i

2

−

(

∑

p

i

)

2

¯

R

2

=1− (1−R

2

)⋅ n−1

n−s

R2 = coefficient of determination (Bestimmtheitsmaß)

R = correlation coefficient

di = positions (distances) on the avenue

pi = logarithms of the planetary distances (q, a, Q)

n = number of positions (i = 1…n)

R2 = adjusted coefficient of determination [7]

s = number of free model parameters

(Linear regression means s = 2.)

21

Position d on the avenue [m]

3. Quantitative analysis Used equations Combined representation of the three options

R2 is almost identical to R2 (0.99955

instead of 0.99962). So, we use R2.

[7] Theil, H.: Economic Forecasts and Policy. Amster-

dam: North-Holland Publishing Co. XXXI (1958)

22

But be careful: Photographic/per-

spective distortion means that the

positions of the pyramids are mostly

not their top. The GPS coordinates

are valid for the ground level.

The central pyramid position is:

1. the intersection of the diago-

nals of the pyramid base, or

2. the arithmetic mean of the

coordinates at the four corners

(for each of latitude and longi-

tude).

Satellite image: © 2017 HERE,

2014 DigitalGlobe, INEGI.

3. Quantitative analysis Pyramid of the Sun

The distance (yellow line) is about 214.8 m according to the GPS data, slide 15.

Satellite image: © 2014 Cnes/Spot

Image, DigitalGlobe

4. Including the Sun

First, we concentrate on the upper

question mark (right figure).

By moving further northward on

the avenue, there is no other ce-

lestial body except the Sun. Is

the Pyramid of the Moon another

marking on the main axis, asso-

ciated with the Sun?

If we look for a distance, mea-

sured from the solar center and

being characteristic for the Sun,

the solar radius seems obvious.

By including the logarithm of

this radius, the curve appears as

it is in the diagram on the next

slide.

?

23

?

24

The logarithm of the solar

radius (695508 km) is

exactly in line with the

data points of the planets

(perihelion distances).

The red point is calculated

by inserting the position of

the “barrier of the asteroids”

into Eq. (1).

(1)

Equation of the trend line:

log

(

q

km

)

=0.0024021⋅d

m+5.8280

4. Including the Sun Correlation including the eight planets + Sun

Position d on the avenue [m]

Remark: If we assume a hypothetical former planet at the position of the asteroids, the corresponding barrier yields

a perihelion distance of 2.353 AU (GPS) and 2.372 AU (map data), respectively, calculated for the year AD 200.

25

?

What about these numbers? In order to

simplify the equation, we replace the

human-made units of length with “nat-

ural” units. Thus, “km” is replaced by

the already-used solar radius and “m”

by the “Sun unit” (next two slides).

(1)

Equation of the trend line:

log

(

q

km

)

=0.0024021⋅d

m+5.8280

4. Including the Sun Correlation including the eight planets + Sun

Position d on the avenue [m]

Remark: If we assume a hypothetical former planet at the position of the asteroids, the corresponding barrier yields

a perihelion distance of 2.353 AU (GPS) and 2.372 AU (map data), respectively, calculated for the year AD 200.

4. Including the Sun Definition of the “Sun unit” 26

An eye-catching position is provided

by the central platform of the Plaza

de la Luna (Plaza of the Moon). So,

we define the “Sun unit” by the hor-

izontal distance from this platform

to the center of the Pyramid of the

Moon (Sun).

Satellite image: © 2020

Maxar Technologies

4. Including the Sun Definition of the “Sun unit” 27

Three base lines of the pyramid are

covered with rubble. So, one must

be careful when determining the po-

sition using the corners of the base.

However, it seems that, accidentally,

this satellite photograph was taken

from almost vertically above the

pyramid.

(Remark: The GPS coordinates for

the pyramid and the central platform

in the table of slide 15 belong to the

lower points on the main axis.)

Satellite image: © 2020

Maxar Technologies

log

(

q

R

Sun

)

=0.47322⋅d

u

Sun

−0.01431

28

(1)

Units: RSun = 695508 km [6], uSun = 197 m

⇒(2)

[6] Brown, T. M., Christensen-Dalsgaard, J.: Accurate Determination of

the Solar Photospheric Radius, Astrophys. J. 500, L195-L198 (1998)

4. Including the Sun Correlation: eight planets + Sun

log

(

q

km

)

=0.0024021⋅d

m+5.8280

Position d on the avenue [m]

log

(

q

R

Sun

)

=0.47322⋅d

u

Sun

−0.01431

28

(1)

Units: RSun = 695508 km [6], uSun = 197 m

⇒

(almost zero)

(2)

[6] Brown, T. M., Christensen-Dalsgaard, J.: Accurate Determination of

the Solar Photospheric Radius, Astrophys. J. 500, L195-L198 (1998)

4. Including the Sun Correlation: eight planets + Sun

This factor would vanish if it would be 1.

What else can we do?

?

log

(

q

km

)

=0.0024021⋅d

m+5.8280

Position d on the avenue [m]

(GPS)

(map)

29

(1)

Units: RSun = 695508 km [6], uSun = 197 m

⇒

⇒

or:

(2)

Base-3 logarithm:

4. Including the Sun Correlation: eight planets + Sun

(Remember: log3 x = log x/ log 3)

log

(

q

km

)

=0.0024021⋅d

m+5.8280

log

3

(

q

R

Sun

)

=0.99181⋅d

u

Sun

−0.02998

log

3

(

q

R

Sun

)

=1.00063⋅d

u

Sun

−0.02022

log

(

q

R

Sun

)

=0.47322⋅d

u

Sun

−0.01431

Position d on the avenue [m]

(GPS)

(map)

29

This leads to the basic equation (3):

(1)

Units: RSun = 695508 km [6], uSun = 197 m

⇒

⇒

or:

(2)

Base-3 logarithm:

4. Including the Sun Correlation: eight planets + Sun

(Remember: log3 x = log x/ log 3)

log

(

q

km

)

=0.0024021⋅d

m+5.8280

log

3

(

q

R

Sun

)

=0.99181⋅d

u

Sun

−0.02998

log

3

(

q

R

Sun

)

=1.00063⋅d

u

Sun

−0.02022

log

(

q

R

Sun

)

=0.47322⋅d

u

Sun

−0.01431

Position d on the avenue [m]

30

(GPS data)

R2 = 0.999804

i celestial body

0 Sun

1 Mercury

2 Venus

3 Earth

4 Mars

5 (Asteroids)

6 Jupiter

7 Saturn

8 Uranus

9 Neptune

(3)

(qi = perihelion distance, except q0 = RSun)

4. Including the Sun Correlation: eight planets + Sun

log

3

(

q

i

R

Sun

)

=d

i

u

Sun

, i =0, ...,9

31

(Map data)

R2 = 0.999904

i celestial body

0 Sun

1 Mercury

2 Venus

3 Earth

4 Mars

5 (Asteroids)

6 Jupiter

7 Saturn

8 Uranus

9 Neptune

(3)

(qi = perihelion distance, except q0 = RSun)

4. Including the Sun Correlation: eight planets + Sun

log

3

(

q

i

R

Sun

)

=d

i

u

Sun

, i =0, ...,9

31

3 · R = 4.56 ·10 km

8

Sun

9

q = 4.46 ·10 km

Neptune

9

(Map data)

8th planet Neptune

R2 = 0.999904

i celestial body

0 Sun

1 Mercury

2 Venus

3 Earth

4 Mars

5 (Asteroids)

6 Jupiter

7 Saturn

8 Uranus

9 Neptune

(3)

(qi = perihelion distance, except q0 = RSun)

4. Including the Sun Correlation: eight planets + Sun

log

3

(

q

i

R

Sun

)

=d

i

u

Sun

, i =0, ...,9

31

3 · R = 4.56 ·10 km

8

Sun

9

q = 4.46 ·10 km

Neptune

9

(Map data)

due to the “Sun unit”

8th planet Neptune

R2 = 0.999904

i celestial body

0 Sun

1 Mercury

2 Venus

3 Earth

4 Mars

5 (Asteroids)

6 Jupiter

7 Saturn

8 Uranus

9 Neptune

(3)

(qi = perihelion distance, except q0 = RSun)

4. Including the Sun Correlation: eight planets + Sun

(The Sun unit, uSun, was probably intended.)

log

3

(

q

i

R

Sun

)

=d

i

u

Sun

, i =0, ...,9

31

3 · R = 4.56 ·10 km

8

Sun

9

q = 4.46 ·10 km

Neptune

9

(Map data)

8th planet Neptune

R2 = 0.999904

Sun in the origin!

i celestial body

0 Sun

1 Mercury

2 Venus

3 Earth

4 Mars

5 (Asteroids)

6 Jupiter

7 Saturn

8 Uranus

9 Neptune

(3)

(qi = perihelion distance, except q0 = RSun)

4. Including the Sun Correlation: eight planets + Sun

(The Sun unit, uSun, was probably intended.)

due to the “Sun unit”

log

3

(

q

i

R

Sun

)

=d

i

u

Sun

, i =0, ...,9

log

3

(

q

i

R

Sun

)

=d

i

u

Sun

, i =0, ...,9

31

How would R2 change

if we consider the remote

past or future?

3 · R = 4.56 ·10 km

8

Sun

9

q = 4.46 ·10 km

Neptune

9

(Map data)

8th planet Neptune

R2 = 0.999904

Sun in the origin!

i celestial body

0 Sun

1 Mercury

2 Venus

3 Earth

4 Mars

5 (Asteroids)

6 Jupiter

7 Saturn

8 Uranus

9 Neptune

(3)

(qi = perihelion distance, except q0 = RSun)

4. Including the Sun Correlation: eight planets + Sun

due to the “Sun unit”

(The Sun unit, uSun, was probably intended.)

GPS data Map and GPS data

The semi-major axis a and eccentri-

city e as functions of time are derived

from VSOP82 by Jean Meeus [5].

Maximum of R2 (perih. distances):

99.985 % in 9930 BC (GPS data)

99.994 % in 9570 BC (map data)

32

4. Including the Sun R2 from 18 000 BC to AD 4000

[5] Meeus, J.: Astronomical Algorithms. Willmann-Bell Inc., Richmond, Virginia (1991) 197–204

Coefficient of determination R2

Coefficient of determination R2

Julian year Julian year

GPS data Map and GPS data

The semi-major axis a and eccentri-

city e as functions of time are derived

from VSOP82 by Jean Meeus [5].

Maximum of R2 (perih. distances):

99.985 % in 9930 BC (GPS data)

99.994 % in 9570 BC (map data)

The pyramid site is probably not so

old, but another theoretical possibil-

ity exists.

In principle, this could be a hint

from the master builders pointing

to an important event in the distant

past around 9900 to 9600 BC.

32

4. Including the Sun R2 from 18 000 BC to AD 4000

[5] Meeus, J.: Astronomical Algorithms. Willmann-Bell Inc., Richmond, Virginia (1991) 197–204

Coefficient of determination R2

Coefficient of determination R2

Julian year Julian year

33

?

Satellite image: © 2014 Cnes/Spot

Image, DigitalGlobe

5. Temple of Quetzalcoatl

Crossing the Rio San Juan

and following the Avenue of

the Dead southwards, we

reach the Temple of Quetzal-

coatl. The given planetary

correlation defines a precise

astronomical scale that can

be easily extended to larger

distances. Passing the Rio San

Juan means entering the trans-

Neptunian area.

This outer region comprises

the Kuiper belt, Pluto, and

several other trans-Neptunian

objects (TNOs). So, is there

any celestial body that can be

attributed to the Temple of

Quetzalcoatl?

34

5. Temple of Quetzalcoatl A special astronomical aspect

Connection between Kepler’s plane-

tary orbits and the logarithmic scale

perihelion distance q = a · (1 – e) (4)

aphelion distance Q = a · (1 + e) (5)

34

5. Temple of Quetzalcoatl A special astronomical aspect

a

a

2

=b

2

+ (a⋅e)

2

⇔

a=b

√

1−e

2

(6)

Connection between Kepler’s plane-

tary orbits and the logarithmic scale

perihelion distance q = a · (1 – e) (4)

aphelion distance Q = a · (1 + e) (5)

log (b) = log (q) + log (Q)

2

34

q⋅Q=(1−e)(1+e)

1−e

2

⋅b

2

=b

2

Replacing a in Eqs. (4) and (5) by means

of Eq. (6) and multiplying q and Q yield

⇔

a

2

=b

2

+ (a⋅e)

2

⇔

a=b

√

1−e

2

(6)

Connection between Kepler’s plane-

tary orbits and the logarithmic scale

perihelion distance q = a · (1 – e) (4)

aphelion distance Q = a · (1 + e) (5)

5. Temple of Quetzalcoatl A special astronomical aspect

log (b

2

) = log (q⋅Q)

⇔

log (b) = log (q) + log (Q)

2

34

q⋅Q=(1−e)(1+e)

1−e

2

⋅b

2

=b

2

So, log(b) is the arithmetic

mean of log(q) and log(Q).

Therefore, log(q), log(b),

and log(Q) follow each

other at equal distances on

the logarithmic scale. See

Q1, Q2, and Q3 on the next

slide.

Replacing a in Eqs. (4) and (5) by means

of Eq. (6) and multiplying q and Q yield

⇔

a

2

=b

2

+ (a⋅e)

2

⇔

a=b

√

1−e

2

(6)

Connection between Kepler’s plane-

tary orbits and the logarithmic scale

perihelion distance q = a · (1 – e) (4)

aphelion distance Q = a · (1 + e) (5)

5. Temple of Quetzalcoatl A special astronomical aspect

log (b

2

) = log (q⋅Q)

⇔

35

5. Temple of Quetzalcoatl Is there any trans-Neptunian object consistent with Q1, Q2, and Q3?

According to the geographical data in slide 15, the radius of the main semicircle is Q Q = Q Q = 223.2 m.

1 2 2 3

Satellite image:

© 2020 HERE,

DigitalGlobe,

INEGI

5. Temple of Quetzalcoatl Visualization of the “Quetzalcoatl positions” as given in the table of slide 15 36

The yellow points allow the GPS data to be checked, e.g., by using HERE WeGo.

37

5. Temple of Quetzalcoatl Astrophysical data of trans-Neptunian objects (TNOs)

TNOs with diameters D ≥ 800 km

[8] JPL, Small-Body Database Lookup. NASA, Jet Propulsion Laboratory, Caltech (retrieved Oct. 2021)

[9] Pluto fact sheet. (Williams, D. R.), NASA, Goddard Space Flight Center, Greenbelt, MD 20771 (2019)

Quantities a, e, and U (orbital period): [8], exception Pluto: [9], (uncer-

tainty: 1-sigma, astronomical unit: 1 AU = 149,597,870.700 km ≈ aEarth )

[10]

[11]

[12]

[13]

[14]

[15,16]

[17]

[18]

[19]

[20,21]

(References

for D [10–21]

are listed in

the Appendix.)

Wikimedia Commons (detailed

description in “TNO”)

5. Temple of Quetzalcoatl

Whereas nine of these objects are

completely out of range, Sedna

fits surprisingly well (GPS data).

Orbital elements of large

TNOs and comparison with

the Teotihuacán site

38

5. Temple of Quetzalcoatl

Whereas nine of these objects are

completely out of range, Sedna

fits surprisingly well (GPS data).

The bold semicircle gives the best

agreement with the astronomical data.

Of the several hundred smaller TNOs,

accurately determined in astronomy,

around 99 % belong to the Kuiper Belt

and are located approximately between

8 and 9 on the given logarithmic axis.

From the four or five TNOs with an or-

bital size similar to that of Sedna, none

fit as well as Sedna and all of them are

orders of magnitude smaller than Sedna.

38

Orbital elements of large

TNOs and comparison with

the Teotihuacán site

5. Temple of Quetzalcoatl

Adaption of the “Sun unit”

On the logarithmic scale (GPS data),

the Rio San Juan is positioned not at

8, but at 8.0845, which relates to the

“Sun unit” of 197 m. By modifying

this unit to 199.08 m, the river moves

exactly to 8, and we have an almost

perfect fit of the data as given in the

diagram on p. 31 according to Eq. (3).

Nevertheless, the agreement in the

histogram on the right changes. If

using 199.08 m, the points Q , Q ,

and Q shift to Q ’, Q ’, and Q ’, rep-

resented by the black dashed lines.

Even if this reduces the concordance,

the agreement with the TNO Sedna

is still remarkable.

However, this discrepancy needs fur-

ther clarification. A possible explana-

tion is given on the next slides.

1 2 3

1 2

3

39

40

Satellite image: © 2017 HERE,

2014 DigitalGlobe, INEGI

5. Temple of Quetzalcoatl

Alternative mapping of positions

At the Rio San Juan the avenue becomes broader

and the east side of the avenue (main axis) has a

parallel shift of about 16 to 18 meters – see slide

35. In order to avoid this shift, an alternative map-

ping of the main points at the Citadel is possible.

If we move the lower two yellow points by this

shift westwards to the positions of the red points,

the latter points are positioned almost exactly on

the Adosada platform and on the extension of the

(now continuous) main axis. Since the radius of

the semicircle is the same, the result in the pre-

vious slides remains unchanged.

Interestingly, the mismatch between point Q ’

and the correlated astronomical value (slide 39)

is about 18 m and is the same size as the shift of

the main axis. Please, note the perspective dis-

tortion visible at the Adosada platform.

2

A possible solution

of the “shift-problem”

The shift of the extended main axis (along the

east side of the avenue) is a parallel shift to the

west border of the Citadel. So, the red points R

to R shift to the points Q ’ to Q ’. We denote

the related distance R Q ’ with s, the radius of

the semicircle with r, and the distance from the

Pyramid of the Moon to point R with R .

By including the shift, the astronomical distances

are now assigned in the following way.

perihelion distance: log (q) → R2 + s – r

semi-minor axis: log (b) → R2 + s

aphelion distance: log (Q) → R2 + s + r

In this way, the shift of the main axis is not ig-

nored but precisely taken into account. Note: In

this drawing r is ca. 220.6 m due to former orbital

data of Sedna. The current value r = 223.18 m

does not yield much change. The following slide

shows the main diagram including Sedna.

41

Satellite image: © 2017 HERE,

2014 DigitalGlobe, INEGI

5. Temple of Quetzalcoatl

3 1 3

2 2

2 2

1

5. Temple of Quetzalcoatl

A possible solution

of the “shift-problem”

The green points in the diagram on the right

are obtained using the following values:

shift s = 18 m, radius r = 223.18 m (slide 15),

“Sun unit” uSun = 199.08 m (slide 39).

On the basis of the GPS data and due to the

assignments on the preceding slide, the points

relating to Sedna are precisely in line with the

planetary data. The trend line fits almost per-

fectly to the main Eq. (3). The coefficient of

determination is 0.999901, and the Rio San

Juan (Neptune) is positioned at exactly 8.

All of the points, except the red one, are used

in the linear regression. If we omit the parallel

shift (⇒ s = 0 m), we obtain R2 = 0.999765,

and, thus, the picture is nearly the same.

One reason for the fact that the avenue be-

comes broader after passing the Rio San Juan

is to symbolize the wide space beyond Neptune.

Two other reasons are given on the next slide.

42

43

5. Temple of Quetzalcoatl

A possible solution of the “shift-problem”

The second reason for the widening of the avenue could be that

most of the space within the Neptune orbit is occupied and “for-

bidden” by the other planets due to their gravitational influence.

This is not the case beyond Neptune. The third reason is the

modus operandi. The “narrow” avenue is mainly associated with

the perihelion distances; the widened avenue includes the peri-

helion distance, the aphelion distance, and the semi-minor axis.

Please note that the previous slides 40–42, concerning the shift

of the main axis at the Rio San Juan, are a preliminary attempt

to explain this phenomenon. This should be seen as a possibility

and is not strictly intended as the final solution.

Nevertheless, the overall picture is not much affected by the way

the calculation is done. Thus, we are dealing with a very robust

relation. Irrespective of the well-defined planetary correlation,

the probability that the connection with Sedna was planned by

the master builders appears to be very high.

Oort_cloud_Sedna_orbit.jpg: Image courtesy of NASA /

JPL-Caltech / Robert L. Hurt (arrangement of pictures

modified and fourth picture, the Oort cloud, omitted)

5. Temple of Quetzalcoatl The solar system Sedna, detected in 2003, will

reach its perihelion in 2076.

[22] Brown, M. E.: The largest Kuiper belt objects. in “The Solar

System Beyond Neptune”, Univ. of Arizona Press (2008) 335 pdf

44

Estimated number of undetected Sedna-like objects (Sednoids): 40–120 [22]. Since the orbits

are rather different in size and shape, the number of alternatives to Sedna is small, if not zero.

45

Sedna and the distant

Sun

If the connection of the

pyramid site to Sedna

was really intended by

the master builders, the

following questions

arise:

What is so special about

Sedna, so far outside the

solar system?

Does a connection be-

tween Quetzalcoatl and

Sedna exist?

Artist’s visualization of Sedna,

author: NASA/JPL-Caltech/

R. Hurt (SSC-Caltech)

5. Temple of Quetzalcoatl

The distances a and b can be

calculated from the GPS data

By using the main axis (yellow

points) and α = arctan(a/b), we

get approx. 15.28° ± 0.11°.

46

6. Geographical alignment Basic positions and orientation of the archaeological site in Teotihuacán

If the angle is determined using

platforms on the center line of

the avenue, we obtain probably

more exactly α = 15.45° ± 0.03°.

Does this angle

have a meaning?

The distances a and b can be

calculated from the GPS data

By using the main axis (yellow

points) and α = arctan(a/b), we

get approx. 15.28° ± 0.11°.

46

If exactly 15° was intended,

the angle would describe the

apparent motion of the Sun in

the sky over one hour. This

would include the dimension

of “time.” Perhaps, the angle

was exactly 15°, e.g., in the

year 9800 BC (polar motion).

6. Geographical alignment Basic positions and orientation of the archaeological site in Teotihuacán

If the angle is determined using

platforms on the center line of

the avenue, we obtain probably

more exactly α = 15.45° ± 0.03°.

47

Something always fits?

R

2 = 0.9886

A constructed example: Correlation of the 9 essential positions

on the avenue (incl. the “asteroid barrier”) with the numbers 1–9

7. Discussion A thought about the significance

47

Something always fits?

Titius-Bode law: a [AU] = 0.4 + 0.3 · 2n with n = –∞, 0, 1, 2, ...

This means that the above R2 simply reflects the regularity

of the exponential Titius-Bode law. It is still consistent

with the significance of the planetary correlation.

Mercury, Venus, Earth, ...

R

2 = 0.9886

(By using the astronomical quantities log(q/km) and

the numbers 1–9 without 5, we obtain R2 = 0.9931.)

A constructed example: Correlation of the 9 essential positions

on the avenue (incl. the “asteroid barrier”) with the numbers 1–9

7. Discussion A thought about the significance

●The real R2 is 58 to 118 times closer to 1 than the “constructed” R2.

●There are neither too many nor too few markings on the avenue.

●The full length of the avenue is used. It is neither too long nor

too short.

●The solid barriers do not make sense, except as markers.

●The “Pyr. of the Sun” represents Earth. (makes sense, our planet)

●It simultaneously defines the position of Mercury (the first planet).

●The Pyramid of the Moon is a bold marker for the Sun (radius).

●Thus, the size relation “Moon Pyramid”–barriers is adequate.

●With Eq. (3), the eighth planet Neptune has the number 8 on both

axes in the diagram (slide 31). The “Sun point” is at the origin of

the diagram, as the Sun represents the center of the solar system.

●The Rio San Juan differs from the other markers. It reflects the tran-

sition from the planetary area to the wide trans-Neptunian space.

Accordingly, the avenue becomes broader when passing the river.

●Eq. (3) represents ten equations. The planetary correlation (R2) is

independent of the choice of the units of length, of the logarithmic

base, and of the zero position of the logarithmic scale (Pyramid of

the Moon). With Sedna we even have thirteen equations.

48

7. Discussion Some more arguments

The platform at the top of the pyramid, with its elongated shape and orientation, looks similar to the barriers.

This confirms that the pyramid is just a bold marker at the origin of the scale, representing the Sun.

(SECRETARIA DE CULTURA.-INAH.-MEX. Reproduction Authorized by the Instituto Nacional de Antropología e Historia, México)

➔A planetary correlation has been discovered in Teotihuacán.

50

8. Summary

➔A planetary correlation has been discovered in Teotihuacán.

➔The central avenue provides an astronomical scale.

8. Summary 50

➔A planetary correlation has been discovered in Teotihuacán.

➔The central avenue provides an astronomical scale.

➔Pyramids, river, barriers, and the temple define markers on the scale.

8. Summary 50

➔A planetary correlation has been discovered in Teotihuacán.

➔The central avenue provides an astronomical scale.

➔Pyramids, river, barriers, and the temple define markers on the scale.

➔The 8 planets and the Sun are represented by the logarithms of the

perihelion distances and the solar radius, respectively (R = 99.98 %).

8. Summary

2

50

log

3

(

q

i

R

Sun

)

=d

i

u

Sun

➔A planetary correlation has been discovered in Teotihuacán.

➔The central avenue provides an astronomical scale.

➔Pyramids, river, barriers, and the temple define markers on the scale.

➔The 8 planets and the Sun are represented by the logarithms of the

perihelion distances and the solar radius, respectively (R = 99.98 %).

➔One barrier belongs to the asteroid belt. This leads to the question:

Did a former planet exist between Mars and Jupiter? (q ≈ 2.36 AU)

8. Summary

2

50

log

3

(

q

i

R

Sun

)

=d

i

u

Sun

➔A planetary correlation has been discovered in Teotihuacán.

➔The central avenue provides an astronomical scale.

➔Pyramids, river, barriers, and the temple define markers on the scale.

➔The 8 planets and the Sun are represented by the logarithms of the

perihelion distances and the solar radius, respectively (R = 99.98 %).

➔One barrier belongs to the asteroid belt. This leads to the question:

Did a former planet exist between Mars and Jupiter? (q ≈ 2.36 AU)

➔Some renaming “Pyramid of the Moon” → Pyramid of the Sun

seems appropriate: “Pyramid of the Sun” → Pyramid of the Earth

“Avenue of the Dead” → Avenue of the Planets

(Calzada de los Planetas)

8. Summary

2

50

log

3

(

q

i

R

Sun

)

=d

i

u

Sun

➔A planetary correlation has been discovered in Teotihuacán.

➔The central avenue provides an astronomical scale.

➔Pyramids, river, barriers, and the temple define markers on the scale.

➔The 8 planets and the Sun are represented by the logarithms of the

perihelion distances and the solar radius, respectively (R = 99.98 %).

➔One barrier belongs to the asteroid belt. This leads to the question:

Did a former planet exist between Mars and Jupiter? (q ≈ 2.36 AU)

➔Some renaming “Pyramid of the Moon” → Pyramid of the Sun

seems appropriate: “Pyramid of the Sun” → Pyramid of the Earth

“Avenue of the Dead” → Avenue of the Planets

(Calzada de los Planetas)

➔Temple of Quetzalcoatl → TNO Sedna. Does Sedna have a companion? (Adosada platform)

8. Summary

2

50

log

3

(

q

i

R

Sun

)

=d

i

u

Sun

➔A planetary correlation has been discovered in Teotihuacán.

➔The central avenue provides an astronomical scale.

➔Pyramids, river, barriers, and the temple define markers on the scale.

➔The 8 planets and the Sun are represented by the logarithms of the

perihelion distances and the solar radius, respectively (R = 99.98 %).

➔One barrier belongs to the asteroid belt. This leads to the question:

Did a former planet exist between Mars and Jupiter? (q ≈ 2.36 AU)

➔Some renaming “Pyramid of the Moon” → Pyramid of the Sun

seems appropriate: “Pyramid of the Sun” → Pyramid of the Earth

“Avenue of the Dead” → Avenue of the Planets

(Calzada de los Planetas)

➔Temple of Quetzalcoatl → TNO Sedna. Does Sedna have a companion? (Adosada platform)

➔The main question does not refer to correctness – within their small uncertainties, the data

are correct. The question is: “Are these findings altogether a great coincidence or not?”

According to the numbers (99.98 %), this is most probably not the case.

8. Summary

2

50

log

3

(

q

i

R

Sun

)

=d

i

u

Sun

51

8. Summary Graphical overview

The positions of the points at the Citadel correspond to the continuous main axis as shown on slide 40.

(More information is provided in the separate article “Planetary correlation of Teotihuacán.”)

Souvenirs for tourists:

Here, we have the planets!

52

Acknowledgments

I am indebted to Dr. José Martínez Trinidad for

driving me to Teotihuacán in 2005. He accom-

panied me for the entire day at the pyramid site,

and thus helped to make this work possible.

My gratitude is expressed to Ms. Nicola Wilton

for accurately proofreading the English text.

Furthermore, I would like to thank the Instituto

Nacional de Antropología e Historia (INAH) for

the permission to use the site plan of the pyramid

area of Teotihuacán (slides 4, 5, and 49).

Thank you for your attention!

Appendix References [10–21] of slide 37, retrieved October 2021 54

This is a scientific and noncommercial presentation. All contents here from H. Jelitto: (CC) BY-NC-SA 4.0. Used pictures from other copyright

holders and authors must be separately checked by the reader if they are to be used.

Use of site plan, Teotihuacán: Any reproduction of this image is regulated by the Federal Law on Archaeological, Artistic, and Historical Monu-

ments and its Regulations, for which the corresponding permit must be obtained from the National Institute of Anthropology and History, INAH.

This presentation was created with the free and open-source software LibreOffice (Impress, Calc, Writer), Inkscape, and GIMP using Ubuntu.

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