Hopewell Lunar Astronomy: The Octagon Earthworks
by Joe Knapp
Email: jmk@copperas.com
posted July 19, 1998

Aerial photo by Richard Pirko, 1994 (Youngstown State University)
"A thing of beauty is a joy forever;
Its loveliness increases;  it will never
Pass into nothingness."
(Endymion by John Keats)
The intricate geometry of the Newark Earthworks as mapped in 1848 by Ephraim Squier and Edwin Davis under the auspices of the Smithsonian Institution has today been largely obliterated by decades of agriculture and indifferent development. We are fortunate however that the most striking features of the complex--the "Octagon" earthwork and the "Great Circle" earthwork--have been preserved in what is today the city of Newark, Ohio.

The Newark earthworks were constructed by the people of the so-called "Hopewell" culture, which was the human presence in this valley during the years 200BC to 500AD. The culture was first identified at an archaeological site on the farm of a man named Hopewell, thus the academic name. Being a non-literate, prehistoric culture which faded out many centuries before any scribe reached these lands, we have no idea what they called themselves. Collectively, this culture in its core area along the lower Ohio River drainage (including the Licking and Scioto Rivers) has been dubbed "The Moundbuilders" for their habit of not only interring their dead in funerary mounds of various sizes, but also constructing vast and mysterious geometric earthworks whose purpose is unclear at best.

Back in the early 1980s Ray Hively, a physicist, and Robert Horn, a philosopher, analyzed the aesthetically ideal geometry of the Octagon (actually a conjoined octagon and circle--see above) for astronomical alignments. Solar alignments were not to be found in the structure, but they found--much to their surprise--several lunar ones. The most important alignment they found is the orientation of the main axis, defined by the geometry of the joined octagon and circle:
 
 


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The axis points to an azimuth of 51.8º, measured from true north. This orientation is interesting because at this latitude, 40º 3' 4" N, the most northerly rising of the moon will occur directly along the axis, viewed from the large so-called "Observatory" mound located on the southwest part of the earthwork.

To analytically determine the exact azimuth of a moonrise it is important to know, besides the geographical coordinates of the observation point, the apparent elevation of the horizon. In the case of the Octagon in its current state as a private golf course, the horizon can't be seen at all due to the numerous trees. However, if the trees were theoretically cleared away, it's possible to use the USGS topographical map to determine what the horizon elevation would be. Below is an expanded area of the USGS map (Newark 7.5' quadrangle):


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Making a plot of altitude along the line in the above figure yields the following cross-section:


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It can be seen that the Octagon rests on a wide flat terrace which begins to slope away after a mile or so into Raccoon Creek, Log Pond Run, and the North Fork of the Licking River. Thus, a relatively limited area of trees needs to be cleared to open up the sightline to the hills several miles distant. The first hill encountered, Firestone Hill, looms up rapidly on the east bank of the river. Behind it is Atherton Hill, which might define the horizon as well, depending on the tree heights. Perhaps a hilltop bonfire might have been employed to accentuate the sightline. It would be interesting to find evidence of Hopewell activity on these hill tops. The hill names are for convenience, and refer to the farmers whose lands formerly included these hills.2

The diagram shows that the horizon elevation, disregarding trees, is about 0.5º at this site. To summarize the site coordinates:

With the above data it's possible to calculate the directions of all the major lunar and solar azimuths from this site. The alignment corresponding to the Octagon axis involves the northernmost risings of the moon. Below is a rough sketch of the view an observer would have, standing on the Observatory mound, during a maximum northerly moonrise at this site:


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To understand this alignment, it's necessary to understand how the rising point of the moon on the horizon changes from day to day, and from year to year.

The Lunar Standstills

The variation in the rising point of the sun is much easier to understand than is the case with the moon, so it will be covered briefly first. The sun rises furthest to the north at the summer solstice, around June 21 each year. Following the summer solstice it will begin to rise a little further south each day, rising due east at the fall equinox around September 21, and reaching its southernmost rising point at the winter solstice around December 21. After the winter solstice the sun will begin rising further north each day, rising due east at the spring equinox around March 21, and finally reaching its northermost rising point again around June 21. The slow sweep of the sun's rising azimuth across the eastern horizon takes a full year, and practically repeats itself exactly from year to year. There is a small yearly variation in its behavior mainly due to the extremely slow change in the tilt of the earth's axis, a fraction of a degree over thousands of years. But for practical purposes, and certainly over the life of any one person, the sun's yearly cycle repeats itself exactly.

Another important aspect of the sun's motion is that the rising point changes very little from day to day when it's rising near either the northern or southern extremes of its motion. This phenomenon is known as the "standstill." For several days around either solstice the sun's rising azimuth will hardly change at all. In constrast, when the rising point is between the extremes, say around the equinoxes, the rising azimuth changes quite a bit from day to day. This phenomenon of "standstills" near the extremes applies to periodic motion of many kinds, including the motions of the moon, as we shall see.

The rising point of the moon changes from day to day in a very analogous way, marking out a sweep from north to south and back again, except that it takes only one month to accomplish one complete cycle. The actual period of this cycle is the "draconitic month" of 27.21222 days, on the average. Unlike the sun, however, the extremes of the northernmost and southernmost rising azimuths will not remain the same for each cycle. After noting the northernmost rising point for the moon during one month, one may very well find it rises at a point even further north the next month. In fact, there is an 18.61-year variation in the extremes of the moon's rising point. A picture here will illustrate the phenomenon clearly:


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The figure graphically represents the rising azimuth of every moonrise at the Octagon for the years 294 BC to 253 BC, a period of 41 years. Thus, a little more than two 18.61-year cycles are represented. It can be immediately seen that:

On this scale, the individual moonrises seem to be a jumble, but if we zoom in, the regular monthly variation in rising azimuth can be seen, in this case for the year 291 BC:


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The expanded diagram reveals that the variation in rising azimuth of the moon is actually comprised of two near-sinusoidal waves, one with a 27.21222-day period, and the other with a 18.61-year period. Note how the northernmost rising point of the moon changes slowly from month to month over the year 291 BC, reaching about 63.5º at the beginning of the year, and approaching 62º at the end of the year. This particular year is evidently far away from the "lunar maximum" year of 283 BC.

Sinusoidal functions by their nature exhibit "standstill" behavior near their extremes, where the function changes slowly. Since the variation of the moon's rising point is a combination of two near-sinusoidal functions, there will be two types "standstills"--one associated with the lunar draconitic month of 27.21222 days, where the moon at its extremes will tend to rise in nearly the same direction for two or three successive nights, contrasting to successive rises in between the extremes, where the rising azimuth changes by up to 5º each day (see diagram above). Thus, the moon cooperates with observers trying to pinpoint the monthly extremes, by conveniently lingering in the area of the maxima for a few days. The other "standstill" is associated with the 18.61-year variation, where the extreme rising points will change very little from month to month in the years where the azimuth range is greatest. In fact, moonrises in "lunar maximum" years, those we are concerned with in the main Octagon alignment, may be observed over a span of two years before the moon is again carried sufficiently away from the alignment. Typically, as we shall see, moonrises will reoccur along the axis in the 18th year after the last one, followed by several more in the 19th year, befitting an 18.61-year cycle.

Moonrise visibility

Now is a good point to introduce an obvious complication, and that is that not all moonrises are visible. The moon may rise during the day, for one thing. Also, the phase of the moon is important, as a new moon obviously can't be seen, nor can a very slender moon that is necessarily near the glare of the sun. There is also the problem of weather or hazy air obscuring the moonrise. While the weather effects can't be predicted, the other factors can be accounted for.

First, let's just redo the diagram above, but leaving out the moonrises that aren't visible due to predictable factors. Also, the size of the data points will be used to indicate the phase of the moon at moonrise, another indication of visibility:


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Looking at just the "maximum moonrises," i.e., those rising near the maximum azimuth for this particular year (around 63º), it can be seen that the maxmum moonrises are not visible for the first half of the year, and only start to become visible as thin crescents in about August, the maximum moonrise gradually becoming more full each month until the maximum moonrise near the winter solstice is a full moon. It's remarkable that this pattern of visibility and phase of the maximum moonrises is not unique to this particular year, but holds indeed for every year. Thus, there is a "season" for observations along the Octagon axis, occurring basically in the last quarter of the year. This will become more evident below when looking at the lists of actual maximum moonrises.

The reason for this constant pattern is not hard to discern. For example, the full moon--by definition opposite to the sun--always rises around the time of sunset on the opposite side of the sky. But at the winter solstice the sun sets as far south as it ever does. The full moon near this solstice, then, will rise in the opposing sky the furthest north it ever does. This is the definition of maximum moonrise.

Likewise, at the summer solstice the sun rises the furthest north it ever does. The new moon, by definition rising in conjunction with the sun, also will boast the "maximum moonrise" near this solstice. Unfortunately for would-be observers, the new moon is invisible, and hopelessly lost in the sun's glare anyway, so June is not a good time to look for maximum northerly moonrises, ever! In August or so the phase of the moon will be between new and full, and far enough away from the sun to be potentially visible. After that, it becomes progressively easier to observe the maximum moonrise, culminating in the full moon near the winter solstice. Following that the maximum moonrises occur during the day, and will not be seen again until the following August.

So it's interesting that this implies a regular pattern of activity of lunar observations at the Octagon, synchronized to the solar year, where activity is concentrated in the latter half of the year. Note that the maximum southerly moonrises exhibit a complementary behavior, where they are only visible during the first part of the year, ending around the summer solstice. An intriguing idea is suggested by the fact that the design of the High Bank earthworks near Chillicothe, Ohio, which include a practical carbon-copy of the Octagon structure, but oriented to the south, has been shown by Hively and Horn to include the maximum southerly moonrise azimuth.1 Thus, as suggested by Hively and Horn, the two earthworks, over 50 miles apart, may be complementary parts of the same observatory. This speculation is strengthened by the remarkable findings of Brad Lepper, Archaeology curator of the Ohio Historical Society, who has traced remnants of a road, marked by two parallel earthen banks, that stretches between the Octagon and its counterpart at High Bank.3

Lepper writes:

Using infrared and aerial photographic surveys, Lepper has found more traces of this road, now all but obliterated by agriculture and other development. He concludes "that the Great Hopewell Road was a virtually straight set of parallel walls 60 m apart and extending a distance of 90 km from the Newark Earthworks to the cluster of Earthworks in the Scioto Valley centered at modern Chillicothe... The function of the Great Hopewell Road is unknown, but similar structures built by the Maya were monumental expressions of politico-religious connections between centers."4


Plan of High Bank (Squier & Davis)

The predictable and complementary nature of the seasons suitable for observations at the two sites suggests that High Bank was used January through June (in our calendar) and the Octagon was used July through December. The solstices mark "the changing of the guard" and quite possibly the attendant ceremonies included a procession along this Hopewellian "Sacra Via," from Chillicothe to Newark after the summer solstice, and from Newark to Chillicothe after the winter solstice.

Maximum moonrises visible at the Octagon, 500BC to 2000AD

If we just consider those moonrises which are visible and which occur very near to the axis of the Octagon--say those with azimuth greater than 52.0º--then the total set of such moonrises even over the span 500BC-2000AD is manageable and interesting to see at a glance. In fact, by these criteria only 277 moonrises over the 2500-year period are found. They are represented graphically below:


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Click here to see the raw data for the above chart

The chart shows an interesting effect where there are fewer and fewer moonrises seen along the Octagon's axis over time. In fact, the last moonrise seen along the axis, where the moon was fully up, was in 1466 AD. The reason for this is the aforementioned slow change in the tilt of the earth's axis, which today is 22º 30', but in Hopewellian times was about 15' (0.25º) greater. This is interesting in that it implies the Octagon would not be a good lunar observatory today (for this alignment), but it was back in Middle Woodland times. As the chart shows, there were plenty of good moonrises to observe then. As one looks back in time before 500BC (not shown), the moonrises occur even further north, perhaps rising too far north of the alignment. Thus it is interesting that the alignment of the Octagon is suitable to gauge the maximum moonrise during the approximate life of the Hopewell culture, 100 BC through 500 AD, and not suitable very much earlier or later.

From the table, it's straightforward to determine the years corresponding to the maximum northerly moonrises. These mark the major lunar milestones that the Hopewell celebrated. For the years between 500 BC and 500 AD we have the following 54 lunar standstill periods:
 

standstill number
year
1 490BC
2 471BC
3 452BC
4 434BC
5 415BC
6 397BC
7 378BC
8 360BC
9 341BC
10 322BC
11 304BC
12 285BC
13 266BC
14 248BC
15 229BC
16 211BC
17 192BC
18 174BC
19 155BC
20 136BC
21 118BC
22 99BC
23 80BC
24 62BC
25 43BC
26 24BC
27 6BC
28 14AD
29 32AD
30 51AD
31 70AD
32 88AD
33 107AD
34 125AD
35 144AD
36 163AD
37 181AD
38 200AD
39 219AD
40 237AD
41 256AD
42 274AD
43 293AD
44 312AD
45 330AD
46 349AD
47 367AD
48 386AD
49 405AD
50 423AD
51 442AD
52 461AD
53 479AD
54 498AD

Click on any of the above standstills to see a chart of the moonrises. I've yet to add titles or legends to the charts, but see the chart for 107AD, which has been completed.

Patterns of Maximum Moonrises

Seasonal Patterns and the Minor Perturbation

Looking at the raw data for the 277 maximum moonrises in the chart reveals some interesting patterns. One pattern was mentioned previously, that is, the tendency of the maximum moonrises to occur in the latter half of the year. In fact, the moonrises can be seen to occur August through November. This then is the season for making observations along the Octagon axis.

A question that arises is why moonrises around the time of the winter solstice, in December or possibly January, do not appear in the list. As described, such winter solstice maximum moonrises will occur when the moon is full and very conspicuous. However, another small but capricious wrinkle in the moon's motion conspires to pull the winter moons off the alignment. This wobble is known as the "minor perturbation." Its discovery is credited to the Danish astronomer Tycho Brahe back in the 1500s. It's caused by a complicated interaction of the earth-moon-sun three-body system, but as such it might be expected to be somewhat synchronized with the solar cycle. Indeed, at the time of the solstices during lunar standstill years, the minor perturbation is always pulling the moon back away from its extremes.

The Metonic and Saros Cycles

Another pattern evident in the table is that the solar calendar dates of maximum moonrises often repeat, 19 years apart! For example, we have:

09/17/452 BC 4:38:29 UT 51.77º
10/14/452 BC 2:31:59 UT 51.72º
08/31/434 BC 5:27:58 UT 51.95º

and

09/17/433 BC 4:30:30 UT 51.81º
10/14/433 BC 2:23:05 UT 51.82º
08/31/415 BC 5:27:23 UT 51.74º

Even the time of day shows close agreement in the corresponding pairs of moonrises. This is the kind of result that makes one suspect a bug in the program, but there is an explanation based on an effect that was known in antiquity, called the Metonic cycle. The Roman historian Diodorous of Sicily, the "universal historian" of the first century BC, describes the "Hyperborean" tribes of north of the Roman Empire:

The close harmony of 19 solar years with 235 lunar months was probably known to Chinese atronomers in the third millenium BC, and was rediscovered by the Greek astronomer Meton of Athens in 632 BC. It is not known how far back in antiquity this knowledge dates.

1 solar year = 365.2425 days
1 lunar synodic month (full moon to full moon) = 29.53059 days

19 years = 365.2425*19 = 6939.6075 days
235 lunar synodic months = 29.53059*235 = 6939.6887 days

This is a difference of only 0.0812 days, or about two hours. So, after exactly nineteen solar years the sun will return to the same position relative to the stars (by definition), and the moon will have very nearly the same phase (just two hours difference). This fact was much appreciated by the Greeks, as the dates of the new moon, full moon, etc., would repeat every nineteen years. Each year was assigned a "golden number," one through nineteen, which indicated immediately the dates of the phases of the moon. The "golden number" still forms the ecclesiastical basis for determining the dates of Passover and Easter. The small error of the Metonic cycle will accumulate and causes a shift of a day every 222 years or so.

For the purposes of maximum moonrises, the above coincidence alone would not be enough to ensure that maximum moonrises will occur on the same date 19 years apart, it only guarantees the phase will be the same on the same dates. We have seen that maximum moonrises occur at intervals of the lunar draconitic period of 27.21222 days. This is the time it takes the intersection of the moon and earth's orbit to complete one revolution relative to the fixed stars. But here we see that actually three cycles converge every 19 years:

255 lunar draconitic months = 27.21222*255 = 6939.1161 days

This is only about half a day different from the other cycles, so the moon is very close to its maximum azimuth again (remember that the rising azimuth changes very slowly near the "standstill"). So, after 19 years, practically the same conditions obtain at the Octagon. If the Hopewell kept a solar calendar, say tied to the day of the summer solstice, they would have noticed that the maximum moonrises occurred on the same dates 19 years apart. It might even have been the key to their (and the "Hyperboreans") noticing the Metonic cycle in the first place.

I'd note that it's not clear in Diodorus' account who cribbed the idea from whom, the Hyperboreans or the Greeks!

Another well-known aspect of the Metonic cycle is that since the sun, moon and earth return to the same relative positions, the pattern of eclipses of the moon and sun may repeat somewhat after 19 years elapses. The half-day difference of the lunar draconitic cycle however is enough to throw the eclipse repeatibility out of kilter fairly rapidly, but three or four eclipses may repeat, on the same dates 19 years apart, before this happens. But an even better interval in this regard is the Saros interval of 223 lunar months:

223 lunar synodic months = 29.053059*223 = 6585.3216
242 lunar draconitic months = 27.21222*242 = 6585.3572

So the two lunar cycles, so important for eclipse prediction, differ by only 0.0356 day, or 51 minutes. This is much closer agreement than in the case of the Metonic cycle, where they differed by a half day, and therefore eclipses will repeat more perfectly. In terms of the solar year, this is unfortunately not an integral number of years, but is rather 18 years, 11 1/3 days. So, eclipses, the phases of the moon, and more importantly for our discussion, the maximum moonrises, will occur exactly this interval apart. Very convenient given that sometimes maximum moonrises are seen in the 18th year as well as the 19th year of each cycle. For example, again from the table we have:

09/06/489 BC 5:04:37 UT 51.7º
10/03/489 BC 2:58:19 UT 51.79º

and

09/17/471 BC 4:50:33 UT 51.84º
10/14/471 BC 2:42:50 UT 51.67º

These pairs of moonrises occur 18 years and 11 days apart.

Again, if the Hopewell kept an accurate solar calendar (even if not written down), and made these maximum moonrise obervations as postulated, I don't think there is any question that they would have noticed these simple relationships of the moonrises occurring on the same dates 19 years apart, and the same dates shifted by 11 days, when observed 18 years apart. Whether or not they had such a solar calendar where the days were clearly enumerated is perhaps the biggest question, but nevertheless it is fascinating that two famous cycles, the Metonic and Saros, naturally fall out of simple observations at the Octagon, or indeed any observatory set up to observe lunar standstills. The "sacred precinct" in Diodorus' account has long been thought to refer to Stonehenge, which in the earliest stages of its construction was a simple circular raised embankment with an opening used for observing the maximum northerly moonrises. I think that it's easier to make the case that the 19-year cycle is something that naturally falls out of making such observations, and the tale by Diodorus is a smoking gun that Meton, and Western science, has taken credit for an idea from a "primitive" people intensely interested in tracking the moon.

They did so for an ancient reason:

The historian Pliny likened this skill to magic: Perhaps it's appropriate to bring in a modern expression:

Notes:

1. Hively R. and R. Horn

2. Everts and Beers, Combination Atlas Map of Licking County Ohio, 1875. 3. Lepper, B. T. 1994: The Great Hopewell Road: a Middle Woodland Sacra Via Across Central Ohio, Paper presented at the joint meeting of the Midwest Archaeological Conference and the Southeast Archaeological Conference, Lexington, Kentucky.

4. Lepper, B. T., The Newark Earthworks and the Geometrical Enclosures of the Scioto Valley: Connections and Conjectures, printed in A View from the Core: A Synthesis of Ohio Hopewell Archaeology, edited by Paul J. Pacheco (Ohio Archaeological Council, 1996).

5. Hawkins, Gerald S., Stonehenge Decoded, Doubleday 1965.

6. The Ley Hunter Journal, No. 130, Summer 1998, p. 6.

7. Pliny's Natural History in Philemon Holland's translation, selected by Paul Turner, Centaur Classics 1962.

Octagon Lunar Calendar

More on the HOPEWELL ROAD

Aeolian wind harp inspired by the Octagon mound, from Sonic Architecture

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