Great-pyramid-S2-astronomical-coordinate-system

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ARCHITECTONICS

From Cosmic Theories to Urban Development

Dr. Hossam Aboulfotouh

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THE HORIZON THEORY, PART-II: Internal Design Concept of the Great Pyramid.

Hossam Aboulfotouh, Ph.D

Assistant Professor, Department of Architecture, Faculty of Fine Arts, Minia University, and Director UIA-WPAHR-V fotouh@mail.com

[Proceedings of the German-Egyptian Conference on Conservation and Restoration, Faculty of Fine Arts, Minia University, 17-18 March 2005]

Section-2: The astronomical Coordinate System of the ancient Egyptians.

In spherical astronomy, one could identify the astronomical location of any observed celestial body, using such spherical coordinate System12. Today as well as in the ancient times, astronomers are using a system wherein the Earth represents its center; or it is the point of origin at which the three spherical coordinates X-X, Y-Y and Z-Z intersect. In this system, astronomers imagine that the Earth is the center of such sphere representing the observed sky that along which all the other observed celestial bodies like stars, the sun, the natural satellites like our moon, and the planets perform their revolutions. The only real case in this system is the revolution of our moon around the Earth. The cases of the other celestial bodies are imaginary and only for identifying their locations in relation to an observer standing anywhere on our planet. In that system, there are two basic circular planes, which intersect with each other, as shown in figure-3. The first is the plane of the Earth's equator. The second is the plane of the Earth's orbit around the sun; astronomers call it the ecliptic.

Click on picture to see high resolution

Figure-3: The spherical coordinate system, wherein the Earth represents its center, or the point of origin of its three coordinates.

The angle between these two planes is called the obliquity angle of the earth, which fluctuate between two extreme but postulated values (21.92° – 24.30°) within a span of time equals to 40 thousand years approximately. Its current value equals 23.45° and diminishes by 0.47 second of arc per year, as now the Earth is in its descending path12. For the pyramids' designer, the minimum value of it equals 21.673° as he coded it in the entrance-passage of the second pyramid; and its maximum value equals 24.30°. It has been proven in part-I that the value of the Earth's obliquity angle was 24.10° at the time of erecting Giza pyramids, implying that the date of their erection is 3055 BC approximately.

Now, if we draw a cross section in that spherical system wherein the coordinates Xe-Xw and Yn-Ys are located, it will be as shown in figure-4. The additional letters n, s, e, and w indicate north, south, east, and west respectively. The coordinate Xe-Xw represents the plane of the Earth's equator and the coordinate Yn-Ys represents the north-south axis of the Earth. The line P1-P2 represents a cross-section in the ecliptic, or the orbital plane of the Earth around the Sun, and q (theta) is the obliquity angle.

As said earlier, this way of representing the Sun's motion is the opposite of reality; thus, it shows that the Sun rotates around the Earth, imitating its daily motion when observed from the Earth. The way that cross-section is being drawn implies that the observer is standing on the North Pole of the Earth, and observes the Sun rotating around it along the plane of P1-P2. Thus, in figure-4, the Sun shall appear to us as it fluctuates between P1 and P2. If the astronomical position of the Sun starts from P1, it takes 6 months to arrive at P2 and another 6 months to return back again to P1, performing by this one orbital cycle in one Earth year or 365.25 days.

Further, as the Earth performs one cycle around its axis in 24 hours (one Earth day), the Sun will appear too that it performs one daily motion around the Earth's axis Yn-Ys. Accordingly, as shown in figure-4, if the sun were at P1, its observed daily motion around Yn-Ys will make it appear, in this cross-sectional diagram, as it had went to P3 and returned to P1, or close to it, in one Earth day. Similarly, if the Sun was at P2 it will go to P4 and returns back to P3 or close to it. In between, the lines P1-P3 and P2-P4 there are an array of similar lines that each represents one observed daily motion of the Sun around the Yn-Ys axis of the Earth. The lines P1-P3 and P2-P4 intersect with Yn-Ys in points Pn and Ps respectively. These two points indicate the projections of the centers of the two extreme-circular-planes of the daily motion of the sun around the axis Yn-Ys of the Earth. The line L1-L2 represents the plane of the ecliptic at its minimum tilt or obliquity angle of 21.673°.

Click on picture to see high resolution

Figure-4: A cross-sectional diagram shows the projection of the observed dual motions of the Sun around the Earth: its yearly motion between P1 and P2; and its daily motion along an array of parallel lines in between, and including, P1-P3 and P2-P4.

This diagram in figure-4 is the simplest cross-sectional representation of the real dual-motions of the Earth: its orbital motion around the Sun and its spin motion around its axis. However, it should be taken in consideration that, for the case of the sun, the diagram shows the opposite of reality because this is the only way for plotting the dual-motions of the Earth in one meaningful cross-sectional drawing in relation to the sun. It is the simplest architectonic analysis for understanding the observed motion of any celestial body, while the observer is standing on earth. As will be discussed hereafter, the designer of the Egyptian pyramids have used that cross-sectional diagram in his design.

In that diagram, the observer is standing either on the North Pole (Yn) or on the South Pole (Ys) of the Earth; in this case, the line Xe-Xw represents the plane of the horizon at which the observer stands. Suppose that the observer is standing on any other location Earth, for example, if he stands on the Earth's equator the diagram will be as shown in figure-5. In this case, the line Ys-Yn represents the horizon of the observer; i.e., the ground whereon he stands.

Click on picture to see

Figure: A cross-sectional diagram shows the projection of the observed dual motions of the Sun around the Earth, while the observer is standing on the Earth's Equator, i.e., Xw-Xe represents the direction of his azimuth.

Section-1: Introduction

Section-2: The astronomical Coordinate System of the ancient Egyptians

Section-3: The pyramidal form and the spherical system of coordinates

Section-4: Great pyramid's shafts and entry passage, and its spherical domain

References:

1- Edwards I. E. S, The Pyramids of Egypt, rev. ed., Pit-man, 1961.

2- Farouk- El-Baz, Gifts of the Desert, archaeology Magazine, Volume 54 Number 2, March/April 2001

3- Encyclopedia Americana, Vol. 23, Grolier Ltd., Canada, 1978

4- Fathy Al-Bedawy, Pyramid and Computer: the symbol of Ancient and Modern Civilization, Cairo, 1991.

5- Aboulfotouh, H.: The Horizon Theory, Part-I: Original Concept Plan of the Pyramids Plateau, Cairo, proceedings of the UIA-WPAR-V International Conference, Bibliotheca Alexandrina, 2002. www.fotouh.netfirms.com/horizon-theory-introduction.htm

6- Petrie, W.M.F., The Pyramids and Temples of Gizeh, London, 1883.

7- Aboulfotouh, H.: Determining Planetary Spin and Musical Gravitation in the Spheres of Cosmic Systems of Perfect Numbers, Cairo, Dar Al-Kutub, 2004. www.fotouh.netfirms.com/spin-gravity-introduction.htm

8- Al-Maqrizie, Al Mawaes Wal A'atebar Bezeker Al-khetat Wal Asar (Sermons and Lessons with the Discourse on Alleys and Monuments), Vol.I, Dar Al-Tahrier, Bulaque Edition, Cairo, 1849.

9- Al-Masoudy, Mrog Al-Zahab Wa Ma'aten Al-Gawher (Golden Lava and Metals of Essence), Asria Library press, Saida, 1987.

10- Plato, Timaeus, (330 BC.).part1-paragraph-6 http://psychclassics.yorku.ca/Plato/Timaeus

11- Olaf Pedersen, Early Physics and Astronomy, a Historical Introduction, Cambridge University press, New York, 1993.

12- A. Weigert & H. Zimmermann, Encyclopedia of Astronomy, Arabic edition, Abdelkawy Aiad translator, The Egyptian General Organization for Book, Cairo, 1990

13- R. Gantenbrink in R. Stadelmann, MDAIK 50 (1994), 285-294. http://www.cheops.org

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