Easter Aquhorthies

Easter Aquhorthies (i.e. apocathery) has eleven stones in a circle and in between the two south-to-south-west stones is a large (bridging) recumbent stone, more commonly found in Scottish circles  and associated (by Alexander Thom) to lunar observatories because, in Scotland at lunar maximum standstill, the moon can rest upon or be hidden by a raised horizon.

Picture by krautrock, a member of megalithic.co.uk in June 2010.

Figure 1 Alexander Thom’s site plan, with cardinal directions and highlighting the diameter .

It is tempting to assume geometry within stone circles and this one invites that by having eleven regularly placed stones,. However, 11 is rarely found in regular geometries or stone circles. But,

  1. Eleven is associated (geometrically) with the simplest approximate ratio for pi, of 22/7 and, being on a circle perimeter 22 units on the perimeter means 7 as the diameter. However, the diameter here is 7 x 9 = 63 so that 7 units of 9 feet in diameter translates into 22 x 9 = 198 feet on the circumference.
  2. The second symbolism of eleven is found in the solar time cycles of 33 years which traditionally references as the Solar Hero cycle as the age when heroes die. 33 years was signified in this way because of an exact alignment, at which Equinox sunrise should repeat on the distant horizon every 33 years. While the solar year is 365 whole days long it takes an extra 32/132 of a day for the Earth’s orbit to complete, and this fraction (of 32/132) depends upon 4 x 33 = 132 losing its 33, 33 years after an earlier Equinox on the horizon. (Note that one did not need to know the data and then calculate, as we do today: instead, observation of in-exact solar risings or settings could notice near exact repetitions occurring after 8 years, but more perfectly after 33 years.

Returning to the circle, the circumference of this stone circle is 198 feet which is 6 x 33 = 198 so that the 11 stones may be referencing 33 solar years.

The 33-year period is strangely linked to the movement of the moon’s nodes, which take 18.618 years (of the nodal period) to progress once around the path of the sun (ecliptic). The area under this precession of the lunar nodes (pi x 18.618^2 = 1,088.970022752789) relative to the earth it orbits, which closely equals the area of a square of side 33 x 33 = 1,089.

The megalithic and ancient world both made monuments conforming to the equal area and equal perimeter geometries and even though the equal area situation is proven unsolvable, one sees that (before the notion of an analytic solution) a perfect example was found of a workable pair of numbers (33 years and 18.618 years) was available as these two very significant astronomical time periods.

If the circle is 63 feet in diameter, then one divided by 14 and multiplied by 11 to obtains the square of equal perimeter: 63 x 11/14 = 49.5, which is 99/2 feet on the side. This can then establish the radius of the circle as 18.618 of the same units: When divided by 33, 99/2 becomes 3/2 which is the unit for the radius of the circle of equal namely 18.618 x 3/2 = 27.927 or nearly 28 feet. Below is a picture showing the square and the circle, equal in area in red while the perimeter of the stone circle is equal in perimeter to the red square.

One can see that the red circle embraces the recumbent stone
and its altar-like appendages.

The Geocentric Orbit of Venus

It is helpful to visually complete the movement of Venus over her synodic period (of 1.6 years) seen by an observer on the Earth.

figure 3.13 (left) of Sacred Goddess in Ancient Goddess Cultures
version 3 (c) 2024 Richard Heath

In the heliocentric world view all planets orbit the sun, yet we view them from the Earth and so, until the 16th century astronomy had a different world view where the planets either orbited the sun (in the inner solar system) which like the outer planets orbited the earth, this view called geocentric. The discovery of gravity confirmed the heliocentric view but the geocentric view is still that seen from the Earth.

The geocentric was then assumed to be wholly superseded, but there are many aspects of it that appear to have given our ancestors their various religious views and, I believe, the megalithic monuments express most clearly a form of astronomy based upon numbers rather than on laws, numbers embedded in the structure of Time seen from the Earth, and hence showing the geocentric view had more to it than the medieval view discarded by modern science.

Venus was once considered one part of the triple goddess and the picture above shows her complete circuit both in the heavens and in front of and behind the sun. The shape of this forms two horns, firstly in the West at evening after sunset. Then she rushes in front of the sun to reemerge in the East to form a symmetrical other horn after which she travels behind the sun to eventually re-emerge in the West in a circuit lasting 1.6 years of 365 days, more precisely in 583.92 days – her synodic period.

Continue reading “The Geocentric Orbit of Venus”

Utility of the Ushtogai Square to count the Nodal Period

Using Google Earth, a large landform was found in Kazakhstan (Dmitriy Dey, 2007); a square 940 feet across with diagonals, made of evenly spaced mounds. We will demonstrate how the square could have counted the lunar nodal period of 6800 days (18.617 solar years)

 images courtesy of Wild Ticket

Counting the Lunar Nodal Period

One can see the side length of the square contains seventeen (17) mounds, with 16 even distances between the mounds. Were one to count each side as 17 mounds, then four times 17 gives 68 which reminds us of the 6800 days in the moon’s nodal period of 18.617 years. If 17 can be multiplied by 100, then one could count the nodal period in days, and to do this one notices that the diagonals have one central space, around which each of four arms are 10 mounds long.

The Ushtogai Square from above, north to the top.

Each side length of 17 mounds forms a triangle to the central space, perhaps for central control, with two sides (left and right) of 10 mounds each. As with our own decimal counting of units and tens (as in 12) there could have been a day marker placed in the center.  On day 1, it was moved to the first mound on the left. Every day, the left marker moves towards the left corner mound. Upon reaching the corner, two things happen.

  1. The day marker returns to the center and,
  2. A ten-day marker then starts its own journey to the right hand corner.

The left-hand day counting would continue on the next day, for ten more days, whereupon the same action, incrementing the ten counter, would mark another ten days in a further step between mounds, towards the right hand corner.

After 100 days, the marker of ten-day periods has reached the right hand corner and a new hundred day marker is deployed, to record hundreds of days per mound. Only after the first 100 days is the hundred marker placed upon the left-hand corner mound (that might have represented 100 days after the maximum standstill of the moon.)

The counting scheme for one quarter of the nodal period, repeated in each quadrant to count 6800 days

All of the above is repeated, slowly moving the hundred-day counter from the left corner to the right, at which time the moon no longer exceeds the solar extremes of summer and winter solstice in its range of rising and setting every orbit of, on average, 27.32166 days.

In conclusion …

There is a very beautiful correspondence between the geometry of Ushtogai and the nodal period of the moon. But in a following article we will explore the parallel meaning of this monument as a counter of lunar months: to use the outer perimeter to study the Metonic and Saros eclipse periods.

There is a second article on Ustogai here.

For more information on this sort of astronomical counting in the prehistoric period, and of the details of the major time periods of the moon and sun,
these can be found in my books,
Sacred Number and the Lords of Time and
Sacred Geometry: Language of the Angels.

Angkor Wat: Observatory of the Moon and Sun

above: Front side of the main complex by Kheng Vungvuthy for Wikipedia

In her book on Angkor Wat, the Cambodian Hindu-style temple complex, Eleanor Mannikka found an architectural unit in use, of 10/7 feet, a cubit of 20/21 feet (itself an outlier of the Roman module of 24/25 feet, at 125/126 of the 0.96 root Roman foot).

She began to find counted lengths of this unit, as symbols of the astronomical periods (such as 27 29 33) and of the great Yuga time periods proposed within Vedic mythology. Hence Mannikka’s title of Angkor Wat: Time, Space, and Kingship (1996). Whilst the temple was built by the Khymer’s greatest king, their foundation myth indicates the kingly line was adopted by a matriarchal goddess tradition.

Numerically Symbolic Monuments

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Gavrinis 1: Its dimensions and geometrical framework

This article first appeared in my Matrix of Creation website in 2012 which was attacked, though an image had been made. Some of this material appeared in my Lords of Time book.

photo For Wikipedia by Mirabella.

Gavrinis and Tables des Marchands are very similar monuments, both in the orientation of their passageways and their identical latitude. Gavrinis is about 3900 metres east of Tables des Marchands but, unlike the latter, has a Breton name based upon the root GVR (gower). Both passageways directly express the difference between the winter solstice sunrise and the lunar maximum moonrise to the South, by designing the passages to allow these luminaries to enter at the exact day of the winter solstice or the most southerly moonrise over many lunar orbits, during the moon’s maximum standstill. Thus both the monuments allow the maximum moon along their passageway whilst the winter solstice sunrise can only glance into their end chambers.

From Howard Crowhurst’s work on multiple squares, we know that this difference in angle is that between a 3-4-5 triangle and the diagonal of a square which is achieved directly by the diagonal of a seven square rectangle.

Figure 1 The essence of difference between the winter solstice sunrise (as diagonal of 4 by 3 rectangle) and southerly maximum moonrise (as diagonal of a single square), on the horizon, is captured in the diagonal of a seven squares rectangle.
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Thornborough Henge as Moon’s Maximum Standstill

The three henges appear to align to the three notable manifestations to the north west of the northerly moon setting at maximum standstill. The distance between northern and southern henge entrances could count 3400 days, each 5/8th of a foot (7.5 inches), enabling a “there and back again” counting of the 6800 days (18.618 solar years/ 19.618 eclipse years) between lunar maximum standstills.

Figure 1 The three henges are of similar size and design, a design most clear in what remains of the central henge. [photo: Iain Petrie]
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