04/16/2026.
The lunar standstill alignments at the Newark Octagon are generally described as "precise". In fact, we are told that they have "remarkable" precision and "uncanny" precision. (Romain 1991:28; Lepper 2016:41) Unsurprisingly, this term is picked up by local media. We find the Cleveland Plain Dealer, in 2023, saying,
That is equally true for our Indigenous neighbors in Northeast Ohio today and of the ancient peoples who once inhabited these lands with their sophisticated understanding of how to build earthworks aligned with extraordinary precision to the movements of the Moon.
The Smithsonian Magazine (2025) put it like this:
The Hopewell likely equated spiritual significance to these moon movements that align precisely with the Octagon.
I'd like to take a look at the level of precision in the Octagon, and also take a closer look at the flip side of what such claims of precision mean.
Ray Hively and Bob Horn (Hively and Horn 2013: 87) tell us how precise they are:
Our initial work at Newark (Hively and Horn 1982) provided a list of reasonable possibilities for alignment of parts of the earthworks’ structure to the lunar standstills. The lunar alignments in this list fall into two distinctly different categories: (1) seven alignments (along intentionally designed linear features or between the centers of geometrical figures whose relative positions were seemingly intentional) that defined points on the horizon to a precision of better than 0.25°; (2) nine additional alignments to the lunar standstills which explain other degrees of freedom in the earthworks' design but which do not involve unambiguous linear structures.
In that 2013 paper, they re-examined one of the assumptions of their 1982 paper, that is, that the alignments were with lunar moonrises and moonsets when they were seen against the (sometimes distant) local horizon. One of the things that prompted that re-examination was the northernmost leg of the Octagon (a moonset), which was something like 1.6° off alignment. In that direction sit the Welsh Hills, which raised the horizon and strongly affected when the moon would touch the horizon. They wondered if maybe the Indigenous Peoples were instead using a zero horizon, that is, pointing the leg to where the moon would set if the hills weren't there.
The following picture shows what the moonset over those hills would look like.
Here, the transition from dark to lighter green marks the horizon if the hills were not there, and the (invisible) location of the moon behind the hills is shown.
Hively and Horn recalculated their alignments using this different assumption. They call the original assumption the local horizon assumption (HL) and the newer one the zero horizon assumption (HZ). Their conclusions:
Evaluating the accuracy of the proposed eight alignments as shown in Table 1, we note the following: (1) under hypothesis HZ the alignments have an average error of 0.46° and a maximum error of 1.6°, with seven alignments having an average error of 0.31°; (2) under hypothesis HL the alignments have an average error 0.56° and a maximum error of 1.7°, with the six best alignments having an average error of 0.25°.
Summarizing, their best candidates for alignment have an error of around 0.25°, while lesser candidates have an error of about 0.5°. Over the length of an Octagon leg, those amount to transverse displacements of 2.7 and 5.4 feet, respectively. Hively and Horn conclude that the zero horizon assumption fits the data better (and in particular fixes that anomalous leg of the Octagon).
The Flip Side of Precision
One thing that I get out of this is there may be less precision than popularly advertised: if you can change your assumptions like that without changing the major conclusions by much, I personally would prefer a different set of adjectives.
Which leads me to the question: how precise ought they be? Given the sorts of tools available to the Indigenous Peoples of the Hopewell Culture at the time, what sort of precision ought we expect from a group of smart people, people who, in addition to their natural artists and natural biologists, would also have people who were natural engineers.
So I ask, how precise really is the phenomenum itself? This is the flip side of the precision involved in making the Octagon.
Let me try to give you a perspective on how precise such astronomical observations tend to be by looking at the equinoxes. How "precise" is the spring equinox sunrise?
At the spring equinox, the sun is really hoofing it on its way from rising in the southeast for the winter to rising in the northeast for the summer. If it rises nearly in the east on March 21, it will rise approximately 0.5° farther north on March 22. That is, every day around the equinox, the sun rises ½ a degree farther north. And that ½ a degree is about the width of the sun.
This picture tries to show that advance of the sun along the horizon. Start at the bottom right 4 days before the equinox, and the sun rises slightly south of east. Move up and to the left to see its set 0.25° closer to due west. By the next morning, it rises 0.5° farther to the north than the previous day. On Equinox Day, you should be able to see that the sun is not right in the middle, due east. (This is what actually occurred for the 2026 spring equinox at Newark, but it is slightly different every year.)
Given the fact that the actual astronomical equinox itself need not occur right at sunrise, that means that the equinox sunrise has an inherent average imprecision of half that 0.5°, that is, 0.25°. [In fact, that imprecision, for any particular equinox sunrise, also depends on where you are. For instance, the equinox in 2026 was on March 29 at 10:46am. Sunrise was at 7:33am, 3 hours before the equinox. However, in Madrid, Spain, their sunrise was 8 hours before the equinox. So, on the day of the equinox, the sun had 5 hours to rise at a slightly more northern point on the horizon than the sun did rising in Madrid. That works out to about a 0.1° difference in the sunrise azimuth.]
Hively and Horn (2013) do address this flip side of precision (again, the precision of the phenomenon, as opposed to the precision of trying to document it). Here is what they say:
In computing the azimuths of lunar events, we have utilized standard algorithms described elsewhere (Hively and Horn 2006). The algorithms correct for the effects of altitude, refraction, and parallax and are believed to yield azimuths accurate to 0.05°. We have computed all azimuths for a date of A.D. 250. Uncertainties in the date (± 200 years) contribute an uncertainty in rise/set azimuths less than 0.05°.
To tell you the truth, this is an easy paragraph to skip over while looking at their more interesting results. However, it illustrates the care they took to carefully analyze and report the details of their research.
However (sorry). The funny thing is, there wasn't a Standstill in A.D. 250. There were Major Standstills in A.D. 238 and A.D. 256. There was a Minor Standstill in A.D. 247. There is something else going on with their numbers.
Don't forget, the original Hively & Horn paper appeared in 1982. Back then, they did not have the computing power we have today. In fact, what they used to compute their azimuths were tables showing broad results published in 1972 (and Hively and Horn modified their calculations based on those tables to add atmospheric effects in 2006). They noted "The computed azimuths we have used for extreme lunar rise/set points are mean azimuths. The observed azimuths would exhibit a cyclic variation about the mean with an amplitude of 0°.2 and a period of 173.3 days." (Hively and Horn 2006: 297). (I'll come back to the 173.3 days.) They also note rather large variable atmospheric effects but say these would "average out with observations repeated over long periods of time." (Emphasis added.)
[I have put a copy of the paper with the tables here: Astronomical Tables Intended for Use in Astro-Archaeological Studies. Look at it just to see what Hively and Horn had to deal with.]
Back in 2015, I posted something on Facebook regarding the northern moonrises around the Major Standstills between the years 10 and 400. This is the graph at the heart of that posting:
I've memorialized that Facebook posting in 400 Years of Major Standstills. I have also flipped the picture up/down to show it here. The original shows the azimuths (degrees south of north) of the moonrises; I find it much more intuitive when looking at moonrises/sets at the earthworks to instead use degrees north or south of east. ["I'm a physicist, Jim, not an astronomer."] Then, on a graph, the maximum moonrise actually looks like a peak (as in a maximum moonrise) rather than a valley.
That picture shows the Major Standstills (one differently colored line for each of the 21 Standstill between the years 10 and 400) looking through a 4-year window, Jan-Dec, Jan-Dec, Jan-Dec, Jan-Dec. What interested me at the time is the way that the peaks occur at the equinoxes with corresponding dips at the solstices. But what I want you to get out of that picture right now regarding the northernmost lunistice moonrise is that the occurrence of the event itself is inherently imprecise.
This is really only something one would see with the advent of easy access to computers. As I've mentioned before, back then in 2015 I grabbed a software package from the Naval Observatory and wrote an interface so that I could (and did) look at every moonrise from the year zero until the year 2043 (or so). And then I analyzed the heck out of it. See, for instance, another Facebook post of mine: The Nutation at the Major Standstill.
I have also written about how motions of the earth, sun, and moon "conspire" to pretty much hide the 18.613 year Standstill cycle that everybody likes talking about (even though that specific interval was something that was almost certainly unobservable by the Indigenous Peoples of the Hopewell Culture). See Calendar Sticks and Lunisolar Calendars. The 18.6 year cycle is overlain onto the yearly seasonal cycle as the latter interacts with the lunistice cycle. The timing of the peak of the 18.6 year cycle is completely obscured.
Here's a table that shows the dates and times of the Major and Minor Standstills between the years zero and 315.
| Table 1 | |
|---|---|
|
Minor Standstill
|
Major Standstill
|
The Inherent Imprecision
Now, let's try to get a handle on the inherent imprecision of the lunistice moonrises.
This graph shows the absolute northernmost boreal (northern) lunistice moonrises and moonsets for the Major Standstills between the years 0 and 300.
I've included moonsets (in red) since, from the equations that govern gravitational physics, moonrises and moonsets should be symmetric. Any difference comes from timing of the events (as we saw for the solstices, above), not the physics. See also Reflecting on Symmetries. What we see, contrary to Hively and Horn's hope that they should have an accuracy of 0.05°, we see, over those three hundred years, a spread of nearly 0.25°. That is half the width of the moon.
We get a similar graph when plotting the absolute southernmost boreal (northern) moonrises and moonsets at the Minor Standstill.
We see the same 0.25° inherent imprecision.
Those pictures ignore the inherent difficulties of observing the absolute northernmost lunistice moonrises or moonset. After all, the moonrises that occur in the Spring happen during the daytime, while the moonsets that occur in the Fall also happen during the daytime. And then there is Ohio weather.
But those graphs only show the absolute peaks in the moon's motion, the one extreme event in a nearly 20-year period. An extreme event that would be easily missed in Ohio's weather, or which occurred near noontime.
A Different Look
Let me try to get a different handle on what was observable, by looking at a specific 1½-year period over those 300 years. Since the peaks are driven by the equinoxes, I look at the 6-month period containing the exact time of the Standstill, and centering on the equinox of that period. (Refer back to Table 1.) And then I include another 6-month period on either side of that. So, for example, for the Major Standstill on April 27, 89, the major 6-month period runs from December 21, 88 to June 21, 89. The 6-month period of interest before it runs from June 21, 88 to December 21, 88; and the 6-month period of interest after it runs from June 21, 89 to December 21, 89.
Those seasons drive the peaks of the lunistices, and as I've noted elsewhere, the seasons are what the natives would have been focused on. Also, from the past few years in which we have been observing the lunistice ourselves, those three 6-months periods really do provide prime viewing. Finally, over that 18 month time-span, the change in azimuth attributed to the 18.6 cycle changes less than 0.1°. It is, after all, at the peak of a cosine curve.
In this figure, I have plotted every northern lunistice moonrise and moonset over that 300-year span during that 18-month period around the central equinox at the Major Standstill. Every vertical "line" is separated by 27.3 days (the lunistice period).
And this is the corresponding figure for the 18 months around the Minor Standstills.
This is what observers see. This shows the inherent imprecision of the phenomenon. And, I might add, this is what the designers of the Octagon were trying to capture.
Possible Implication
So, what are we to think about all this? On the one hand, the vertical lines have quite a bit of "imprecision", even right on top of the extremal northern lunistice moonrise or -set. But on the other hand, there is also fuzziness between the equinoxes and the solstices. The latter more-or-less doubles the "imprecision".
I have written in the past about how the archaeological and astroarchaeological culture around the Newark Octagon tends to assume that the Indigenous Peoples of the Hopewell Culture were targeting the absolute extrema. Their resident astronomer would give the specific date of the one, most important moonrise along the axis of the Octagon. We were told what the one date would be 18.6 years from now. People even went out to try to witness the noon moonrise on March 7, 2025 since it was the absolute maximum this cycle. See The Northernmost Moonset and the Invisible Northernmost Moonrise.
Yet as I wrote about in Calendar Sticks and Lunisolar Calendars, for the Zuni, it is about the seasonal cycles, and strong-sun/weak-moon vs. weak-sun/strong-moon. So, maybe the alignments at the Octagon care about the whole (18-month?) period. Maybe the alignments really are about a broader, more holistic cyclic process, rather that a very "western culture" emphasis on the absolute maximum
I suspect that the fuzziness of the "precision" of the phenomenon speaks more for the former. There simply is no single maximum that is maintained cycle over cycle.
Clean-up on Aisle 173
The following is a bit of an addendum. I want to talk a bit about Hively and Horn's 173.3 day cycle. If you've been following my stuff, you'll know I claim a 177.84 day cycle.
This is not a slam on Hively and Horn. As I wrote above, they were using tables of data to try to extract what they needed. I had the luxury of being able to generate a data set of every moonrise/set for over 2000 years. Who knew that the nutation that affected the equinoxes was not the 173.3 day one?
I described my process of looking for resonances in The Nutation at the Major Standstill. There, I indexed the moonrises (which do not occur exactly regularly, introducing some fuzziness) and then looked for resonant frequencies. The main one there was of course the 18.6 year cycle (with some overtones), followed by the 177.83 day cycle that particularly manifests itself at the equinoxes. That was followed by a much weaker 8.85 year cycle regarding the rotation period of the argument of perigee for the ellipse the moon traces around the earth.
One could ask why I just didn't do a Fourier analysis. Part of that was laziness. But another reason is that a Fourier analysis does a frequency analysis on one's data points which, particularly for a long-term frequency of 18.6 years embedded in a relatively short 2000 years, is locked into a set of equally-spaced frequencies that do not necessarily match the relevant period the way a resonance does.
But I finally got to it, and this graph shows the result of a Fourier analysis. You can click on it to get a much larger, readable version. (There are a LOT of frequencies represented.)
You can see that the 18.6 year cycle shows up as 18.4 years (which is exactly what I was concerned about with this method). That was the closest frequency available. The 9.3 year cycle shows up as 9.2 years. It does catch the 177.84 day and 173.31 day cycles pretty accurately, and also shows which one dominates (177.84).
But we can see that another way, too.
The 173.31 day cycle is related to eclipses. It tracks when, over the 18.6 year cycle, the moon crosses the equator (called for some strange reason, a "node") when the moon, sun, and earth are all lined up. In other words, it indicates when an eclipse can happen. The 177.84 day cycle is a bit different—it is a gravitation effect related to the difference between the moon crossing the equator when the axis of the earth is closest to the axis of the tilt of the moon's orbit, and when it is farthest. These two equations show how all these numbers are related. 18.613 years is 6798.247 days,
Both cycles are aligned with the seasons, but they do so in different ways. I could throw some fancy math with sines and cosines to prove that, but let me go instead with a couple of pictures.
This picture shows how the four different cycles interact, and how they can reinforce each other. The dark blue line shows the 18.6 year cycle with some of its overtones (the 9.3 and another at 6.2). It of course is what drives the Standstills. The green line has a period of half a year. It of course illustrates the seasons. It does not effect the moonrises; it is there to show you where the seasons are. The red line shows the 177.84 day gravitational effect. Its height (also true for the light blue line) means nothing in this context—it has that height just to make it visible. The light blue line is showing the 173.31 day eclipse cycle.
Only the red line affects the lunistice moonrises at the Major Standstill. The other two just show where they are in their phase compared to it. What you can see (I hope) is that the 177.84 day cycle drives the moon a bit farther north at the equinoxes, and a bit farther south at the solstices. The blue line could do the same if it had any strength (it doesn't).
Now, let's look at what those cycles are doing at the Minor Standstill.
Because of that missing "2" in the equations above, the 177.84 day cycle is exactly out-of-phase at the Minor Standstill. At the equinox, it drives the moonrise farther south (which is what we are looking for at the Minor Standstill: a southernmost northern moonrise). Note that this is exactly what we see in the Minor Standstill "precision" graph, above. This confirms that what we are seeing is the 177.84 day cycle, not the 173.31 day cycle.
One of the really cool things about this (to me!) is that this 177.84 day cycle, by being out-of-phase with the seasons, widens the spread between the Major and Minor Standstills. If it weren't out-of-phase, then the entire spread would move north or south together. However, instead, the entire spread of northern moonrises gets spread even more, making it even more noticeable.
In the end, all this precise astronomical tomfoolery results in a phenomenon that's not really all that precise: there are all these additional odd cycles that add jitter. Nonetheless, the Indigenous Peoples were able to look past that jitter and distill it into their grand demonstration and celebration of the motions of the moon.
I would not call the alignments "precise". They cannot be more precise than the moon, which isn't very. However, I would call the alignments "manifest". Based upon what is happening in the sky, it is obvious (even if I did have to write all of the above to make it so) that the Octagon is aligning with the moon, based more on the weight of the evidence than the precision.
The Octagon is manifestly aligned with the moon.
References:
Cleveland Plain Dealer 2023
Finally, attention to the diversity and importance of Ohioʼs Indigenous history and people. Editorial. Cleveland Plain Dealer, Feb. 10, 2023.
Hively and Horn 2006
A Statistical Analysis of Lunar Alignments at the Newark Octagon, by Ray Hively and Robert Horn. Midcontinental Journal of Archaeology 31(2):281–321.
Hively & Horn 2013.
A New and Extended Case for Lunar (and Solar) Astronomy at the Newark Earthworks, by Ray Hively and Robert Horn. Midcontinental Journal of Archaeology, Vol. 38, No. 1 (Spring 2013), pp. 83–182.
Lepper 2016.
The Newark Earthworks. A Monumental Engine of World Renewal, by Bradley T. Lepper. In The Newark Earthworks, ed. Lindsay Jones and Richard D. Shiels. University of Virginia Press (1991), pp. 41-61.
Romain 1991.
Evidence for a Basic Hopewell Unit of Measure, by William F. Romain. Ohio Archaeologist, 41:4, 28-37 (1991).
Smithsonian Magazine 2025
An Ohio Earthwork Where Thousands Once Gathered for Celestial Observations and Religious Ceremonies Is Open to the Public, by Kevin Williams. Smithsonian Magazine, May 9, 2025.