Tag: circumpolar

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.

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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 1: Knowing North and the Circumpolar Sky

about how the cardinal directions of north, south, east and west were determined, from Sacred Number and the Lords of Time, chapter 4, pages 84-86.

Away from the tropics there is always a circle of the sky whose circumpolar stars never set and that can be used for observational astronomy. As latitude increases the pole gets higher in the north and the disk of the circumpolar region, set at the angular height of the pole, ascends so as to dominate the northern sky at night.

Northern circumpolar stars appearing to revolve around the north celestial pole. Note that Polaris, the bright star near the center, remains almost stationary in the sky. The north pole star is constantly above the horizon throughout the year, viewed from the Northern Hemisphere. (The graphic shows how the apparent positions of the stars move over a 24-hour period, but in practice, they are invisible in daylight, in which sunlight outshines them.)
[courtesy Wikipedia on “circumpolar star”, animation by user:Mjchael CC-ASA2.5]

Therefore, the angular height of the pole at any latitude is the same angle we use to define that latitude, and this equals the half angle between the outer circumpolar stars and the pole itself. For example, Carnac has a latitude of 47.5 degrees north so that the pole will be raised by 47.5 degrees above a flat horizon, while the circumpolar region will then be 95 degrees in angular extent.

It is perhaps no accident that the pole is called a pole since to visualize the polar axis one can imagine a physical pole with a star on top, like a toy angel’s wand. The circumpolar region is “suspended” around the pole like a plate “held up” by the pole. Therefore, a physical pole, set into the ground, can be used to view the north pole from a suitable distance south (i.e., with the pole’s top as a foresight for the observer’s backsight). Such an observing pole would probably have been set at the center of a circle drawn on the ground, representing the circumpolar region around the north pole. This arrangement, a gnomon,* existed throughout history but usually presented as part of a sun dial.

*According to the testimony of Herodotus, the gnomon was originally an astronomical instrument invented in Mesopotamia and introduced to Greece by Anaximander. It was innovated even earlier, in the megalithic period, because structures that could operate one still exist within megalithic monuments.

It now appears a gnomic pole was also used in prehistory to locate the north pole in the middle of circumpolar skies. The north pole is opposite the shadow of the equinoctal sun at midday. The gnomic pole could also be used to find “true north,” as located halfway between the extremes of the same circumpolar star above the northern horizon. This can make use of the fact that when the sun is at equinox, it lies on the celestial equator and therefore is at a right angle to the north pole (see figure 4.4). This right angle is expressed at the top of the gnomic pole used and hence can enable the alignment of the pole through the similarity (or congruence) of all the right-angled triangles within the arrangement.

Figure 4.4. From pole to pole. It is possible to determine the angle of the north pole using a gnomic pole as shadow stick, but only at noon on the equinox. The laddie on the left cannot do this to a possible few minutes of a degree, but the geometry of the stick and shadow length can, providing true north and equinox alignments of east and west can be determined. Illustration on left from Robin Heath, Sun, Moon and Stonehenge, fig. 9.3.

Figure 4.4. From pole to pole. It is possible to determine the angle of the north pole using a gnomic pole as shadow stick, but only at noon on the equinox. The laddie on the left cannot do this to a possible few minutes of a degree, but the geometry of the stick and shadow length can, providing true north and equinox can be determined. Illustration on left from Robin Heath, Sun, Moon and Stonehenge, fig. 9.3.

To achieve an accurate bearing to true north, a circumpolar observatory can use the gnomic pole method, not just at noon on the equinox but every night, by dividing the angular range of circumpolar star, in azimuth. The north pole’s altitude, known to us as latitude on the Earth, can then be identified by dividing the angular range in altitude of a circumpolar star, a task achievable through geometry and metrology, so as to create a metrological model of the latitude upon the Earth.

It would seem obvious today that the pole star Polaris could have been used, but this is a persistent and widespread misunderstanding of the role of pole stars within the ancient and prehistoric world. Epochs in which there is a star within one degree of the pole are very rare and shortlived. Our pole star, Polaris (alpha Ursa Minor), is currently placed two thirds of a degree from a pole that is moving through the northern sky (figure 4.3 on p. 83) in a circle around the ecliptic pole of the solar system. Polaris will be nearest the pole (about ½ degree) at the end of this century.

The last time there was a star at all near the north pole was prior to the construction of the Great Pyramid in 2540 BCE . That pole star was Thuban (Alpha Draconis), and it was just one-fifteenth of a degree from the pole in 2800 BCE . The Great Pyramid has a narrow air shaft that pointed to Thuban, at which time it was already departing the pole and nearly one-third of a degree from it. Therefore, the megalithic people at Carnac, as well as almost all cultures throughout time, did not have the convenience of a pole star in approximately locating the north pole.

From 5000 to 4000 BCE , the time of megalithic building at Carnac, the north pole was a dark region surrounded by many bright stars. The inability to locate the north pole using a pole star challenged the people of the megalithic to develop a more sophisticated and accurate method. In any case, true north and latitude needed to be located more accurately than by using a pole star, which can only ever approximate the position of the north pole. Also, through the circumpolar observatory, sidereal time and even longitude between sites could be measured once the movement of the circumpolar stars could be exploited. True north, based upon these stars around the pole, can give the cardinal directions to an observatory.

The equinoctial sunrise in the east and sunset in the west can give a mean azimuth (horizon angle) to obtain south and north but only if the horizon is dead flat to each of these alignments. Far better then to observe the extremes of motion of a single circumpolar star, to the east and the west, to then find the North pole in between those two alignments.

Defining North by bringing the “clock in the sky” down to earth


One can therefore see that the circumpolar stars and sighting techniques, involving a gnomon, allowed north and the cardinal directions in a more reliable way than recording sunrise and sunsets since the sun on the horizon is variable between years due to the solar year having nearly ¼ day more than 365 days. The circumpolar stars enabled buildings and long sights to be built to true north-south-east-west, and by ignoring this, a building such as the Great Pyramid of Giza surprises us with its accurate placement relative to the cardinal directions.

Astronomical Methods
Knowing North and the Circumpolar stars

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.

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The Roof Axe as Circumpolar Device

This article explores the use of axe motifs within a form of carved schematic art unique to the megalithic monuments near Carnac, southern Brittany, France. First published in February 2014.

A diagram found on the underside of the capstone of a chambered dolmen called Kercado (see figure 1) appears to hold metrological and astronomical meanings. Classified as a type of AXE, local axe motifs are said to have three distinct forms (a) triangular blades, (b) hafted axes and (c) the Mane Ruthual type [Twohig, 1981[1]]. 

Figure 1 Well preserved sculpted-stone axe-head motif in Kercado dolmen

Types b and c are often found in the singular on the undersides to roof slabs and in the case of form (b), the hafted axe, I have attributed its display below the roof slab of Table des Marchands at Locmariaquer (inset right) as being used to represent the north pole between 5000 and 4000 BC, at a time when there was no star near to the pole itself. The abstract point of the north pole, the rotational axis of the earth, is shown as a loop attached to the base of the axe haft, whilst the axe head then represented a chosen circumpolar star, as this rotates counter-clockwise in the northern sky, at the fixed distance of the haft from the pole itself. Note how compatible this idea of an axe ploughing the northern skies is to our own circumpolar constellation, The Plough. Note also that the eastern horizon moves through the equatorial stars at the same angular rate as the marker star moves around the north pole.

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