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Methods of Finding Cardinal Points


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Finding Cardinal Points - Introduction



The meridian* of a place (and the True North) can be located with high degree
of accuracy with the use of few fairly simple methods (possibly available to ancient builders):

  • the stars

  • the sun

Note: Using Polaris (Northern Star) or magnetic compass would be much less reliable at the time ancient monuments were built.

* The line on the surface of the earth through the place and both poles is called the meridian of the place: it is a half-circle since the earth is spherical.

- - -

Pyramids, and many other types of religious structures, required strict orientation to the cardinal points. The ancient builders oriented their monuments using either the sun or the stars.

The Ancient Egyptians managed to line up the sides of their pyramids to the points of the compass, with extraordinary accuracy. The most accurate is the Pyramid of Khufu, also called the Great Pyramid. The east and west sides miss true north by less than three minutes of arc (roughly one tenth the diameter of the full moon). With this kind of accuracy, it's no wonder they were one of the Seven Wonders of the World. It took over 4,000 years before the astronomer, Tycho Brahe, was able to take astronomical measurements to a greater accuracy.

And this led to a problem that has bothered Egyptologists for a long time - how did they manage to line up the east and west sides of the Great Pyramid so accurately with the North Pole?

Now we're not talking about Magnetic North. We're talking about Geographic North which is the pole about which the Earth seems to spin. The Magnetic North Pole is currently wandering at a few kilometres per year through the far north of Canada, while the Geographic North Pole is in the Arctic.

One way to find Geographic North would be by looking at the Sun. You'd note the rising position of the Sun in East, and the setting position of the Sun in the West, and halve the angle between them. This would give the direction of the True North.

The other way to find Geographic North involves the stars at night.
The Celestial North Pole is a point in the sky about which the stars appear to rotate. If you took a time lapse photograph over a full night, you would see that all of the visible stars would appear to move in circles (some big and some small).

The star Polaris would make an incredibly small circle because it's right next to the Celestial North Pole. So it's called the Pole Star.
But there's a slight problem with this method. The North-South spin axis of the Earth is not fixed, but rotates slowly like a giant top. Imagine you have a big basketball and it's spinning. Now the spin axis is not straight up-and-down, but tilted by 23 degrees from the vertical. This how the Earth is currently spinning. Now start off with the North Pole of your spinning basketball slightly to the right. Gradually, the North Pole sweeps out a circle, so that it's next facing away from you, and then over to your left, and then coming around to face you, and then finally back over to the right again. The spin axis of the Earth sweeps through one complete rotation in 26,000 years.

The most likely way to find Geographic North would be by bisecting the angle formed by the two extreme positions of a circumpolar star. The best candidate for such a star would be Vega.

Using Magnetic Compass to locate local meridian



Considering that ancient civilizations most likely were lacking magnetic compasses,  this is the least likely explanation how precise alignments of ancient structures had been accomplished. In fact, the magnetic compass would provide lesser than observed precision due to errors inherent in this method.

Early Compass A floating fish-shaped iron leaf, mentioned in the Wu Ching Tsung Yao which was written around 1040. The book describes how iron can be heated and quenched to produce thermoremanent magnetisation. The first clear account of suspended magnetic compasses in any language was written by Shen Kua in 1088]
Modern Compass     Compass Professional Liquid filled

The magnetic poles are not situated in the same place as the true geographic poles (defined by the northern end of the earth's axis of rotation) and thus an error (variation) occurs in the true reading of the compass (which varies in time and from place to place across the world).
Another magnetic compass errors, deviation, is caused by the magnetic influence of anything that can distort local magnetic field located near the compass needle. Therefore, compass readings must be corrected for such errors. Also, the magnetic compass needle reading can be distorted by disturbances on the sun, and magnetic influence of anything near the compass needle.

- - -

Magnetic Variations - Finding True North

Magnetic variations had first been noticed in the Age of Discovery. Until then, compass bearings and charts based upon them referred to magnetic north rather than true north as measured by the position of the Pole Star. This distinction only became vital when sailors began using latitude as the way to determine their course. As they were sailing along a latitude they noted that the compass needle varied unexpectedly. It 'northeasted' or ‘northwested' that is, the position of magnetic north shifted with the position of the ship (Berthon and Robinson, 1991:118).

This discovery initially greatly dismayed the Portuguese pilots who first discovered it. Having no idea of the real reason - alterations in the magnetic field of the earth which varies greatly in direction from both decade to decade and place to place - they wrongly attributed the moves to badly hung compass needles, inferior lode stones or the leeway caused by ocean currents. Compass makers began to make their own 'allowances' for the variations by off-setting north on the compass and off-setting different points on the journey. Hence it was that Columbus found that his Flemish and Italian compasses provided different readings (Berthon and Robinson, 1991:119).

Soon the idea developed that one "true" meridian may exist along which the magnetic variation from true north was zero. On either side of this meridian, it was believed, the variation would increase uniformly in opposite directions, thus creating the effect of northeasting and northwesting. If this was reality it meant that the direction of magnetic north relative to true north could be predicted at any point around the earth's circumference and this could then be used by a ship to calculate longitude by comparison with its measured north.

Unfortunately this was not actually the case as first established by a Chief Pilot of the Portuguese Indian Fleet, John de Castro. He was the first to show that the variation did not follow any pre-determined pattern and certainly not that of a true meridian. In 1638, more than a century later Henry Gellibrand, a professor of mathematics confirmed that the variation altered over time as well as place. It was in fact even more unpredictable than sailors had feared (Berthon and Robinson, 1991:120).

Despite this finding, in 1698 Edmund Halley arranged to be commissioned captain of a ship, the Paramour. Sailing through the Atlantic he measured the magnetic variation from true north and then used these data to plot lines of equal variation for the year 1700. However the map caused much scepticism amongst sailors when Halley drew 'north' lying east-west at the coast of the now United States and a 'true' meridian "that looked more like a parabola than a straight line." (Berthon and Robinson, 1991:120). Halley’s research excluded magnetic variation as a practical solution for the calculation of longitude, although it remained theoretically possible if a great enough spread of reference values, such as those plotted by Halley, were monitored year by year. This was not a condition that was to be fulfilled until the twentieth century with the advent of satellite (Berthon and Robinson, 1991:120 and Taylor, 1956:240).

Sailors were not able to rely on magnetic variation to determine longitude. Another solution was required.

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Using Polaris to find True North


Using Polaris to find True North would lead to errors due to precession
(in fact, few thousand years ago Polaris was much further from the North than it is today).

Polaris's location less than 1° from the pole (1992 position R.A. 2h23.3m, Dec. +89°14′) makes it a very important navigational star even though it is only of second magnitude; it marks due north from an observer.

The northern Precession Circle;
the circular path of the Northern Celestial Pole
around the Northern Ecliptic Pole, a journey that takes
nearly 26,000 years.

Because of the precession of the equinoxes, Polaris will not remain the polestar indefinitely; in 2300 B.C. the polestar was in the constellation Draco, and by A.D. 12,000 the star Vega in the constellation Lyra will be the polestar.

Polaris hasn't always been the Pole Star. In fact, it has only been close to the Pole for the last thousand years or so, and over the next millennium it will gradually move further away. This is because the Earth's motion is constantly affected by the pull of other bodies in the Solar System, especially the Moon and the Sun, which causes a 'wobble' in its orbit. This, in turn, causes the Pole to move relative to the stars.

Prominent Pole Stars

c.3000 BCE Thuban
c.1000 BCE Kochab
c.2000 CE Polaris
c.4000 CE Alrai
c.7500 CE Alderamin
c.14000 CE Vega

The effect of this wobble (properly called precession) is that both Celestial Poles follow a broad circle through the sky. For most of the time, there is no Pole Star at all, but occasionally the Pole will pass near a conspicuous star - we are lucky to live in a time when Polaris fulfils this role. For the ancient Egyptians, the Pole Star was not Polaris, but Thuban in Draco, while observers in the far future will see yet other stars at the Northern Celestial Pole.

More about Precession>>

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Using Circumpolar Stars to find the True North


The primary theory of how the ancient Egyptians oriented most any building that had to conform to true primary coordinates has been by stellar measurements.

At the time of pyramid building, Polaris (our current Northern Star) was too far from the North Celestial Pole to mark the true North so the most likely method would be based on bisection of the angle created by lines pointing to a star-rise and star-set.)

The circumpolar stars viewed from a northern hemisphere
trace circles around the Celestial North Pole -- a point in the sky
about which the stars appear to rotate.

A time lapse photo over a full night, shows that all of the visible stars appear to move in circles (some big and some small). The star Polaris makes today an incredibly small circle because it's right next to the Celestial North Pole.

An example how Vega could be used to find true North 2,250 B.C.

The pyramids were oriented to the North likely by the observation of stars.
The position of the meridian could have been obtained by bisecting the angle formed by the two extreme positions of a circumpolar star. The best candidate for such a star would be Vega.
Bisecting the angle between the set and rise of Vega would reveal the exact location of the meridian (the true North).

Setting Vega viewed from the location of the Great Pyramid
on December 21, 2550 BC at 7:28 pm

Rising Vega viewed from the location of the Great Pyramid
on December 22, 2550 BC at 5:25 am

The measurements would involve using  perfectly leveled string or circular wall.
A man would stand in a designated spot and through a straight pole with a forked top called a bay, sight a circumpolar star as it rises. A second man at certain distance from the first would then mark the "spot" where the star rose using a type of plumb line, or merkhet. When the star set, the process would be repeated. Measuring between the two spots would then provide true north from the center sighting pole.

Bisection the angle created by lines pointing to a star-rise and star-set.

Method believed used to find true north for Pyramids and other buildings

Egyptian Merkhet


Using Merkhet

Crocodile god Sobek using Merkhet


Relief from the temple Kom Ombo.
Ancient "sighting" tools?

Circumpolar Stars Correlation - two stars in simultaneous transit


Back in 2467 BC, it would be quite easy to find True North. All you'd have to do would be to build some scaffolding, and hang a string with a heavy weight. This would hang perfectly vertically, pointing to the centre of the Earth. You'd then wait until two stars, Mizar and Kochab,  were vertically aligned exactly with your hanging string. Then a line from you, to the hanging string, would point due north to the horizon.

In the year 2467 BC (when building pyramids was all the rage), two stars appeared to rotate around the Celestial North Pole. These stars were Mizar (Eta-Ursae Majoris) in the Big Dipper and Kochab (Beta-Ursae Minoris) in the Little Dipper.

A British scholar named K. Spence believes that the Egyptians used these two stars to determine the position of  True North. Spence identifies that method as the observation of two stars in simultaneous transit — that is, two stars on exact opposite sides of true north which appear to rotate around it. When they are in vertical alignment, as judged by a plumb line, their direction can be taken to be true north with a high accuracy. By running computer simulations of the night sky back to the time of the Egyptian kingdoms, she has identified the stars that were most probably used — Mizar and Kochab — one each from the constellations of The Great and The Little Bear, which had simultaneous transits in 2467 BC.

Because of the precession of the Earth’s axis, these two stars would have simultaneous transits only for a year or so. One would therefore expect errors in alignments to increase with time away from 2467 BC. This is exactly what is seen — plotting the estimated construction date of the pyramids against their error in orientation produces a remarkably straight line, with those built before 2467 BC pointing slightly east and those built afterwards pointing slightly west. Two pyramids, Khafre and Ashure, do not fall near the straight line, but even this can be explained by assuming that the measurement was made when the two key stars were the other way up in the sky, reversing the deviation.

Obtaining such a strong correlation confirms Spence’s theory, and the plot can also be used in reverse, as a tool to refine the estimates of construction dates. Thus, Spence calculates that the Great Pyramid (Khufu) was set out in 2478 BC ± 5 years. Historians currently place the beginning of King Khufu’s reign at 2554 BC at the latest, so the result may trigger a rethink of the chronology of the ancient Egyptian kings.

K. Spence believes that in order to find True North
the Egyptians used two circumpolar stars:
Mizar (Eta-Ursae Majoris) in the Big Dipper and
Kochab (Beta-Ursae Minoris) in the Little Dipper.

The position of the Celestial North Pole changes with time, and this is what Kate Spence tried to use, to work out when the pyramids were built. She took an existing proposal that a vertical alignment between two stars was used to identify North, and attempted to correlate the slow drift of this particular pair of stars with the slight clockwise variation in alignments found on pyramids of sequential construction dates. In many respects this correlation proved to be very good, although there is a minority of cases that do not fit into this sequence.

It could be that this is just a coincidence - after all, she was looking at only half a dozen pyramids. That's a very small sample size. But if her method is correct, it means that we can calculate the dates when the pyramids were built to within five years or so - which is much better than the currently accepted hundred-year error.

Perhaps the only real error the Egyptian pyramid builders made was forgetting to install some doors.

Related Links and References:

Solar Compass method of finding Cardinal Points


A line corresponding with the true meridian of the place may be made by the solar method.

It turns out that highly precise alignment can be easily achieved with very simple methods. With help of the Sun, few sticks and two ropes of equal length would be all that was needed to find the cardinal points with high degree of accuracy.

It is very likely that the ancient builders oriented their monuments using the sun,
by means of wooden stakes and ropes. There are in fact references in ancient texts referring to "the shadow", the "stride of Ra" and "stretching the cord ceremony".


Direct Sighting method

The local meridian can be located by observing the shortest shadow of a vertical obelisk. However much more accurate result can be obtained by bisection the angle created by lines pointing to the sunrise and sunset.

With help of the Sun, few sighting poles and two ropes of equal length
would be all that was needed to orient a pyramid with high degree
of accuracy (and mark its corners). The Equinox sunset would mark True West-East direction.  Click on the image to view more detailed geometry behind this method.

In Teotihuacán, Mexico the sun sets directly opposite the "Pyramid of the Sun" (the azimuth of the sunset  is 285º.5) on August 13. The above method would be ideal for orienting the pyramid to the sunset on that day.

Using Shadow of an Obelisk

Another variation of this method (of finding the true meridian) would be based on using the shadow of an obelisk (instead of direct sighting of the rising and setting sun).

The sun rises and sets in equal but opposite angles to true north. Using a plumb line, a pole would have been set as vertically as possible. Then, few hours before noon, its shadow would be measured. This length then becomes the radius of a circle. As the sun rises higher, the shadow shrinks back from the line and then becomes longer in the afternoon. When it reaches the circle again it forms an angle with the morning's line. The bisection of the angle is true north.

Finding the true meridian using the path of an obelisk's shadow.
Click on the image to enlarge.

Learn more about obelisks>>

A sacred ritual ceremony to find the cardinal directions


A sacred ritual ceremony to find the cardinal direction indicated in ancient manuscripts. Among those ancient manuscripts the Vishvakarmiam and Maymata are the oldest manuscript. Vishvakarma (Vishvakarmiam) said to the chief architect for Gods and Mayan (Maymata) said to be the architect for human beings
The ancient geometry may be originated and developed for finding the cardinal points with reference with sun. In the beginning our ancestors would have been initially intend to know sun's path to know the direction East and West. Later they found four directions East, South, West and North, then other sub directions Southeast, Southwest, Northwest and Northeast. In ancient time our ancestors considered this as a most sacred practice and strictly followed as ritual ceremony. Also a selected person called Sthapati (Architect) will perform this ancient practice. It appears the ancient geometry would have developed from this prime ritual practice. This ritual practice narrated in details in various ancient texts. Even though I am not intended to go in depth; the following few information is essential to understand the ancient geometry of finding the cardinal points.

Ancient manuscript, Maya Mata,  describes the geometrical method of  finding out the cardinal directions:

Chapter 6 - Orientation

6.1-2a: Now I give the method of determining the cardinal points with the help of gnomon. (One should proceed) at sunrise during a month when the solar path is towards the north during a bright fortnight when sunrise is beautiful, when there are no spots in the solar disc and when the sun is in the asterism of the appropriate fortnight.

6.2b- 3a: First of all a piece of ground in the middle of the chosen site should be leveled by the water method; this must be square one square pole in the center in the center of which the gnomon should be set.

6.3b- 5: Herewith the dimensions of the gnomon (Sanku): the largest kind is one cubit long, its diameter at is one digit at the top and five at the bottom, it is perfectly circular and without irregularities; one of medium size (has a length of) eighteen digits and a small one a length of twelve or nine digits, their diameter at the top and bottom being (in all case) proportionate to their length.

6.6- 7a: The materials prescribed for the making the gnomon are as follows: Ivory, sandalwood, wood of khadira, kadara, sami, saka or tinduka or other hard wood; its tip should be perfectly circular.

6.7b- 8a: When the gnomon has been made it is set up in the chosen place at sunrise, then a circle is drawn of which the gnomon is the center and which the diameter is double the length of the gnomon.

6.8b-11a: The line which join the two points where the shadow (of gnomon) has touched the circle in morning (A) and in the evening (B), gives the east - west direction. The line which passes through the space between these two points and (which is like that which) connects the head and tail of a carp, is the north - south axis; the sage should draw these two lines, Then the circles which have their centers at the east and west points should be drawn.

6.11b- 13: (When the sun) is in Taurus or Virgo there is apaccya; when it is in Aries, Gemini, Leo or Libra the (east-west axis) must be put back two digits; when it is in Cancer, Scorpio or Pisces it must be adjusted by four digits, when it is in Sagittarius or Aquarius (it must be adjusted) by six digits and when it is in Capricorn by eight digits. The east-west line is to be fixed after it has been moved to the right or to left of the shadow.

6.27: (The east=west line) should be established with adjustments of the following numbers of digits for each ten day period of each month: (Aries) two, one, zero, (Taurus) zero, one, two, (Gemini) two, three, four, (Cancer) four, three, two, (Leo) two, one, zero, (Virgo) zero, one, two, (Libra) two, three, four, (Scorpio) four, five, six, (Sagittarius) six, seven, eight, (Capricorn) eight, seven, six, (Aquarius) six, five, four, (Pisces) four, three, two.

6.28: When the course of the sun has been taken into consideration in relation to the constellations, the indicated adjustment should be made, when necessary; the correction once made, the line is drawn from the stake and the ground can be prepared.


Related Links:

Nazca Lines - GGF
(Geometrical Nazca Marking)

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