2009.01.09 - In 1991, I first noted the arc distance between Ohio's ancient Newark and Marietta earthworks equaled circumference (cir) of the earth divided by days per year. In part, excitement about this finding prompted improvement of my crude method, simply measuring maps. I was soon employing spherical trigonometry and traveling to University libraries, seeking out site plans and topographic maps to derive accurate coordinates. I confirmed the arc distance equaled cir/365.25, and I later noted the degrees longitude difference matched.

I took a great leap forward in methods in 2005, traveling to Ohio for GPS readings on the mounds, then confirming the GPS positions in Google Earth. Coordinates and site codes are appended below in Appendix A and the figures herein display the site codes. Technology had caught up with my hypothesis, so to speak, and using GPS data I repeated and expanded on a preliminary 2001 study, Possible Geodetic Properties and Relationships of Some Monumental Earthworks in the Middle Ohio Valley. Several Newark Octagon to Marietta relationships presented astronomical constants accurately. Not unlike grinding and polishing a lens, with each step in methods improvement, arc distances resolved more accurately in relation to astronomical constants. An ancient geodetic codex is now unveiling with some clarity, and this article discusses those research results. I also compiled some Newark results in a Google Earth file.

Marietta Conus Mound and Ellipse

Initial Findings

Initially I observed, on a National Geographic 1:267,000 map, the Newark-Marietta arc distance equaling circumference divided by days per year. With GPS coordinates and trigonometry, I also noted the arc distances from the Octagon to the two truncated pyramids in Marietta Square (Figure 1), Quadranau Mound (maqum) and Capitoleum Mound (macam), match two lunar orbit values (Table 1). Significantly, lunar astronomy correlates with the capacity for navigation and longitude determination.

The Octagon centerpoint datum (nocp) is the average of the GPS readings for the eight embankment vertices. From the Octagon to Capitoleum Mound, arc distance and degrees E - W (longitude difference) are equal. From the Octagon centerpoint the arc distance cir/365.24 and the same longitude difference converge within 250 feet of the center of Marietta Square, one of the largest Hopewell squares (1510' per Romain). The arc distance cir/365.01 and the same longitude difference from the Octagon centerpoint converge atop Marietta Capitoleum mound, the high point of Marietta Works. In 365 lunar orbits, there are 10,000 rotations.

Figure 1. Marietta Earthworks

There are 10,000 rotations in 365 lunar orbits
and in 366 orbits there are 10,000 days.  

Calendar keepers count days and years, or rotations, or moons. Astronomers count all these and more. Three fundamental astronomical motions, earth rotation and lunar and solar orbits, present the following ratios in integers; there are 10,000 rotations in 365 lunar orbits and in 366 there are 10,000 days. The two lunar orbit numbers, 365 and 366, are repeated in the Octagon to Marietta arcs, with Octagon-Quadranau arc equaling cir/366 and Octagon-Capitoleum equaling both cir/365 and E-W cir/365 (Table 1) Fundamental astronomy is discussed in Eclipses, Cosmic Clockwork of the Ancients.. A primer on fundamental astronomy in the Archaeogeodesy pages discusses formulas and precession. Appendix B below references the astronomy code terms and abbreviations herein.

Marietta Quadranau Mound deskpicture

The Ancient Earthworks of Eastern North America pages provide photo galleries, site descriptions, collected data, survey maps, references cited, and placemark and data file links. Google Earth users can view earthwork survey drawings using Eastern Woodlands placemark overlays of Squier and Davis 1848 survey maps.

Newark Latitude and Longitude

The Figure 2 ground plan represents the actual spatial relationship of the Octagon and Great Circle features of the Newark works. Newark Earthworks has been termed the largest geometric earthwork in the world. The Octagon is certainly the largest single geometric earthwork form at 2898.5 feet long. While several earthen circles in Ohio are larger in diameter, Newark's Great Circle probably represents the largest circular work in labor investment. The Great Circle (ncec) is actually an ellipse, measuring 1189 by 1163 feet (mean 358.4 m. The Octagon's Observatory Circle (nocc) is nearer a true circle at 1059 by 1050 feet (mean 321.4 m). The Newark circles are centered over a mile apart, at about 1,934 meters.

Figure 2. Newark Earthworks ncec-nocp   N-S = 0.01366° = 0.0005 S22 ncec-nocp   E-W = 0.01319° = 0.0010 C27

The Newark circles align to Marietta's Capitoleum Mound (Figure 2), with an angle of 180.02° on Eagle Mound (nccm) near the center of the Great Circle (ncec). The Capitoleum Mound to Eagle Mound ratio of arc distance to degrees longitude difference is 1.0 to 0.9966. From the Octagon centerpoint (nocp) the ratio is 1.0 to 0.9999, hence local latitude to longitude ratio at Newark is also accurately expressed by the Newark-Marietta relationship. Arc distance equaling longitude difference may have function when comparing astronomical observations from two positions, both mathematically and for time keeping. At the same diurnal time of night in the two locations the cosmos is precisely one day apart in overhead position.

At the Octagon latitude, linear measure of latitude (N-S) equals 1.3012 times equal angular measure of longitude (E-W). The Octagon latitude-Capitoleum longitude intersection is eastward from the Octagon 1.3011 times the distance northward from the Capitoleum. Possible builder intention expressing Newark's latitude to longitude ratio is even more convincing in the relationship to Serpent Mound. The Newark-Serpent Mound N-S and E-W distances match the actual latitude:longitude triangle by having the long dimension expressed along the N-S meridian.

Serpent Mound

2009.01.13 - Serpent Mound undulates across a ridge, from a spiral at the tail to open maws facing an oval mound. The centerpoint of Serpent Mound Oval Mound is one degree (cir/360) west of Newark's Great Circle centerpoint (ncec-smom E-W = 1.00001°). Eastward from the oval mound to the longitude of the Great Circle compares to their latitude difference in the ratio 1.0 to 1.30067. The longitude to latitude ratio at Newark Circle is 1.0 to 1.30102. At the apex of the Octagon, the ratio was 1.0 to 1.3013 during the Hopewell epoch. The tangent of a 3.65010 to 1.0 right triangle equals 1.3034 radians. The ratio also approximates the lunar illumination variance due to elliptical orbit; apogee to perigee ratio is about 800:701 and the square of their ratio is 1.3025 (illumination is formulated with the square of distance).

Serpent Mound photos, maps, placemarks, PowerPoint

Newark Astronomy and Geodesy

The Newark archaeoastronomy discussion in Temporal Epoch Calculations considers local latitude to longitude ratio and other possible reasons for the Octagon's alignment (51.45° Thomas). Temporal Epoch Calculations also provides some academic history of Newark studies and of claims Newark is an observatory and associated with lunar standstills. The following excerpts from my previous Archaeogeodesy articles discuss several North American site-to-site relationships expressing the 0.0365010 lunar orbits per rotation module (R27):

"At Fort Center, Florida, an about 1,188 foot in diameter prehistoric earthen circle was built, near the same size as the 1,189 foot Newark Circle. Outside of the Middle Ohio River Valley, the large Fort Center Circle is unique in North America. Large earthen circles are also known in Northeastern Europe and smaller earthen circles are not uncommon. The arc distance between Fort Center and Newark expresses the fundamental equation of lunar orbits per earth rotation (R27 = 0.036501 cir). The center-on-center arc distance between the Fort Center Circle and ... Observatory Circle equals 13.14059° or 1.000016 R27. This is an excess of only 23 m in relation to a center-on-center line over 900 miles long between two earthen circles up to 360 m in diameter.

"Grave Creek Mound is the largest mound along the Ohio River, the highest Adena mound, and one of the largest conical mounds in the Americas. It is located upriver from Marietta Earthworks. The arc distance from Grave Creek Mound to Newark Observatory Mound is 1.3136° (0.09997 R27, 0.00365 cir).

"... One R27 is the longitude difference between the Pyramid of the Sun, the second largest pyramid in the Americas, and the largest platform mound in the American Southwest, Pueblo Grande, in Phoenix, Arizona. The longitude difference between Newark and Teotihuacan is 1.25 R27."

The spacing of Fort Center's circle at precisely 0.0365010 circumference from Observatory Circle is impressive in and of itself, without the redundancy of the module and ratio repeating in relation to other sites. Equating earth rotation and lunar motion to fixed space (0.03650 lunar orbits per rotation, 365 lunar orbits in 10,000 rotations) is fundamental to accurate lunar astronomy and temporal measure. Geodetic monuments accurately expressing sidereal astronomical ratios on a one-to-one planetary scale implies accuracy in both astronomy and geodesy.

GPS reading on the Great Circle in Newark, Ohio, Fall 2005.

Ancient Surveyors and Mounds

2009.01.26 - As mentioned, the spacing from Grave Creek Mound to Observatory Mound is 0.00365 circumference. Unfortunately, much of the monumental works at Grave Creek have not survived modern developments. Recently, one of the stone towers was used as road fill by a subdivision developer. Thanks primarily to their imposing sizes I suspect, at least the largest mounds at each complex have so far escaped destruction. With time, already-fragmentary archaeological records become more diminshed. An ethnohistorical source, the Chilam Balam of Chumayel, conveys details of surveying the landscape and construction of over 6,000 mounds.

NEW -   Newark Archaeogeodesy PPT   3.2 MB PowerPoint

Latitude Geometry and Astronomy

2009.04.04 - I've discussed geodetic geometry of monument latitudes, 4/5 atan at Monks Mound, 3/5 atan atop Ur Ziggurat, 3:4:5 at Harran, cir/7 in Avebury, cir/14 at Karnak, and other sites. One of the oldest known stone circles, situated one-fourth the distance from equator to pole at Nabta Playa, Egypt, implies intentional latitude placement originates at an early date. In contrast to simple integeral ratios of spatial geometry, the latitudes at Newark and Marietta present solar and lunar motion modules (Table 2). Marietta's latitude equals 40 times solar orbit per day (40 SO). The same astronomy module relates to Ur Ziggurat (Marietta and Ur latitudes equate at 4 to pi):

"Divide earth's circumference by days per solar orbit (0.98561° = SO),
multiply by 10 pi, and the result is the latitude of the Ur ziggurat,
or 30.9638° = 31.4159 SO."

Marietta latitude presents a low integer ratio for rotations and lunar orbits. Llatitude baselines transecting the site equal three times lunar orbit per rotation (3 R27) and 40 times solar orbit per day (40 SO). Figure 1 illustrates the relationships of the monument to these latitudes today. The 40 SO - 3 R27 latitude difference equals 0.0032° or 357 m (also the diameter of the Great Circle). Around 322 A.D. earth's rotation axis was inclined 3/5th's of Marietta latitude, an arc equal to 1.8 R27 and 24 days of solar orbit (24 SO). The 55 SO latitude at Thornborough equals eleven-eights Marietta's latitude.

The Quadranau and Octagon colatitudes (angle to the pole) express the ratio of the lunar nodal and anomalistic periods, 1.0 : 1.012580. Thornborough latitude expresses the ratio of lunar synodic period in relation to Newark and Marietta colatitudes representing the nodal and anomalistic periods, expressing S29:S22:S25. Table 3 compares these monument latitudes and colatitudes.

In a previous article, Thornborough Henges and the Ure-Swale Monuments Assessing Evidence of Geospatial Intelligence in the Neolithic, I noted arc distance from Newark to Thornborough South is 2.0 times solar orbit per nodal period (S22), and that Thornborough's latitude equals 1.8623 times solar orbit per lunar synodic period (S29). Eclipse cycles are intercalations of two lunar periods, the synodic and nodal periods (Table 2). The multiple "1.8623 times" presents an astronomical number; eclipse nodal period was 18.6228 days (UT) less than a tropical year. Newark Octagon colatitude equals 1.86226 S22. Capitoleum colatitude equals 1.86234 times lunar orbit per anomalistic period (S25). The modules are each 1.8623 multiples of the three lunar periods, thus expressing the ratio of the three significant eclipse cycle constants.

2012.08.05 - The lunar standstill period results from the turning of the axis of lunar orbit.  Inclination of the earth's axis (obliquity) together with solar orbit results in the sun rising and setting north and south of due east and due west during the course of each year. In the case of the moon, lunar orbit inclination either adds to or subtracts from the moon's swing back and forth across the celestial equator.  Unlike the sun, the moon shifts north and south on the horizon every 27.22 days (the lunar nodal period).  The moon's maximum rise-set angle from east-west recurs in a mean period of 18.613 years, one lunar standstill and just over one turn in space of the direction of the lunar orbit axis.

One long-standing interpretation of Newark Octagon is intentional alignments to the lunar standstill rise and set extrema. The hypothesis first appeared in John A. Eddy's article Archaeoastronomy of North America: Cliffs, Mounds, and Medicine Wheels (in In Search of Ancient Astronomies, 1978, E.C. Krupp, editor). Eddy's map examination revealed the alignment as possible. Hively and Horn's survey (1982) determined standstill rising and setting positions coincide with the architecture of the earthwork.  Azimuth identifies horizontal direction, while elevation corresponds to vertical direction. The azimuths of the octagon sides closely correlate with the lunar standstill horizon extrema as observed in the three-dimensional landscape surrounding the Octagon.  Most importantly, the primary axis of the entire earthwork (octagon, circle, and connecting parallel walls) aligns to the lunar major moonrise, the northern-most moonrise position of each standstill (arrow in image above).  I discuss details and other possible interpretations of the Octagon Earthwork primary alignment in Temporal Epoch Calculations.

Recently, Google Earth updated some Andean areas with high-resolution imagery.  One of the important sites now visible in detail is a UNESCO World Heritage site, the Chavin Archaeological Site in Peru. The Google Earth illlustration below incorporates an image overlay of CyArk's archaeology map.  While ground-truthing with GPS equipment needs to be accomplished for precise coordinates, especially when rugged Andean terrain is combined with oblique camera angles, reasonably accurate coordinates can now be derived using Google Earth. The first image below identifies newly-derived coordinates for specific site features. 

The Chavin latitude arcsine equals one-sixth (asin 0.1666... = 9.5941 degrees).  A right triangle at Chavin with sides extended to the pole star and to the geodetic center expresses the ratio 1:6; the axis is the hypotenuse equaling six and the geodetic radius equals one.  Latitude properties expressing integral number relationships to the pole and equator reinforce astronomical observation interpretations of major monuments. Today, a precise asin(1/6) geodetic triangle intersects the latitude of Building F.  Secular polar motion has shifted local latitude slightly since construction.

In the next image, a tessellated line extending from Newark to Pachacamac, Peru, is visible passing 2.5 km east of Chavin de Huantar. Newark, Chavin, and Pachacamac form a nearly straight line spanning 5,826 km. The Archaeological Complex of Pachacamac is on the UNESCO World Heritage Centre's Tentative List.

South America Sites
code	site	latitude	longitude	source
chhap	Chavin de Huantar Huaca A Portal	-9.594358	-77.177889	GE 2011-01
pachs	Pachacamac Huaca Sol	-12.262789	-76.901822	GE 2011-01

The three sites together may also express a more complex understanding of lunar astronomy, specifically of the fundamental astronomical constants and motions which determine lunar standstills.  The arc distances from Pachacamac to Newark and to the Chavin Huaca (pachs-chhha and pachs-nocc) present the ratio 1.0 : 19.5981.  From Chavin (chhap) the ratio of the arcs to Pachacamac and Newark is 1.0 : 18.5982. The lunar standstill constants below for 900 BCE, the approximate epoch of Chavin construction, matches these proportions.

Another set of numbers repeats the ratio of the arcs.  The astrogeodetic module s22 represents mean angular solar orbit of the moon and earth per lunar nodal period. The arc distance from Pachacamac to Chavin equals one-tenth of s22 (pachs-chhap = 0.100004 s22).  The mean arc from Chavin to the Newark circles (chhap-nocc and chhha-ncec) equals 1.8600 s22, that from Pachacamac to Observatory Circle (pachs-nocc) equals 1.9600 s22, one-tenth multiples of the values in the table above (et and ot).  The difference between the arcs from Newark to Chavin and to Pachacamac is 0.10 s22.  The mean arc from Pachacamac to the Newark circles is 1.9598 s22, from Chavin the mean is 1.8598 s22. 

Further Readings

• Newark Archaeogeodesy PPT   3.2 MB PowerPoint
• Eclipses, Cosmic Clockwork of the Ancients
• UNESCO Astronomy and World Heritage Initiative
• Hopewell Lunar Astronomy: The Octagon Earthworks - by Joe Knapp
• VIDEO: Cracking the Maya Code
• von Hagen, Victor Wolfgang 1948 Maya Explorer, John Lloyd Stephens and the Los Cities of Central America and Yucatán University of Oklahoma Press
• Bienias, Michelle. Shooting the Mayan Pyramids of Tikal for UNESCO VRMAG Feb 2006
• The Dresden Codex Lunar Series and Sidereal Astronomy

Bibliography and References on the Eastern Woodlands Page

Appendices

2009.04.20 - The Deseret News reports:

Four Corners - the only place in the United States where four state boundaries come together - was first surveyed by the U.S. government in 1868, during the initial survey of Colorado's southern boundary line. Its intended location was an even 109 degrees west longitude and 37 degrees north latitude.

However, due to surveying errors, it didn't come out that way.

According to readings by the National Geodetic Survey, today's official marker sits at 109 02 42.62019 W longitude and 36 59 56.31532 N latitude.

That means the current monument marking the intersection of Utah, Colorado, New Mexico and Arizona is approximately 2.5 miles west of where it should be. ...

ArchaeoBlog - An archaeology web log by James Q. Jacobs

• 2008.04.25 - The Ur and Harran Latitudes, and Göbekli Tepe
• 2007.07.16 - Southwest Spring 2007 Travel Posts
• 2007.03.02 - Ancient Peruvian Astronomical Observatory at Chankillo

Betatakin Ruin Alcove. Download the deskpicture - 1280 pixel image.