Introduction
Herein,
I assess Dresden Codex numbers and ancient Mesoamerican astronomy and
calendar intervals generally in relation to sidereal astronomical
cycles and intervals. Various entries appeared in series as ArchaeoBlog posts while I conducted the original
research. This page permalinks those June 2009 posts and adds further
reflections. Rather than deviate from that chronology, I continue posting the most recent research down page. The contents present the chronology as topics.
Contents
The Dresden Codex Lunar Series
2009.06.13
 The Dresden Codex Lunar Series presents a span of 11,457 days,
equaling 11,292 degrees solar orbit. This amount has a sidereal
correspondence with 857 days of lunar orbit motion
(Table 1). Also, 11,457 lunar orbits equates to 857 solar orbits and
10,600 lunar synodic periods (moons). And, 857 full moon
periods represents a precise integer number of earth rotations:
857.0 full
moons
857.0 solar orbits

=
930.013 lunar nodal
= 11,457.016 lunar orbits

=
25,377.003 earth rotations
= 10,600.016 full moons

The "image series" of 11,457 days
consists of the nine date intervals between ten images. The full ten
intervals span 11,959 days, rather than the 11,960 days more accurately
equaling 405 full moons. The 11,959 day interval also has a sidereal
correspondence equating solar and lunar orbits. Angular lunar orbit
motion during 897 earth rotations equals solar orbit motion during
11,959 days.
Table
1. Dresden Codex Lunar Series Astronomical Periods.

interval (TT)

degrees orbit

lunar periods

solar

lunar

synodic

nodal

orbit

11,959 days

11,786.90


404.9700

439.4717


897 rotations


11,786.92




857 days


11,292.14




11,457 days

11,292.12


387.971

421.024


11,457 lunar orbits

308,519.6

4,124,520.0

10,600.001

11,503.08

11,457.000

857 solar orbits

308,520.0

4,124,525.3

10,600.015

11,503.09

11,457.015

857 moons


24,943.5

857.0

930.0128


25,377 rotations

24,943.512


856.9999

930.0129


Apparently, the focus of the
lunar series is lunar nodal (the eclipses) and ratios far more accurate
than either the Saros or Metonic eclipse periods represent or the
eclipse intervals presented in the lunar series. Is sidereal astronomy the
reason why the Maya astronomer utilized, instead of the Saros or
Metonic eclipse cycles, a lunar series span of 11,457 days equaling
387.97 full moons? The accuracy of the sidereal ratios is very
convincing:
Lunar orbits : moons accuracy, 10,600.0 : 10,600.0012
Earth rotations : moons accuracy, 25,377 : 25,377.0022

= 1.0 : 1.000 000 110
= 1.0 : 1.000 000 086

The lunar series 11,457 and
11,959 day intervals are apparently based on sidereal astronomy. Is
there any question that the Maya were doing sidereal astronomy?
Hopefully, this new perspective presents a useful template, the stellar
backdrop, upon which to now interpret the Dresden lunar series and
other aspects of Native American astronomy.
Download the Dresden
Codex in PDF format (95.7 MB) from FAMSI.
Intervals
separating the day glyphs series are divided into nine major groups by
pictographs in the 69 intervals (source Verbelen 2006):
 502 =
(177), 177, 148, image
 1742 =
177, 177, 177, 178, 177, 177, 177, 177, 177, 148, image
 1034 =
178, 177, 177, 177, 177, 148, image
 1211 =
177, 177, 177, 178, 177, 177, 148, image
 1742 =
177, 177, 178, 177, 177, 177, 177, 177, 177, 148, image
 1034 =
178, 177, 177, 177, 177, 148, image
 1210 =
177, 177, 177, 177, 177, 177, 148, image
 1565 =
177, 177, 178, 177, 177, 177, 177, 177, 148, image
 1211 =
177, 178, 177, 177, 177, 177, 148, image
 708 =
177, 177, 177, 177, image

Long Count Intervals
2009.06.18
 The finding above prompted a closer look at some Long Count academic
literature discussing both codices and stelae. To the best of my
knowledge, Mesoamerican or any other prehistoric equation of lunar and
solar orbit motions is a new consideration. I needed to amend my
research applications for Long Count conversions and to do solarlunar
orbit conversions and comparisons.
In the Long Count glyphs at
Uaxactun is a seven katun interval of 50,400 days, nearly equaling 138
years. A katun is a 7,200 day Mesoamerican calendar period consisting
of 20 tuns of 360 days. A tun consists of 18 uinals of 20 days. The
seven katun interval presents an equation of integer days of lunar and
solar orbit motion (Table 2). Accuracy is within 20 minutes of lunar
motion (1 : 1.000 003) when equating 50,400.0 days solar orbit (seven
katuns) and 3,770.0 days lunar orbit. Seven katuns represents 138
tropical years less 3.4 days (1 : 1.000 068). By comparison, accuracy
of the equation of 50,400 days solar orbit to 3,770 days lunar orbit is
1 : 1.000 003.
Table
2. Equation of Katuns to Astronomical Motions.

interval

degrees orbit

periods

solar

lunar

rotations

years

orbits

50,400 days

49,674.70


50,537.985

137.99058

137.985 solar

50,538 rotations

49,674.71


50,538.0

137.99062


3,770 days

3,715.75




137.986 lunar

282 days


3,715.73




2,820 lunar orbits

75,938.32

1,015,200.0

5,779.004


2,820.0

5,779 rotations

75,938.26

1,015,199.3



2,819.9980

Seven katuns represents an
integer equation of days and rotations; 50,538.0 rotations equals
50,400.0147 days. Accuracy of the 50,400 days to 50,538 rotations
integer equation is 1.0 : 1.000 000 3,
about 10 times
more precise than the 50,400 days earth orbit to 3,770 days lunar orbit
integer equation. Solar orbit for 3,770 days equates with 282 days of
lunar orbit (1.0 : 1.000 004). An accurate sidereal commensuration
exists between 138 solar orbits and 573 Mercury orbits (1.000 001).
Onehalf of the seven katun
period is well known in Maya astronomy:
"The
use of the threeandahalfkatun interval to strike approximately the
same positions in the natural year (70 X 360 = 25,200 days. 69 tropical
years = 25,201.7 days) is pretty clearly indicated at Copan, Palenque,
Tikal, etc." Ernst Wilhelm Förstemann 1906

An obvious question follows
on these findings. Was the accuracy of the wellknown seven katun
interval improved upon over time, leading to observing solar and lunar
eclipses in relation to the 11,457 and 11,959 day spans and their
corresponding sidereal correlations?
"...
the sidereal period is very close to the tropical period for both the
lunar cycle and the year. They differ only by the small amount of the
precession. Therefore to distinguish between both is difficult to
prove." Dr. Andreas Fuls (personal communication June 18, 2009)

The 819Day Count
2009.06.19
 A common Classic Maya cycle is the 819day count, best known from
Palenque, Quirigua, Copan, Tikal, and later from the Dresden Codex.
Lunar orbit motion for 819 days equates to 10,949.0017 days of solar
orbit (Table 3). Compared to integer days, accuracy is 1.0 : 1.000 000
4. Mean daily lunar motion is 13.17636 degrees, therefore the equation
difference represents 25 seconds of lunar motion in comparision with
819 days. Draw a line from the center of the earth to the orbiting
moon, and the difference, 0.0039 degrees, amounts to about 432m on
the earth's surface in proportion to nearly 30 circumferences (29.976 lunar orbits = 819 days).
Table
3. Integer Equation of Solar and Lunar Orbits.

interval

degrees orbit

cycles

solar

lunar

rotations

orbits

819 days


10,791.438°


29.9762

10,949 days

10,791.434°


10,978.9762

29.9762

819
solar orbits = 10,949 lunar orbits = 10,130 moons

The Venus Table
2009.06.24
 Another section of the Dresden manuscript has been termed the Venus
Table. The 584day intervals in the table closely correlate with the
Venus synodic cycle. Subdivisions of the 584day spans recongizably
match the periodic appearances of the inner planet as Morning Star and
Evening Star, albeit not precisely. Given 365 lunar orbits equals
10,000 rotations and 365 times eightfifths equals 584, the 584day
period also correlates with lunar orbit; 584 days equals 21.3750 lunar
orbits (Table 4) and just eight 584day periods represents an integer
number of lunar orbits. The 584day increments express eights of lunar
orbit.
Table
4. The Venus Table, Lunar Orbit and Planetary Periods.

interval

period

Lunar orbit

Venus synodic

Venus orbit

Mars synodic

365 days

584 days

21.3750

1.00013

2.600

0.749

1.60

1168 days

42.7500

2.00027

5.198

1.498

3.20

4,672 days

170.9999

8.0011

20.792

5.990

12.80

23,360 days

854.9993

40.0054

103.960

29.951

64.0

The 365day count is usually
interpeted as the whole number approximation of the year. That is
simply a coincidence. Only two fundamental sidereal motions can readily
be counted, rotation and lunar orbit. Counting these two motions for
just three decades reveals the ratios of 365 lunar orbits equaling
9999.71 rotations, 10,000 rotations equaling 365.01 lunar orbits, and
366 lunar orbits equaling 9999.73 days.
In 365 lunar orbits there are 10,000 rotations
and in 366 lunar orbits there are 10,000 days.

This sidereal equation, one of the most
obvious and most neglected facts of ancient astronomy, is the
foundation of accurate naked eye astronomy. It likely also is the
sidereal foundation for the 584 day interval in the Venus Table and,
combined with the regularity of earth rotations, a cosmic clockwork for
observing the moon, Venus, and the other planets. Mean lunar orbit is a
readilyvisible, siderealreferenced motion, especially compared to
Venus observations.
10,000 rotations = 365.0106 lunar orbits = 9,972.70 degrees
9,999.710 rotations = 365.0 lunar orbits =
9,972.41 degrees
10,000 : 9,999.710 = 1.000 029 : 1.0

Given multiples of 365, integer lunar
orbits do not equate until 855 lunar orbits with 23,360 days (64 times
365 = 40 times 584). Given 584 day modules (eightfifths of 365), at
onefifth this interval 171 lunar orbits equate to 4,672 days (8 times
584).
The 584day interval more accurately
commensurates as a lunar number (Table 4). In 855 lunar orbits there
are 23,360.022 days (1.0 : 1.000 001), compared to 40 Venus synodic
periods with 23,357 days (40.0 : 40.00539 = 1.0 : 1.000 134). Even the
Mars orbit cycle has a slightly more accurate commensuration (34.0 :
34.00391 = 1.0 : 1.000 115) than Venus synodic.
Reflections
More will follow, no doubt, as I dig
deeper. Meanwhile, I'm refining planetary orbital constants in my
application. I do not want to assume the Maya were anything less than
precise. I note modern astronomers were very recently formulating
precise values of planetary orbit periods, and current references are
not consistent. Too bad they burned all those Maya libraries!
2009.06.27
 The online version of archaeogeodesy.xls
is updated. The new lunarsolar equation formulations and the planetary
orbit conversions are in a worksheet. The AeGeo
code is expanded with new terms. New Epoch v2009 versions
will feature the same updates.
2009.06.30
 Epoch_Calc is
online. The "calc" worksheet has an orbit calc table to equate lunar
and solar orbit motion. You enter the number of days and read the
calculations. Planetary orbits and their synodic cycles are now also
converted. I've added new code terms for the planetary periods using
the latest values available. Epoch Calc (250 KB), derived
from archaeogeodesy.xls, is astronomy focused. The larger archaeogeodesy.xls
application is focused on ancient monuments.
2009.07.19
 Eclipses, Cosmic Clockwork of
the Ancients discusses eclipses in the context of ancient
cultures and nakedeye astronomy. Eclipse Calc, an eclipse calculator
describes the eclipse related features in Epoch Calc.
2010.01.03
 Addition to Table 3: the equation "819
solar orbits = 10,949 lunar orbits = 10,130 moons" represents
an integer ratio of the orbits and moons. This accurate proportion
likely determined use of 819 in astronomy counts, and infers a
threshold date for knowledge of accurate orbital proportions. For
integral solar orbits, 819 has a more
integeraccurate ratio to both lunar orbits and moons than all smaller numbers except multiples of 160 orbits. I continue to
discuss integer representation of astronomical ratios in Ancient Astronomy, Integers, Great
Ratios, and Aristarchus.
2010.10.16  Further consideration of the Maya "819day" count revealed the integer equation of 819 years with 44 lunar standstill periods and 863 eclipse nodal intervals (1.0 : 1.000 001 65).
2012.02.01  Bob Patten noticed a typo above, the lunar series span of 11,457 days now equals 387.97 full moons, a oneday correction matching the table value for same.
2012.08.08  Portions of this page edited for clarity and precision using refined astronomy constants.
Related Readings
Bricker, Harvey M. and
Victoria R. Bricker 1983 Classic Maya Prediction of Solar Eclipses. Current
Anthropology, 24:1, 124.
Fuls, Andreas 2007 The
Calculation Of The Lunar Series On Classic Maya Monuments, Ancient
Mesoamerica.
Fuls, Andreas 2008
Reanalysis of Dating the Classic Maya Culture, AmerIndian Research,
Bd. 3/3 (2008), Nr. 9.
Fûrstemann, Ernst W. 1906 Commentary
on the Maya manuscript in the Royal Public Library of Dresden.
Harvard University, Peabody Museum, Papers, 4(2):51267. Peabody
Museum, Cambridge, MA.
Houston, Stephen D., Oswaldo
Mazariegos, David Stuart 2001 The Decipherment of Ancient Maya
Writing, University of Oklahoma Press.
Lounsbury, Floyd G. 1978 Maya
numeration, computation and calendrical astronomy. Dictionary of
Scientific Biography. Vol. 15, Supplement 1. New York.
Powell, Christopher 1977 A
New View on Maya Astronomy, The University of Texas at Austin,
M.A. thesis.
Severin, Gregory M. 1981 The Paris
Codex: Decoding an Astronomical Ephemeris. Transactions of the
American Philosophical Society 71:5.
Thompson, John Eric Sidney 1972 A
commentary on the Dresden codex; a Maya hieroglyphic book.
American Philosophical Society, Philadelphia.
Verbelen, Felix 2006 Eclipses and
Supernova 1054 in the Dresden Codex. PDF
Readings on jqjacobs.net
Mesoamerican Archaeoastronomy
A Review of Contemporary Understandings
of Prehispanic Astronomic Knowledge 1999
Archaeoastronomy
Bibliography  Mesoamerica Articles and Photo
Galleries
Newark Archaeogeodesy
Assessing
Evidence of Geospatial Intelligence in the Americas
