Jupiter’s gravitational and numerical influence

This post begins a Theme relating to the Trigon event occurring on 21st December 2020, when Jupiter and Saturn are conjunct at dusk in the sky. This touches upon what such synchronicities mean for other long term periods seen from Earth, such as the Moon’s nodal period of 6800 days and even the Precession of the Equinoxes over 25,800 ± 120 years.

Jupiter is the second largest body in the solar system next to the sun itself. In fact, Jupiter is not far short of being a sun itself and, being the closest giant planet to the Earth, our planet is strongly influenced by Jupiter’s gravity which, unlike the Sun’s continuous pull to maintain Earth’s orbit around it, Jupiter pulls upon the Earth and the Moon on an episodic basis when the Earth is passing between the Sun and Jupiter.

The Trigon Period of Jupiter and Saturn

Being a dark, planetary body, the episodic pull of Jupiter follows a different pattern to each of the inner, terrestrial planets; Mercury, Venus, Earth and Mars, since each has a different orbital period which, combined with Jupiter’s orbit, brings each under Jupiter’s influence or absence. The combined episodic pull of Jupiter and Saturn, is visually seen in their conjuction every 20 years, which occurs just over a third of the Zodiac onwards, thus giving a cosmic significance to the equilateral triangle as a sacred geometry.

Figure 1 The series of Trigon conjunctions of Jupiter and Saturn, as will be the case on 21st December 2020

Only Earth’s large moon stops the axial tilt of the Earth from varying significantly, then causing large changes in climate which would have restricted the development of the relatively stable habitats and biomes we enjoy.

361 days: Jupiter and the Zodiac

The combination of Jupiter’s orbital period (of 4332 days) and Earth’s (of 365.2422 days) generates an interesting set of numerical facts since Jupiter passes through each of the twelve signs of the Zodiac in 361 days. This number is 19 times 19 days so that 12 times 361 days equals 4332 days. But these numbers are a product of the solar year of 365.2422 days, since the day length on Earth is 1 year divided by the 365.2422 days due to its rotation. If the day length were less or more then Jupiter’s complete orbit would still be as long but the numbers from Earth would not.

This is a major aspect of what the megalithic astronomy had to learn, that the relative time lengths of the many cosmic periods, counted in days, could be numerically interrelated when quantified. The situation of the earth orbit and its rotation would present Jupiter as a bright moving star which completed its journey through the stars in 12 times 361 days. Jupiter and the Zodiac of 12 constellations would inevitably become fused as seen in the story of Zeus, the Greek god name for Jupiter whose symbol is the twelve-fold circle. The pre-Classical Greeks were matriarchal, following the lunar month of twelve whole lunar months within the solar year and, the solar year only arose as the patriarchal northern tribes occupied Greece after the Bronze Age collapse. The name Zeus is therefore not matriarchal since the Greeks had no “Z”. Zeus arrived in ancient Greece with the tribes displaced from the North escaping the worsening climate at higher latitudes. And, whilst 12-foldness is associated with the Sun being in one of the 12 zodiacal constellations, Jupiter defines these through passing through each sign (on average) in 361 days.

399 days: Jupiter’s synodic period

Twelve-ness is a massively widespread tradition (see John Michell – Twelve-fold Tribes for instance) and the brightest celestial body next to the Sun is the Moon which expresses twelve whole lunar months a year (plus 7/19 of a lunar month). The common lunar year was therefore twelve months long, taking 354.367 days to complete, this countable between thirteen full moons. It is no accident that the 12-ness of the lunar year is connected with Jupiter’s 12-ness of its 361 day years, since the Jupiter synod has a strong grip on our moon: the synod is 9/8 lunar years long – a musical whole tone. And Saturn also has a similar grip, its synod of 378 days being 16/15 lunar years long.

When the Earth passes by Jupiter, the latter goes retrograde or backwards relative to the stars, meaning it appears to travel east night-by-night, rather than the norm for all planets (and the sun and moon) of slowly travelling west in our skies, as they orbit. During this retrograde period, the planet describes a loop in the sky relative to the stellar background, before returning to where it should be in the stars. Between the loops of Jupiter’s synodic period the 398.88 days could be counted in days. This can only mean that over millennia, the Moon became synchronised by the regular proximity of Jupiter to our moon.

Our months today have divided the solar year into twelve months of 30 or 31 days, to resemble Jupiter’s 12-fold zodiac and 12-month lunar year, the Roman emperors vying to lengthen a month and name it after themselves (examples being October after Octavius, September after Septimius and August after Augustus). And since a zodiacal sign is traversed after 361 days by its definer, it is inevitable that there are not 12 solar years in a Jupiter orbit but just less (11.86 years). However, the fact that 4332 days is not 12 times 365.2422 days accesses, through its deficit, more subtle possibilities hidden in a numerical world of differences.

Differences between periodicities, especially involving the moon that rotates the Earth, define those periods through the fact that they endlessly repeat so that differences accumulate over longer periods and when these differences are divided into the periods, a new set of numbers are generated. One could call orbital systems differential calculators and modern math would describe them as potentially discrete systems, which form due to gravitational recurrence. This idea that the planetary and lunar systems generate numbers is somewhat hidden by our modern description of such systems as subject to gravitational dynamics. The numbers allowed the ancient astronomers to discover a static numerical view of planetary astronomy through counting days. In contrast, modern astronomy calculates the location of celestial bodies from first principles; especially when trying to visit planetary bodies in spacecraft.

Before, during and after Sacred Geometry

above: Carreg Coetan Arthur portal dolmen in Newport, Pembrokeshire.

The prehistory of sacred geometry was the late stone age, when the stone circles, dolmens, and long alignments to astronomical events on the horizon, used megaliths (large stones) in geometrical ways. Their geometries served their quest to understand the heavens, without telescopes or arithmetic, by using counted time periods as geometrical lines, squares and circles. Geometry, supplemented by the days counted between alignment events, was therefore a prelude to sacred and then secular geometry.

By developing early geometrical methods, they forged an enduring cultural norm lasting millennia, as part (or not) of the more-familiar aspect of the neolithic, innovating an agricultural pastoralism, that could support settlements, cities and, only then, the great civilizations of the middle and far east. It was civilization that generated our earliest written histories; these still powering our historical context and leading the basic notion of economic progress and territorial expansion, as superior to all that went before.

Our surviving megaliths are hence deeply enigmatic, a mysterious and mute presence in a world far less mysterious. The megaliths may have something we have forgotten in a collective way, something pushed out by millennia of later ideas and now relatively recent ones too.

There seems little trace of the megalithic astronomers themselves, their geometricized landscape overlaid by our notions of a primitive Stone Age.  And, as the prelude to world history, their geometry gave birth to sacred geometry and sacred buildings; pyramids, ziggurats, temples and religious complexes. In some way, therefore, geometry obtained its sacredness from the skies or the earth itself, as if these had been built from the harmonious organization of the solar system seen from Earth and given to it by one or more gods or angels.

Sacred geometry the became a secular and analytical geometry, which would become an encyclopedic exploration of all that geometry could do, rather than a set of techniques dreamt up by a band of roaming astronomers. In our schools, many lose interest in having to learn geometry in the abstract and so, in this, the megalithic had an advantage. They could learn geometry as and when they needed it, as their astronomy brought up new questions to solve, learning by finding methods to answer questions.

If one truly travels backwards in time, to discover what the megalithic astronomers had understood, I believe one has to decide which bits of your own skills have to be applied to solve the riddles of the megalithic mind. Each modern researcher must not assume the megalithic could calculate using numbers, use trigonometry, knew Pythagoras’ theorum, and so on. And yet, one can employ modern equipment to help investigate the megalithic. Google Earth, for example, can allow megalithic alignments to be studied, their azimuth, length and interrelation, whilst the context of sites can be seen that may provide clues not available in site plans, written descriptions and so on, which are sometimes difficult to obtain or require a personal expedition. The most basic tool for me has been the Casio scientific calculators, since the megalithic interaction with space (geometry) was blended with the interaction of numerical time counting, numbers which exist in the geocentric world of time.

Finally, one must realise the past is only in the present through our attention to it and, in the absence of much official interest in applied geometry, dimensionality and astronomical intent of the sites, it is left to non-specialists to become new specialists in the sense of recovering and conserving the true achievements of the megalithic, for our present age, while the monuments still exist as living mysteries. In this I advocate the path leading to what this website is about.

Gavrinis R8: Diagram of the Saros-Metonic Cycle

The Saros cycle is made up of 19 eclipse years of 364.62 days whilst the Metonic cycle is made up of 19 solar years of 365.2422 days. This unusually small number of years, NINETEEN, arises because of a close coupling of most of the major parameters of the Earth-Sun-Moon system which acts as a discrete system, a system also commensurate with Jupiter, Saturn, Uranus and Venus. It is this type of coherent cyclicity which lies at the centre of what the megalithic were able to achieve through day-inch or similar counting of visible time periods and comparing of counts using geometric means. [see my books, especially Sacred Number and the Lords of Time, for a fuller discussion].

It would have been relatively easy for megaithic astronomy to notice that eclipses occur in slots separated by eclipse seasons of 173.3 days and also to see that the difference between lunar and solar years resolves over the 19 year of the Metonic so that lunar orbits, lunar months, the starry sky and the rotation of the earth provide a close repetition of alignments over 19 solar years which equal 235 lunar months and 254 lunar orbits. The Saros period is 223 lunar months long and is therefore one lunar year of 12 months short of the Metonic of 235 lunar months.

The situation in the last year of the Metonic is therefore identical but (symmetrically) in-reverse to the first year, on a continuous but discrete basis [that is, providing you start counting on an eclipse]. The Saros then ends12 months before the Metonic so that the Saros is 18 solar years long plus, quite closely, the 10.8 day difference between the lunar and solar years. This phenomenon is clearly presented on Gavrinis’ stone R8, in the middle “register”, such engraved art at Gavrinis dividing their stone pallettes into different elements of a related summary of astronomical phenomena seen through the tools of a megalithic science involving counting, alignment, geometry, and metrology.

Central section of Gavrinis stone R8 clearly shows the Saros and Metonic Cycles as ending between 18 and 19 years less the difference between the lunar and solar years

 In the figure above, the right shows the four-square geometry whose diagonal is the length of the solar year relative to the length of the base (=4) as being the length of the lunar year of 12 lunar months. The difference in length of these two years is shown “centre stage” and is accurately 10.8 inches long, numerically representing the difference in terms of day-inch counting. The curvilinear lines around the vertical are emblematic of counting as fundamental to this type of art. The diagonal actually shown here is continued into the representation of a series of solar years, here numbered so that, in the 19th year, something new happens: the year rises up but is bent leftwards in what is one of the most distinctive patterns in Gavrinis’ art.

We know, as stated above, that the Metonic is 19 years long and that the Saros is a year less, plus the 10.8 day difference between lunar and solar years, so that the 10.8 day-inches is shown centrally above on R8 both refers to the initial four-square relating the solar and lunar year, by the excess then found over 18 years, of 10.8 day-inches.

This is a very compact and intuitive diagramming language which communicates, without words but with an implicit familarity of day-inch counting, an inter-related cyclicity of crucial importance discoverable using this megalithic science. Similar components are to be found on other stones and astronomy appears to be the purpose of this notational art, designed to educate and explain important facts, within an oral megalithic culture.

What stone L9 might teach us

image of stone L9, left of corridor of Gavrinis Cairn,
4Km east of Carnac complex. [image: neolithiqueblog]

This article was first published in 2012.

One test of validity for any interpretation of a megalithic monument, as an astronomically inspired work, is whether the act of interpretation has revealed something true but unknown about astronomical time periods. The Gavrinis stone L9, now digitally scanned, indicates a way of counting the 18 year Saros period using triangular counters  founded on the three solar year relationship of just over 37 lunar months, a major subject (around 4000 BC) of the Le Manio Quadrilateral, 4 Km west of Gavrinis. The Saros period is a whole number, 223, of lunar months because the moon must be in the same phase (full or new) as the earlier eclipse for an eclipse to be possible. 

On the roof with Anthony Blake (left) on the DuVersity Albion Tour, in August 2004.

Handling the Saros Period

223 is a prime number not divisible by any lower number of lunar months, such as 12 in the lunar year. 18 lunar years equates to 216 lunar months, requiring seven further months to reach the Saros condition where not only is the lunar phase the same but also, the sun is sitting upon the same lunar node, after 19 eclipse years of 346.62 days.

However, astronomers at Carnac already had a number of 37 lunar months (just less than three solar years) in their minds and, it appears, they could apply this as a length 37 units long, as if each unit was a lunar month. We also know that the unit they used for counting lunar months was originally 29.53 inches (3/4 metre) or later, the megalithic yard. Visualising a rope of length 37 megalithic yards, the length can be multiplied by repeating the rope end-to-end. After six lengths, 222 or 6*37 lunar months were represented, one lunar month less than the 223 lunar months which define the Saros period.

Figure 1 The near-integer Anniversary of Lunar Months over Three Years

This six-fold use of the number 37 appears to be used within the graphic design of Gavrinis stone L9 (see figure 2), as the triangular shape which has an apex angle of 14 degrees and which refers to the triangle formed at Le Manio between day-inch counts over three solar and three lunar years. It appears that this triangular shape was used to refer to the counting of solar years relative to a stone age lunar calendar (see 2nd register of stone R8) but it could also have the numerical meaning of 37 because three solar years contained 37 whole lunar months just as a single solar year contains 12 whole lunar months (the lunar year).

I believe this triangle, already symbolic of 37, appears in pairs within stone L9, as a single counter showing two axe heads, their points adjacent so that they have one side also adjacent. The two triangles are found to be held accurately within the apex angle of another triangle, known to be in use at Carnac, the triangle with side lengths 5-12-13, with apex angle 22.6 degrees. These pairs would then effect the notion of addition so that each is valued at 37 + 37 = 74 lunar months.

Figure 2. The use of two three-year triangles, made to fit within the 5-12-13 triangle to form a single counter worth 74 lunar months. (MegalithicScience.org eventually became this website)

All of the three pairs have this same apex angle, of the 5-12-13 triangle, chosen perhaps because 12+12+13 = 37 whilst the 14 degree triangle was known to be rationally held within it when the 12 side is seen as the lunar year of 12 months. The third side is then 3 lunar months long (¼ lunar year) forming an intermediate hypotenuse within a 5-12-13 triangle, which is equal to the 12.368 months of the solar year. Robin Heath first identified the smaller triangle when studying the properties of the 5 by 12 rectangle of Stonehenge’s Station Rectangle, arguably made up of two 5-12-13 triangles joined by their 13 sides. Three solar years then seems to have become associated with the pattern 12+12+13 (= 37) by the historical period, since Arab and medieval astronomers came to organize their intercalary months within the Callippic cycle of 4 Metonic periods (= 4 x 19 years equaling 76 solar years).

Figure 3. The quantification of the Saros as 18 solar years and 11 days equal to 223 lunar months. The language of days and years at Gavrinis might well have been the primary perception of light and dark periods.

The Saros period of 223 lunar months then also appears indicated on stone L9, below these triangles, within the main feature of this stone, a near-square Quadrilateral having one right angle. It has a rounded top, containing a wavy engraved design emanating from a central vertical, not unlike a menhir. The waves proceed upwards but then narrow to a vestigial extent after the 18th, which would be one way to symbolise the Saros period as 18 years and eleven days in duration. A different graphical allusion was used on stone R8, again showing lines as years but giving the 19th year as a shortened “hockey stick”.

Conclusions

In Gavrinis stone L9, a “primitive” numerical and phenomenological symbolism appears to have expressed a useful computational fact: that the Saros period was one lunar month more than six periods of 37 lunar months. These three periods of 37 months were shown as blade shapes, each symbolising three solar years, but shown as pairs within three 5-12-13 triangles above a quadrilateral shape indicating 18 wavy lines plus a smallest period, this symbolising the 11 days over 18 years of the Saros Period, defined by 223 lunar months. This allowed the Saros to be seen as six periods of 37 lunar months, equal to 222, plus one lunar month. Once the count reached 222, attention to the end of the next lunar month would be key. This enabled a pre-arithmetic culture to approach prime number 223 from another large prime (37) which was nearly expressed by 3 solar years, then repeated six times yo become 222 lunar months. This same counting regime appears to have been employed elsewhere:

  1. Astronomical Rock Art at Stoupe Brow, Fylingdales.
  2. Eleven Questions on Sacred Numbers.
  3. Counting lunar eclipses using the Phaistos Disk.

Many thanks to Laurent Lescop of Nantes University Architecture Dept,
for providing the scan on which this work is based.

Astronomy 3: Understanding Time Cycles

above: a 21-petal object in the Heraklion Museum which could represent the 21 seven-day weeks in the 399 days of the Jupiter synod. [2004, Richard Heath]

One of the unfortunate aspects of adopting the number 360 for calibrating the Ecliptic in degrees is that the megalithic counted time in days and instead saw the ecliptic as divided by the 365¼ days. In transferring to the number 360, with all of its easy factors, 8 x 9 x 5, moderns cannot exploit a key advantage of 365¼ days.

If the lunar orbit takes 27.32166 days then each day the moon moves by 1/27.32166 of the ecliptic every day. For this reason, after 27.32166 days the orbit completes because the Moon’s “year” then equals one as the angular motion has been 27.32166/ 27.32166 = 1.

The same is true of the lunar nodes, which retrograde to the east along the ecliptic in 18.618 years. For this reason one can say, the lunar nodes move by 1/18.618 DAYS (in angle) every day and to travel one DAY in angle, the nodes take 18.618 DAYS per day (needing the new term “node day” equal the 18.618 days.*** A solar year takes 19.618 node days (since 365¼ equals 18.618 x 19.618) and an eclipse year takes 18.618 x 18.618 – 346.62 days

*** These are average figures since the moon comes under variable gravitational influences that are episodic.

A general rule emerges in which the larger, whole cycles, lead to reciprocals which can be numerically characterized by knowing the number of the days in the larger period.

For instance, Jupiter has a synodic excess over the solar year of 398.88 days and this means its angular motion is 1/ 398.88 DAYS per day while Saturn’s synod is 378.09 days and its angular motion is 1/ 378.09 DAYS per day. These synods are, by definition, differential to the Sun at 1/ 365.2422 DAYS per day.

Without seeing astronomy as calibrated to day and year cycles, one is robbed of much chance to appreciate the megalithic view of time and the time-factored buildings that came to be built in pursuit of quite advanced knowledge.

Looking from the relatively large cycles to the extremely small, daily angular changes of celestial bodies seen from Earth, reveals a further obscuration created, in this case, by the heliocentric view of the solar system, rather than the geocentric view which is obviously founded on days and years seen from the surface of the planet.

The largest cycle the megalithic could see using their techniques, reverses the direction from large-to-small to small-to-large since the precessional cycle (of the equinoctal nodes of the earth’s obliquity) is around 25,800 ± 100 years long. A star or constellation on the ecliptic appears to move east, like the lunar nodes, and using the angular measure of DAYS, it is possible to estimate that the equinoctal points move by a single DAY, in a given epoch, something like 71 years. The precessional cycle is therefore 71 years multiplied by the 365.2422 DAYS of the whole ecliptic.

The most important benefit of using DAY angles is that knowledge of a few celestial periods opens up a realm in which different scales of time can be derived from first principles. And added to that, the celestial periods appear related to one another so that so-called sacred numbers emerge such as the seven day week which divides into both the Saturn synod (54 weeks), Jupiter synod (57 weeks), the 364 day saturnian year (52 weeks) and others.

To understand the full scope of megalithic astronomy requires a geocentric calibration of the ecliptic as having 365¼ angular DAYS.

Astronomy 2: The Chariot with One Wheel


What really happens when Earth turns? The rotation of Earth describes periods that are measured in days. The solar year is 365.242 days long, the lunation period 29.53 days long, and so forth.

Extracted from Matrix of Creation, page 42.

Earth orbits the Sun and, from Earth, the Sun appears to move through the stars. But the stars are lost in the brightness of the daytime skies and this obscures the Sun’s progress from human view. However, through observation of the inexorable seasonal changes in the positions of the constellations, the Sun’s motion can be determined.

The sidereal day is defined by the rotation of Earth relative to the stars. But this is different from what we commonly call a day, the full title of which is a tropical day. Our day includes extra time for Earth to catch up with the Sun before another sunrise. Our clocks are synchronized to this tropical day of twenty-four hours (1,440 minutes).

The Sun circumnavigates the zodiac in 365 tropical days, within which 366 sidereal days have occurred. There is one full Earth rotation more than there are sunrises within a year. This hidden oneness within the year is recapitulated in the one-unit difference between the number of sidereal days and the number of tropical days in a practical year.

The small catch-up time in every day is about three minutes and
fifty-six seconds long. This unit defines not only a sidereal day with 365 such units but also the practical year of 365 tropical days. The catchup unit is the difference between the duration of a sidereal day and that of a tropical day. It relates the Sun’s daily motion to the rotation of Earth and is a fundamental unit of Earth time (figure 3.6).

Figure 3.6. A polar view of Earth’s equator showing sunrises for two consecutive days. Compared with clock time, the stars rise three minutes and fifty-six seconds earlier each evening. (Drawn by Robin Heath)

THE MOON GATHERS THE TEN THOUSAND WATERS

The sidereal day (the duration of one rotation of Earth) is a very significant cosmic unit. The Jupiter synodic period of 398.88 tropical days is within 99.993% of four hundred sidereal days long. Therefore, twenty-five Jupiter synods (365 lunar orbital periods) equal 10,000 sidereal days since four hundred times twenty-five is 10,000.

A sidereal day differs from a tropical day due to the motion of the Sun during one tropical day. The three-minute-and-fifty-six-second time difference between these two days, the aforementioned catch-up unit, is quite useful when applied as the unit to measure the length of these days. A tropical day has 366 of these units while the sidereal day has 365 of the same units. The difference between the two is one unit.

Since 365 lunar orbits equal 10,000 sidereal days, it follows that a single lunar orbit has a duration of 10000/365 sidereal days. There are 365 units in a sidereal day, and therefore 10,000 units in a lunar orbit, so this new unit of time is 1/10000 of a lunar orbit. One ten-thousandth of a lunar orbit coincidentally is three minutes and fifty-six seconds in duration. The proportions in the Jupiter cycle combine with the lunar orbit, solar year, and Earth’s rotation to generate a parallel number system involving the numbers 25, 40, 365, 366, 400, and 10,000.

This daily catch-up unit I shall a chronon. Its existence means that the rotation of Earth is synchronized with both the lunar orbit and the Jupiter synodic period using a time unit of about three minutes and fifty-six seconds.

The sidereal day of 365 chronons is the equivalent of the 365-day practical year, the chronon itself is equivalent to the sidereal day, and so on. The creation of equivalents through exact scaling enables a larger structure to be modeled within itself on a smaller scale. This is a recipe for the integration of sympathetic vibratory rhythms between the greater and the lesser structures, a planetary law of subsumption.

The exemplar of the chronon was found at Le Menec: It’s egg-shaped western cromlech has a circumference of 10,000 inches and, if inches were chronons (1/365th of the earth’s rotation), then the egg’s circumference would be the number of chronons in the lunar orbit of 10,000. Dividing 10,000 by 366 (the chronons in the tropical day) gives a lunar orbit of 27.3224 – accurate to one part in 36704! The forming circle of Le Menec’s egg geometry provided a circumpolar observatory of circumference 365 x 24 inches, which is two feet per chronon versus the chronon per inch of the egg as lunar orbit.

The quantified form of the Le Menec cromlech was therefore chosen by the builders to be a unified lunar orbital egg, with a forming circle represented the rotation of the Earth at a scaling of 1:24 between orbital and rotational time.

The form of Le Mence’s cromlech unified the 10,000 chronon orbit of the Moon and 365 chronon circle of the Earth rotation because Thom’s Type 1 geometry naturally achieved the desired ratio. When the circle’s circumference (light blue) was 24 x 365 inches there were 10,000 inches on the egg’s. Underlying site plan by Thom, MRBB.

This design is further considered in Sacred Number and the Lords of Time, chapter 4: The Framework of Change on Earth, from the point of view of the cromlech’s purpose of providing a working model of the lunar orbit relative to the rotation of the circumpolar sky, leading to the placement of stones in rows according to the moon’s late or early rising to the East.

Capturing Sidereal Time


We can now complete our treatment of Carnac’s astronomical monuments by returning to Le Menec where the challenge was to measure time accurately in units less than a single day. This is done today at every astronomical observatory using a clock that keeps pace with the stars rather than the sun.

The 24 hours of a sidereal clock, roughly four minutes short of a normal day, are actually tracking the rotation of the Earth since Earth rotation is what makes all the stars move. Even the sun during the day moves through the sky because the Earth moves. Therefore, in all sidereal astronomy, the Earth is actually the prime mover. The geometry of a circumpolar observatory can reveal not only which particular circumpolar star was used to build the observatory but also the relatively short period of time in which the observatory was designed. Each bright circumpolar star is recognizable by its unique elongation on the horizon in azimuth and its correspondingly unique and representative circumpolar orbital radius in azimuth. …

The knowledge that was discovered due to the Le Menec observatory is awe inspiring when the perimeter of the egg shape is taken into account. It is close to 10,000 inches, the number of units of sidereal time the moon takes to orbit the Earth. The egg was enlarged in order to quantify the orbit of the moon as follows: every 82 days (three lunar orbits) the moon appears over the same part of the ecliptic. Dividing the ecliptic into sidereal days we arrive at 366 units of time per solar day.*

*These units are each the time required for an observer on the surface of the Earth to catch up with a sun that has moved within the last 24 hours, on the ecliptic, a time difference of just less than four minutes.

82 days times 366 divided by the three lunar orbits gives the moon’s sidereal orbit as 122 times 82 day-inches. Instead of dividing 82 by three as we might today to find the moon’s orbit, the pre-arithmetic of metrology enabled the solar day (of 366 units) to be divided into three lengths of 122. If a rope 122 inches long is then used 82 times (a whole number), to lay out a longer length, a length of 10,004 inches results. If 10,004 is divided by 366 units per day then the moon’s orbit emerges as 82/3 or 27⅓ days.

If a moon marker is placed upon the Le Menec perimeter and moved 122 inches per day, the perimeter becomes a simulator of the moon. …
Knowing the moon’s position on the western cromlech’s model of ecliptic and knowing which parts of the ecliptic are currently rising from the circumpolar stars enabled the astronomers to measure the moon’s ecliptic latitude.

Hence the phenomena related to the retrograde motion of the lunar orbit’s nodal period could be studied and its 6800 day length.