Using Circumpolar Marker Stars

The marker stars within the circumpolar or arctic region of the sky have always included Ursa Major and Ursa Minor, the Great and Little Bear (arctic meaning “of the bears” in Greek), even though the location of the celestial North Pole circles systematically through the ages around the pole of the solar system, the ecliptic pole. In 4000 BC our pole star in Ursa Minor, called Polaris, was far away from the north pole and it reached a quite extreme azimuth to east and west each day, corresponding to the position of the sun (on the horizon in 4000 BCE at this latitude) at the midsummer solstice sunrise. This means angular alignments may be present to other important circumpolar stars in some of the stones initiating the Alignments at Le Menec, when these are viewed from the centre of the cromlech’s circle implicit in its egg-shaped perimeter.

This original “forming circle” of the cromlech could be used as an observatory circle, able to record angular alignments. Therefore the distinctive “table” stone which aligns to the cromlech’s centre at summer solstice sunrise, also marked the extreme angle (to the east) of Polaris, alpha Ursa Minor, our present northern polestar. That is, in 4000 BCE Polaris stood directly above the table stone, once per day – whether visible or not.

Such a maximum elongation of a circumpolar star is the extreme easterly or westerly movement of the star, during its anti-clockwise orbit around the north pole. Thus, if the northern horizon were raised (figure 5) until it passed through the north pole, the maximum circumpolar positions for a star to east and west would be equally spaced, either side of the north pole. If these extreme positions are brought down to the Horizon in azimuth, the angles between these extremes forms a unique range of azimuths on the ground between (a) the horizon (b) a foresight such as a menhir and (c) an observer at a backsight. Observations of these extreme elongations naturally enable the pole (true north) to be accurately established from the observing point as the point in the middle of that range. A marker stone can usefully locate a circumpolar star at one of these maximum elongations and come to symbolize that important star. A star’s location could have been brought down to the horizon using a vertical pole or plumb bob, between the elongated star and the horizon, at which point menhirs could later be placed, relative to a fixed viewing centre or backsight. This method of maximum elongations would have escaped the atmospheric effects associated with observing stars on the horizon which causes a variable angle of their visual extinction below which stars disappear before reaching the horizon.

Figure 5.The Maximum Elongation of Circumpolar Stars is a twice daily event when, looking at the horizon, the star’s circumpolar “orbit” momentarily stops moving east or west at maximum elongation in azimuth and reverses its motion.

At Le Menec the azimuths of the brightest circumpolar stars, at maximum elongation, appear to have been strongly associated with the leading stones of the western alignments (see figure 6). However, it is likely that only one of these circumpolar stars was used as a primary reference marker, for the purpose of measuring sidereal time at night when this star was visible.

Figure 6 Some of the associations between circumpolar stars and stones in the western alignments. These alignments are all to the maximum easterly elongations, perhaps established during the building of the sidereal observatory and only later formalized into leading stones at the start of different rows. Dubhe was then selected as the primary marker star for the Le Menec observatory.

To achieve continuous measurements of sidereal time from the circumpolar stars requires a simple geometrical arrangement that can draw down to earth the observed position of maximum elongation to east and west for one bright circumpolar star, the observatory’s marker star. A rectangle must then be constructed to the north of the cromlech’s east-west diameter and containing within it the observatory’s northern semicircle. The northern corners must align with, relative to the centre of the circle, the eastern and western elongations of the chosen marker star. For Le Menec the rectangle had to be extended northwards until it reached the first stone of row 6[1]. This stone is aligned, from the centre, to the maximum eastern elongation of Dubhe or alpha Ursa Major. The first stone of row 6 is therefore the menhir marking Dubhe. To the south, the initial stones of further rows all stand on the eastern edge of this rectangle, so that any point on the rectangle’s north face could be brought down, unobstructed, to the circumference of the circle.

Figure 7 shows how the form of the circumpolar region, within the “orbit” of Dubhe, is repeated by the cromlech’s forming circle. It is also true that the “northern line” then has the same length as the diameter of the forming circle, which has therefore been metrologically harmonized with row 6’s initial stone and the alignment to Dubhe in the east.

This arrangement has the consequence that wherever Dubhe is (above the northern line and when seen on a sightline passing through the centre of the cromlech) its east-west location in the sky can be brought down, directly south, to two points on the forming circle of the observatory – all due to the star observation having been made upon a length equal to the circle’s diameter (the Northern Line of figures 7 and 8). One of these two points, on the northern or southern semicircle of the observatory, must then correspond exactly to where Dubhe is in its “orbit” around the north pole, as in figure 8.

So, what is being measured here and what would be the significance of having such a capability? Whilst the movement of all the stars is being accurately measured, using this northern line and forming circle combination, the monument also has a reciprocal meaning. The forming circle also represents the earth’s rotation towards the east, the cause ofthe star’s apparent motion. This is because, when looking north, the familiar direction of rotation of the stars, when looking south, is reversed from a rightwards motion to a leftwards, anticlockwise motion. Circumpolar motion therefore directly represents the rotation of the earth. The Dubhe marker star would have represented the movement of a point on the surface of the earth, moving forever to the east. Perhaps more to the point, the eastern and western horizon are moving as two opposed points on its circular path, each moving at about the same angular speed as Dubhe. This deepens the view of the forming circle as representing those ecliptic longitudes in which the fixed stars, rising or setting on the eastern and western horizons, are fixed locations on the circle through which these horizons are moving as markers on the circle’s circumference.

These two views, of a moving earth and of a moving background of stars, could be interchangeable when understood and both viewpoints are equally useful and were probably relevant to the operation of this observatory. Whilst the circumpolar stars move around the pole, the eastern and western horizon move opposite each other, running along the ecliptic, as the Earth rotates. The first view enables an act of measurement which would have given astronomers access to sidereal time and the second view provided knowledge of where the eastern and western horizons were located viz a vis the equatorial stars and therefore knowledge of which part of the ecliptic was currently rising or setting.

Figure 8 Recreating the circumpolar region with marker star Dubhe at the correct angle on the forming circle of the western cromlech. The star’s alignment on the northern line is dropped to the south so as to touch the two points of the circumference corresponding to that location on the circle’s diameter: one of these will be the angle of Dubhe as seen within the circumpolar sky but now accurately locatable in angle, on the observatory circle.

Dubhe had, in 4000BCE, a fortunate relationship to the circumpolar sky and equatorial constellations which would have been very useful. When Dubhe reached its maximum eastern elongation (marked by the first stone in the sixth row) the ecliptic’s summer solstice point was rising in the east. However, Dubhe’s maximum western elongation did not correspond to the winter solstice, this due to the obliquity of the ecliptic relative to north. It is the Autumn Equinoctal point of the ecliptic that is rising to the east at Dubhe’s maximum western elongation. It was when Dubhe was closest to the northern horizon, that the other, winter solstice point was found rising on the ecliptic. It is important to realize that these observational facts were true every day, even when the sun was not at one of these points within the ecliptic’s year circle.

NEXT:

CONTENTS

This paper proposes that an unfamiliar type of circumpolar astronomy was practiced by the time Le Menec was built, around 4000 BCE.

  1. Abstract
  2. Start of Carnac’s Alignments
  3. as Sidereal Observatory
  4. using Circumpolar Marker Stars
  5. dividing the Circumpolar stars
  6. maintaining Sidereal Time in Daylight
  7. measuring the Moon’s Progress
  8. as Type 1 Egg
  9. transition from Le Manio
  10. the Octon of 4 Eclipse Years
  11. building of Western Alignments
  12. key lengths of Time on Earth

[1] Thom’s row VI.

Le Menec: as Sidereal Observatory

Today, an astronomer resorts to the calculation of where sun, moon or star should be according to equations of motion developed over the last four centuries. The time used in these equations requires a clock from which the object’s location within the celestial sphere is calculated. Such locations are part of an implicit sky map made using equatorial coordinates that mirror the lines of longitude and latitude. Our modern sky maps tell us what is above every part of the earth’s sphere when the primary north-south meridian (at Greenwich) passes beneath the point of spring equinox on the ecliptic. Neither a clock, a calculation nor a skymap was available to the megalithic astronomer and, because of this, it has been presumed that prehistoric astronomy was restricted to what could be gleaned from horizon observations of the sun, moon, and planets.

Even though megalithic people could not use a clock nor make our type of calculations, they could use the movement of the stars themselves, including the sun by day, to track sidereal (or stellar) time provided they could bring this stellar time down to the earth. This they appear to have done at Le Menec, using the cromlech’s defining circle, which was built into its design so as to become a natural sidereal clock synchronized to the circumpolar stars.

Figure 4 The Circumpolar Stars looking North from Le Menec in 4000 BCE, when the cromlech was probably built. There is no north star but marker stars travel anti-clockwise and these can align to foresights at their extreme azimuthal “elongation”, as explained below.

The word sidereal means relating to stars and, more usually, to their rotation around the earth observer as if these stars were fixed to a rotating celestial sphere. This rotation is completely reliable as a measure of time since it is stabilized by the great mass of the spinning earth. However, in a modern observatory this sidereal time must be measured indirectly using an accurate mechanical or electronic clock. These clocks can only parallel the rotation of the earth in a sidereal day, which is just under four minutes less than our normal day. Nonetheless, a sidereal day is again given 24 ‘hours’ in our sky maps and it is these hours which are then projected upon the celestial sphere as hours (minutes and seconds) of Right Ascension, hours in the rotation of the earth during one sidereal day.

NEXT: using Circumpolar Marker Stars

CONTENTS

This paper proposes that an unfamiliar type of circumpolar astronomy was practiced by the time Le Menec was built, around 4000 BCE.

  1. Abstract
  2. Start of Carnac’s Alignments
  3. as Sidereal Observatory
  4. using Circumpolar Marker Stars
  5. dividing the Circumpolar stars
  6. maintaining Sidereal Time in Daylight
  7. measuring the Moon’s Progress
  8. as Type 1 Egg
  9. transition from Le Manio
  10. the Octon of 4 Eclipse Years
  11. building of Western Alignments
  12. key lengths of Time on Earth

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.

Le Menec: Start of Carnac’s Alignments

The Meaning Of Le Menec

“Alignments” are long rows of stones, that run in parallel for long distances through the landscape. The alignments in Carnac, Brittany, often have a starting point in what the French call a cromlech. Based upon a circular geometry, these monuments are made up of stones following arcs to form a single compound shape. The stones of a cromlech can be touching or they can be spaced out and in some cases, stones might have been removed during the historical period but in some cases also, gaps in the “walls” of a cromlech were probably intentional and are there on purpose.
Originally published July 2012

Continue reading “Le Menec: Start of Carnac’s Alignments”

THE MEANING OF LE MENEC (PDF)

This paper proposes that an unfamiliar type of circumpolar astronomy was practiced by the time Le Menec was built, around 4000 BCE. This observatory enabled the rotation of the earth and ecliptic location of eastern and western horizons to be known in real time, by observing stellar motion by night and solar motion by day. This method avoided stellar extinction angles by measuring the circular motion of a circumpolar marker star as a range in azimuth, which could then be equated with the diameter of a suitably calibrated observatory circle. The advent of day-inch counting and simple geometrical calculators, already found at Le Manio’s Quadrilateral, enabled the articulation of large time periods within Carnac’s megalithic monuments, the Western Alignments being revealed to be a study of moonrises during half of the moon’s nodal period. Le Menec’s Type 1 egg is found to be a time-factored model of the moon’s orbit relative to the earth’s rotation. This interpretation of Le Menec finds that key stones have survived and that the gaps seen in the cromlech’s walls were an essential part of its symbolic language, guiding contemporary visitors as to how its purpose was to be interpreted within the pre-literate megalithic culture.

Two key lengths are found at Le Manio and Le Menec: The first, of 4 eclipse years is a day-inch count of the Octon eclipse cycle; the second is a four solar year count that, with the first, forms a triangle, marked clearly by stones at Le Menec. The principles worked out at Le Manio appear fully developed in Le Menec’s western cromlech, including the use of an 8 eclipse year day-inch count, consequently forming a diameter of 3400 megalithic inches which equals in number the days in half a nodal period. The scaling of the Western Alignments is found to be 17 days per metre, a scaling naturally produced by the diagonal of a triple square geometrical construction. A single sloping length on the top of the central stone initiating row 9, indicates a single lunar orbit at 17 days per metre, a length of 1.607 metres. This control of time counting within geometrical structures reveals that almost all of Le Menec’s western cromlech and alignments express a necessary form, so as to represent a megalithic study of (a) circumpolar time as having 365 time units, (b) the moon’s orbit as having 82 times 122 of those units and (c) the variations of successive moonrises over most of a lunar nodal period of 18.6 solar years.

Locmariaquer 1: Carnac’s Menhirs and Circumpolar Stars

Read 1458 times when last published on MatrixOfCreation.co.uk, Wednesday, 16 May 2012 14:22

At megalithic sites, the only alignment of note on the northern horizon has usually been the direction of the north pole or “true” North on the site plan. “Megalithic” cultures worldwide, both the later manifestations in the Americas or the old world cultures of Northwest Europe or Egypt, built structures oriented in a very accurate way to North. The builders of the Great Pyramid for example or of the geo-glyphs of the Amazon rainforest, seemed to have had an unexpectedly good method for determining North, no easy task when a pole star is never exactly north and, in many epochs, there is no star near to the pole.

Continue reading “Locmariaquer 1: Carnac’s Menhirs and Circumpolar Stars”