An Archaeogeodesy Study of the Miami River Circle:

Possible Evidence of Astronomical and Geodetic Knowledge in Prehistoric Florida.

©1999 by James Q. Jacobs. All Rights Reserved.


(This page was created as a personal communication forum. It was written on the Spring Equinox of 1999 and was publicly published on the WWW on May 28, 2000. For more detailed astronomical information see my earlier Miami Circle page and the links therein. )

This article is intended to communicate my findings and foster discussion regarding the Miami River Circle. I welcome your responses. This page assumes the reader has an understanding of astronomy and geodesy.


I created an application for my archaeogeodesy studies, entitled Aegeo_Calc_3. It is programmed to adjust astronomical constants and geodetic values according to the epoch specified by the user. The formulas employed in the programming are illustrated in Table 1. The sources of these formulas and other data used are listed on my Archaeoastronomy hub page.

Table 1. Astronomy Formulas.
Sidereal Orbit
(365.25636042 + 1.1 x 10-7 TE) days
Tropical Year
(365.24219878 - 6.14 x 10-6 TE) days
Sidereal Lunar Orbit
(27.3216610 - 2.0 x 10-7 TC) days
Lunar Mean Daily Sidereal Motion
(13.1763582975 - 1.0224 x 10-8 TC)º
Obliquity of the Ecliptic
23.4392911111° - 0.0130041666... T 
- 0.00000163888... T2 + 0.0000005036111... T3
Annual Secular Polar Motion
0.00000972222....° along the meridian 65° W.
Given TE = Julian centuries (36,525 days) from day 0.5, 1900 ET
Given TC = Tropical centuries from day 0.5, 1900.0 
Given T = Julian centuries from 2000.0

Aegeo_Calc_3 solves, for three sites, site to site arc distances, site to site bearings, the differences in latitude and longitude between sites, and other determinations.  Level horizon solar and lunar (major and minor) illumination angles (obliquity / latitude cosine) and bearings are solved for one site. All these results plus the site latitudes and colatitudes are converted from degrees to radians, diameters, ratio to circumference, sine, cosine, tangent and modules based on fundamental astronomical motions. Several of these modules are illustrated in Figures 1 and 2, together with data corresponding to 2000.0 A.D. and my abbreviated computational code terms.

Figure 1. Relationships of Lunar Orbit to Earth Motions.

Figure 2. Relationship of Lunar Orbit to Earth Orbit.

What information I have for the location of the Miami Circle is based on information collected from several sources. I scaled the coordinates from a 1:24,000 USGS topographic map. The result is assumed to be within a block of the true location. While this is sufficiently accurate for the considerations herein, I continue to seek more precise coordinates. Latitude was scaled at 25.768595° N. (25° 46' 6."94). Herein longitude is not relevant.

The Archaeogeodesy Study

Based on recent radiocarbon dating of charcoal samples from the Miami River Circle I tentatively set the Aegeo_Calc_3 epoch to 0 A.D. The solstice level horizon illumination angle revealed a very obvious result of interest. The angle between the summer and the winter solstice rise/set positions expressed a nearly precise integer of the module: 'lunar motion per earth rotation' (R27). This module expresses the ratio of two of the three fundamental cosmic motions. By adjusting the temporal epoch I determined that the relationship was precise near the year 250 A.D. Figure 3 illustrates the sunrise view at the Miami Circle latitude and the solstice angle (obliquity / latitude cosine) relationship for 250 A.D..

Figure 3. Sunrise View from Miami River Circle.

The latitude where 'obliquity / latitude cosine' equals 4 R27 today is about an eight of a degree (about 9 miles) north of the Miami River Circle. Due to the temporal change in the obliquity of the ecliptic, this position in latitude shifts about 25 feet per year. The same angle at the Miami River Circle's location also once expressed the mean daily lunar motion module, four times C27 around 500 years earlier. These findings offer two alternate possible inferential dates for the monument. At first one date seemed as likely as the other. Because R27 is a more significant and fundamental relationship, and also nearer the radiocarbon dating results, I set the Aegeo_Calc_3 epoch to 250 A.D. This led to noticing another obvious result of interest.

While reviewing the spreadsheet that displays the temporally adjusted astronomical constants, I noticed that the number of days per year for 250 A.D. was an even 1/1000th fraction of a day, at 365.2423000 days. An even 1/1000th fraction occurs only once in about 1680 years. The number of days per year around 3114 B.C. (very near the beginning date of the prehistoric Mesoamerican calendar and the ancient Indian Kali era) was 365.2425000. Aegeo_Calc_3 resolved that the number of days per year was exactly 365.24230000 at epoch 251.5 A.D. At that exact time the solstice angle equaled precisely 4 R27 at latitude 25.770250 degrees. That latitude is just 600 feet north of the scaled coordinates I am using for the circle! Table 2 compares the geodetic and astronomical results for 251.5 A.D. and 2000.0 A.D.

Table 2. Temporal Comparison.
251.5 A.D.
2000.0 A.D.
Latitude of the Miami River Circle
Obliquity of the Ecliptic (OB)
Obliquity / latitude cosine at the Circle
Days per Year (DY)
365.24230000 days
365.24220492 days
Lunar Motion per Rotation (R27)
Days per Lunar Orbit (S7)
27.32166430 days
27.32166120 days

I also examined the site to site relationship of the Miami River Circle to other prominent ancient sites and monuments. This inquiry was not particularly fruitful. The arc distance to Big Mound equals 1/50th of a radian, to Crystal River Shell Mound 1/15th. The site is 1/4 radian almost due south of the Meadowcroft Rock Shelter. A relationship to Tikal, and other sites on the Maya Meridian, was noticed. These will be discussed in a future communication when I release findings about the Chaco and Tikal meridians. The arc distance to the Boyne Valley (Newgrange) complex in Ireland is precisely 60 degrees. Relationships to numerous other sites were checked and the above relationships noted do not exceed the number that might be expected due to chance. And, excepting Tikal and the distance to Boyne Valley, the results do not fit the pattern of relationships observed for other monuments. Additionally, the Miami River Circle does not fit the class of the other major monuments considered, large mounds and earthworks that remain visible place marks in the landscape for many millennia. Therefore, there was little expectation that these should have site to site relationships with the Miami River Circle.

Suggested Further Study

What can be done to further assess the possibility that the site is an intentional astronomical monument? Some obvious questions come to mind.

  • Is there another monument at the latitude where the solstice angle equaled 4 C27 in 251.5 A.D., that being at latitude 26.092409° (26° 5' 32."67) or at precisely 0.323814° (19' 25."73) north of the Miami River Circle?
  • Are alignments to the solstice sunrise and sunset positions evidenced in the ground plan?
  • Are there any outlier features or other monuments along the 251.5 A.D. solstice alignments?
  • Are the solstice angles, 2 R27 or 4 R27 (26.28076° or 52.56152°), evidenced in the ground plan? Are R27 or C27 evidenced?
  • Does the ground plan evidence the 251.5 A.D. obliquity of the ecliptic angle (23.666667°) or twice the obliquity angle (47.333333°)?
  • Does the ground plan evidence the latitude or colatitude angle?
  • Are there any other monuments at the same latitude elsewhere in Florida or North America?


If the Miami River Circle was created to monumentalize astronomical knowledge, it was done with amazing accuracy. If not, the probability of such exactive coincidence is also amazing.

Accurate astronomical knowledge is evidenced elsewhere for the era considered. Several years ago I discovered, in ancient Indian (Asia) literature dating to 500 A.D., a nearly precise ratio of lunar orbits to earth rotations (57,753,336 : 1,582,237,500). Details of that research are presented on another Web page, entitled "The Àryabhatiya of Àryabhata. The oldest exact astronomical constant?" It is therefore not surprising, at least to me, to find this inference of accurate astronomy in other cultures during approximately the same period. Precise knowledge of the number of days per year and earth rotations per lunar orbit can be arrived at by counting or keeping records for a long period of time. This could plausibly have been accomplished during the prehistoric period by any stable culture with arithmetic and notation. Determination of the obliquity of the ecliptic and the precise latitude would also have been necessary to situate the monument. This can be accomplished using a gnomon and comparing the local noon angles of illumination to plumb. Also, the relationship of local level (quite obvious on a shoreline) to the celestial pole or celestial equator can be easily determined. These methods are assumed to be easier than measuring the actual solar positions on the horizon. Knowledge of a computational approach to level horizon angle is herein utilized, that being obliquity / latitude cosine, not the actual horizon of the site or solar position on the horizon. That knowledge is a trigonometric function of latitude in combination with obliquity. The quantities considered can also easily be measured using zenith transit illumination angles and shadow measures.

It would have been possible to create an astronomic monument at the Miami River Circle latitude when the solstice angle equaled 4 R27 without noticing that the number of days per year equaled exactly 365.24230000. Because R27 expresses the sidereal relationship of earth rotation and lunar orbit, no knowledge of days per year would be necessary to determine the angle of the module. The R27 module is also monumentalized by the arc distance between Great Circle monuments in Florida and Ohio, as discussed in the Archaeogeodesy Pages.

In conclusion, a range of inferences is possible. At one extreme the monument can be inferred to be located where it is simply because of the river mouth and without relationship to astronomy. At the other extreme, the site can be seen as a monument encoding very exactive astronomical and geodetic knowledge, including some or all of the following:

  • Understanding of the fundamental motions of the earth and the moon and their precise periodicities,
  • Knowledge of the shape of the earth,
  • The precise latitude,
  • Knowledge of the inclination of the axis of rotation,
  • Knowledge of the temporal change in the number of days per year, and
  • Awareness of the uniqueness of the length of the year as 365.2423000 days around 250 A.D.
  • A level of mathematical sophistication, including, at a minimum, geometry, and possibly trigonometry.

Finding a similar monument at the latitude where the 4 C27 angle occurred on 251.5 A.D. would provide difficult to refute evidence that the monuments were intentionally astronomical.

This article was written and posted on the Spring Equinox, 1999. I discovered these possibilities only three days ago. Certainly more study and consideration are in order. The Miami River Circle, while certainly singular and unique, is not a monument in total isolation, and should not be judged as such. It should be assessed in the context of other constructions during the same era, such as the surveying and geometrical knowledge evidenced by Teotihuacan, the Hopewell Earthworks and many other monumental sites in the Americas during the same and previous epochs. Before concluding that the astronomy of the Miami River Circle is just coincidence, we should also keep in mind that our paradigms can limit what we may or may not learn. 

Read the Archaeogeodesy Pages.

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©1997 by James Q. Jacobs. All rights reserved.
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Published May 28, 2000. Edited only slightly thereafter.