Ancient History & Civilisation

8. The Cosmic Landscape in the Age of the Pyramids

Giulio Magli

Faculty of Civil Architecture - Politecnico di Milano Piazza Leonardo da Vinci 32, 20133 Milan, Italy

Abstract

The pyramids of Egypt are to be counted among the most outstanding works of architecture in the whole of human history. The sites for their construction were chosen in accordance with topographical criteria which, while taking practical needs into account, were also profoundly and intimately connected with Maat, the cosmic order. As a consequence, the pyramid’s fields are criss-crossed by geometrical axes which were - and partially still are - easily perceptible on the ground. In the 4th and the 5th dynasty, such axes ideally connected the monuments with the temple of Heliopolis on the opposite bank of the Nile, while during the 6th dynasty new pyramids were ideally connected with older ones by means of meridian - south to north - alignments. In recent years, the present author attempted to provide a comprehensive analysis of this sacred landscape, and of its astronomical and symbolical interpretation in terms of the “cosmovision” of the ancient Egyptians. The present paper offers a brief but complete overview of the results of this analysis.

1. Introduction

In Egyptian history, the so-called Old Kingdom (2686 BC - 2181 BC circa) is distinctive for what we might call the Age of the Pyramids, a short, intense burst in human history during which the most amazing funerary monuments of humanity were created (Lehner 1999, Verner 2002).

Pyramid-building commenced with king Djoser - around 2630 BC, according to Baines and Malek (1984) chronology - who built the so-called Step Pyramid in Saqqara, and was to continue up to the reign of Pepi II (2278 BC). The pyramids were built on the edge of the desert, just above the floodplain on the west bank of the Nile. With the single exception of Meidum, all the royal pyramids tend to be concentrated in “clusters” (Giza, Abusir, Saqqara, Saqqara South) along a relatively short line which goes from Abu Roash down to Dashour, less than 30 Kilometres to the south.

It is known from the end of the 19th century that an interesting feature exists in the layout of the 4th dynasty “cluster” of pyramids at Giza: the presence of a main topographical axis (Lehner 1985, Goedicke 2001). This axis governed the placement of the subsequent buildings, connecting the south-east corners of Khufu, Khafre and Menkaure’s pyramids. A similar axis exists in Abusir, the pyramid field of the kings of the 5th dynasty, connecting in this case the north-west corners of the pyramids of Sahure, Neferirkare and Neferefre (Verner 2002); a somewhat similar feature can be seen at Saqqara as well (Lehner 1985).

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Figure 1. Giza. A view from the east of the Great Pyramid of Khufu, looking south-west. The main axis of the Giza Necropolis, touching the south-east corners of Khufu (foreground) Khafre (in the middle) and Menkaure (in the background) pyramids is clearly perceptible.

In recent years, the author investigated on such topographical features in order to put in evidence their underlying symbolic meaning. In the course of this work, several interesting points emerged; for instance, new hints at the possibility that the two main pyramids of Giza belong to a single project initiated by Khufu (Magli 2009a,b), the likely existence of further “axes” at Abusir and Saqqara south (Magli 2010a,b) and a proposal for the location of a long-sought pyramid, that of king Userkare (Magli 2010b,c). From a general point of view, it turned out that the alignments of the pyramid’s have nothing to do with utilitarian purposes; on the contrary, in some cases, the desire to align monuments in harmony with pre-existing axes involved enormous technical difficulties, as, for instance, in the Unas project in Saqqara. In order to understand the underlying reasons which moved the ancient Egyptians to such huge efforts, Archaeoastronomy must be used in its broad, modern sense of “science of the ancient sky and landscape” (Ruggles 2005, Magli 2009b). It is, indeed, necessary to consider the ancient Egyptian concept of Maat, the “cosmic order” on which the power of the pharaohs was founded. It was a complex interplay between a solar-stellar religion and the contemporary presence of the living God, the pharaoh himself. The king was the keeper of the cosmic order on the earth and was later doomed to live in eternity - as well as his dynastic ancestors before him - together with the circumpolar stars and the Sun God. As a consequence, astronomy played a key role for the builders of the pyramids. These monuments were indeed the maximal expression of art, ideology, and power during the Old Kingdom, and were designed and placed with the aim to show such “cosmographical” principles. The result is that the pyramid’s fields are magnificent examples of sacred landscapes, conceived in accordance with the Cosmic Order as “applied” on the ground; the role of the alignments is to recall explicitly this idea.

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Figure 2. Abusir. A view from the summit of the south wall of the Neferefre monument, looking north-east. The pit of the unfinished pyramid is visible in the foreground. In the background, the huge mole of the Neferirkare pyramid covers Sahure’s monument. The main axis of the Abusir necropolis passes to the extreme left of the picture and points to the outcrop of the Cairo citadel (and to Heliopolis straight behind) on the other bank of the Nile.

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Figure 3.Saqqara. A view taken from the south of Unas pyramid (foreground) looking north-east. The Saqqara axis connecting Unas’ base diagonal with the south-east corners of the Step (middle) and Userkaf (background) pyramids can still be perceived today, in spite of the ruined state of the monuments.

It is the aim of the present paper to give a brief but systematic overview of all these alignments and of their interpretation. To this end, I shall classify the alignments into three “families”: a “Heliopolitan” family, a “quarter-cardinal” family, and a “meridian” family. Of course, we are talking about very small families: each one contains very few lines and each line contains very few monuments per line. However, the reader should bear in mind that to give concrete form to such lines it was necessary to build some of the most magnificent examples of architecture ever produced by humanity.

The first - or “Heliopolitan” - family is composed by axes which run straight from the pyramid’s fields of Abu Roash, Giza, and Abu-Gorab/Abusir to the Sun temple of Heliopolis, on the other bank of the Nile (Section 2). Their principal meaning is, therefore, symbolic: they call attention to a direct ascendance of the pharaohs from the Sun God. Interestingly, two of these lines correspond to pyramids that had a “stellar” name; further, Heliopolis (whose Egyptian name was Iunu - pillar) besides being the most important religious center of that period, was a place were astronomy was practiced. This raises the possibility that, further to the “solar” character of being oriented towards the Sun temple, these lines might also have a “stellar” character, and therefore that astronomy may have influenced the choice of the sites. Indeed, at the time of the construction of the pyramids, all the azimuths of the pyramid’s fields as seen from Heliopolis can be associated to the setting of Decanal stars, i.e. those stars used to (ritually) count the hours of the night.

The second family can be defined as “quarter-cardinal” (Section 3). It probably originated as an imitation of the most important of the Heliopolitan axes, that of Giza, which, besides being aligned to Heliopolis, is directed along the north-east/south-west axis; this was also the azimuth of the setting of the brightest part of the Milky Way during the pyramid age. Finally, the third family is composed by “meridian” (i.e. north-south) alignments (Section 3). Here, the interplay between astronomy and power becomes even clearer. There is indeed no doubt that astronomy was practiced in Egypt, at least at the site today called Nabta Playa, since the Neolithic period, and therefore already in pre-dynastic times (Malville, Wendorf, Mazar and Schild 1998, Malville, Schild, Wendorf and Brenner 2008). Later in the age of the pyramids, the planners of the king’s monuments were skilled skywatchers (see Magli and Belmonte 2009 and references therein). Determination of true north using precise observations of stars’ motion is indeed a key component of the architecture of the pyramids from Meidum onward; in particular, the two giant pyramids of Giza were oriented with an astonishing accuracy (3 arc minutes for Khufu and 6 arc minutes for Khafre). Such an accuracy was probably obtained with nocturnal observations aimed at the transit of “imperishable” stars, i.e. either circumpolar or, at any rate, sufficiently close to the north pole to be visible every night of the year (Krauss 1997). Besides their practical function, these stars play a fundamental role in the Pyramid Texts, i.e. those texts aimed to assure the “rebirth” of the king which are carved in the funerary chambers of all the 6th dynasty pyramids belonging to the meridian family. As an example, a famous passage of these texts can be mentioned:”I will cross to that side on which are the Imperishable Stars, that I may be among them” (Pyramid Texts 520, §1223, transl. by A. Faulkner).

In the present overview, I will thus put the accent on the astronomical-symbolical features of such topographical choices, which were operational during the relatively short - about 300 years - “Age of the Pyramids”. The main inspiring criteria were the sky, on the one hand, and the pre-existing monuments - the “dynastic” element - on the other. In spite of the existence of persistent claims to the contrary in scores of “fringe” books and websites, no “pre-ordained” or “universal” plan comes to light. I cannot stress strongly enough, therefore, that from the comprehensive study I will briefly outline here, no “hidden”, arcane or esoteric legacy emerges from the Architecture of the Old Kingdom; quite the reverse - as we shall see, the pharaohs wished to make their ideas and the origins of their power as explicit and concrete as possible in the planning of their funerary complexes.

2. The “Heliopolitan” Family

Topographical alignments first appear with the 4th dynasty at Giza (Lehner 1985, Goedicke 2001). As mentioned above, the “Giza axis” connects the south-east corners of the main pyramids (as well as other features, such as the diagonal of the first subsidiary pyramid of Khufu). It points north-east (43° north of east) towards the area where the temple of the sun of Heliopolis once stood, on the opposite bank of the Nile. This area is quite far from Giza (about 24 km) and today there is no possibility of seeing the pyramids from there. Yet a simple calculation shows that, in spite of earth’s curvature, a sign-post - say 20 meters tall - placed in Heliopolis would have been visible from Giza, and of course the reverse was true for the pyramids when viewed from Heliopolis. Khufu - the first king to choose Giza - must thus have wished to emphasize the importance of the Heliopolitan temple. According to authoritative scholars such as Stadelmann (1991) and Hawass (1993) Khufu depicted himself as the incarnation of the Sun God Ra. If this is true, then it appears quite natural that his building location and those of his descendants were chosen in such a way as to be visible from Heliopolis. In this way the kings could declare their “affinity” with the Sun God in their funerary complexes (Jeffreys 1998). Moreover, as a consequence of the alignment, when looking from Heliopolis, the images of the Giza pyramids created a perspective effect, a sort of mirage: they “contracted” on each other, merging into that of the Great Pyramid. The axis was therefore also meant to give a visual, explicit representation of the lineage of the subsequent Pharaohs and thus of the divine ascendance of their power.

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Figure 4. A satellite image of the Giza pyramids with the Giza axis highlighted. 1-Pyramid of Khufu 2-Pyramid of Khafre 3-Pyramid of Menkaure (image courtesy of Google Earth, diagram by the author).

A similar effect was present also at Abu Roash, a site some 5 km north of Giza, where Khufu’s son Djedefre built his pyramid (Magli 2010b). Indeed, the line which connects Heliopolis with Djedefre pyramid’s south-west corner crosses the south-west corner of a second Abu Roash pyramid (Lepsius 1), which probably dates from between the end of the 3rd and the beginning of the 4th dynasties (Swelim 1983). The two pyramids thus form a “Abu Roash axis” again pointing to Heliopolis.

At the end of the 4th dynasty - around 2472 BC - a break in the funerary traditions occurred: in fact Shepsekaf preferred to build a sort of giant Mastaba at Saqqara South. The monument was located in an area quite far from both the two pre-existing necropolises of Saqqara and Dashour, and its placement probably aimed at establishing a visual, perspective connection with the two pre-existing pyramids of Snefru, Khufu’s father (Magli 2010a).

The successor of Shepsekaf, Userkaf, devised a building program aimed at a return to old traditions: to show his affinity with the 3rd dynasty he built his pyramid as close as possible to that of Djoser in Saqqara. To demonstrate explicitly his connection with Heliopolis and the “solarised kings”, he chose to erect a completely new monument, the first of the so-called sun temples, in Abu Gorab. Interestingly, the temple was constructed very near the southernmost available point of the west bank of the Nile from which Heliopolis is still visible (Kaiser 1956). With Userkaf’s successor, Sahure - whose name means “Close to Re” - kingship definitively returned to the solar tradition. The natural choice for Sahure’s pyramid building site would surely have been Giza, to the south west of Menkaure along the “Giza axis”. However, building a pyramid complex so far away in the desert would have been nonsensical. Thus, the architects had to come up with a new way of allowing the monument of their king to fit in with both the solar and the dynastic lineage. It has been suggested by the present author that this was the reason for placing the pyramid in the first available location in the south of Giza from which Heliopolis is not visible: Abusir, some 500 meters further south in relation to Abu Gorab. Approaching Heliopolis from the north and looking west, an observer would indeed have seen the king’s pyramid - called “Sahure’s soul shines” - disappear on the horizon and merge with the profile of the rocky outcrop today occupied by the Cairo citadel, while the shining golden apex of the Userkaf sun temple remained in view, to testify to the solar character of the king’s bloodline.

Once a new Necropolis had been inaugurated by Sahure at Abusir, the successors Neferirkare and Neferefre aligned their pyramids in such a way as to create the “Abusir axis” mentioned above.

To summarize, then, the Heliopolitan axes are three ideal lines which, originating from Heliopolis, align three clusters of pyramids: two pyramids at Abu Roash and three pyramids at Giza and Abusir. A further line from Heliopolis can conveniently be traced up to the pyramid field of Zawiet el Arian, where a huge but unfinished monument of the 4th dynasty - supposedly belonging to an obscure king called Nebka - is located.

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Figure 5. A satellite image of the Abu Gorab - Abu Sir area. Numbering of the monuments is in chronological order. Abu Gorab: T1- Userkaf Sun temple, T2- Niuserre Sun Temple; Abusir: 1/2/3/4 Pyramids of Sahure, Neferirkare, Neferefre, Niuserre. The Abu Sir main axis (A) the Niuserre “dynastic” axis (B) and the Niuserre-Sun Temples axis (C) are highlighted. (Image courtesy of Google Earth, diagram by the author).

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Figure 6 . The “Heliopolitan” lines connecting the pyramid fields with Heliopolis (H): 1-Abu Roash, 2-Giza, 3-Zawiet el Arian, 4-Abu Gorab-last visibility line. Abusir lies a few hundred meters to the south, but visibility is obstructed by the outcrop of the Cairo citadel (C). The azimuth of each of these lines as measured from Heliopolis corresponds to the setting of a Decanal star at the (likely) time of construction of the pyramids as follows: 1-Djedefre-Sirius, 2-Khufu-Rigel, 3-Nebka-Fomalhaut, 4-Sahure-Canopus. See text for more details. (Image courtesy of Google Earth, diagram by the author).

Each royal pyramid had a “name” aimed at glorifying his owner, and two of the Heliopolitan lines correspond to pyramids that had a “stellar” name (“Djedefre is a shining star” and “Nebka is a star”). This raises the possibility that, further to the “solar” character of being oriented towards the Sun temple in Heliopolis (this topographical feature being certain and proved without any doubt, see appendix) these lines might also have a “stellar” character, which may have influenced the choice of the sites. Such “stellar” alignments actually exist, although the reader must be warned that the will of the builders in obtaining them is difficult to prove. Looking at the azimuths of the pyramids from north to south as measured from Heliopolis, one can easily see that they start with the azimuth of the winter solstice sunset (~26° south of west) corresponding to the Abu Roash axis. This means that the Abu Roash axis acts as a boundary: the sun can never be seen setting on any other pyramid from Heliopolis. At the time of the construction of the pyramid, however, this azimuth was close also to that of the setting of Sirius, the first of the Decans, the stars used for the (ritual) count of the hours of the night (Belmonte 2001, Belmonte, Shaltout and Fekri 2009). Actually, it turns out that all the azimuths of the pyramid’s fields as seen from Heliopolis can all be associated to the setting of Decanal stars, and that these stars had heliacal setting in successive periods of the year. From north to south we have the following associations: Sirius-Abu Roash, Rigil-Giza, Fomalhaut-Zawiet el Arian, Canopus-Abu Sir (for technical details and a discussion of related problems see the appendix).

3. The Inter-Cardinal Family

In the Age of the Pyramids the brightest part of the Milky Way - to which the star Rigil belongs - set at azimuths close to 45° south of west (and accordingly, with a flat horizon, rose 45° south of east). As a matter of fact, there exist in the pyramid fields several topographical axes aligned closely to such “inter-cardinal” directions; the Giza axis might be considered as the first member of this family.

The first to inaugurate new quarter-cardinal axes was the “solar” king Niuserre. He reigned after Neferefre (the pyramid of the intermediate king Shepseskare has not been identified with any degree of certainty), and so the place destined for him was to the south-west of Neferefre along the Abusir axis, unquestionably too far off in the desert. Consequently, the planners of his monument had to find another way to exhibit the lineage of the king and his solar ascendance. The solution they came up with was to split the dynastic and the solar content inaugurating two new, different axes. The king’s pyramid is in fact located to the east side of that of his father Neferirkare in such a way that a “dynastic” line (oriented ~41° north of east) connects the south-east corner of the pyramid with that of Neferefre to the south and of Neferirkare to the north (Lehner 1985). In this way, the dynastic problem was solved; naturally, however, the line does not point to Heliopolis. Perhaps it was for this very reason that Niuserre was inspired to construct his own Sun Temple, located at Abu Gorab, north-west of the Userkaf’s one and therefore in plain view of Heliopolis. What remained to be done was to connect the project of the temple with that of the funerary complex: to achieve this goal Niuserre’s architects planned the temple in such a way that another inter-cardinal axis (this time ~45° south of east) connects the base of the obelisk of the temple, the south-east corner of Userkaf’s temple and the apex of the Niuserre pyramid (Magli 2010b). If the line is extended further to the north-west, it intersects with the south-west corner of a 3rd dynasty pyramid in Zawiet el Arian and appears to end at the centre of the unfinished pyramid in the same site (whether such an alignment was deliberate or not is a moot point and requires further study).

Yet another “quarter cardinal” axis was inaugurated with the project of king Unas, the last king of the 5th dynasty (Lehner 1999, Magli 2010a). The pyramid of Unas is located near the south-west corner of the precinct of Djoser’s Step Pyramid, quite a distance from the Nile floodplain. The likely reason for this inauspicious choice is symbolic: for in this way the king instituted a “Saqqara axis”. The Saqqara axis is again a line oriented roughly NE-SW (~39° east of north), which connects the south-east corner of Userkaf’s pyramid with the south-east corner of Djoser’s pyramid and then crosses over Unas’ base diagonal, ending at the north-west corner of the (unfinished) 3rd dynasty pyramid of Sekhemkhet. The result is that, after the building of Unas’ monument, the placement of the three pyramids of the Saqqara central field resembles that of the three pyramids of Giza. Clearly, the axis does not point to Heliopolis, and therefore this similarity has to be construed as an ideal relationship with the pre-existing Giza monuments, perhaps first conceived of by Userkaf (Goedicke 2001).

If extended north-west, the Saqqara axis touches the north west corner of Teti’s pyramid (Lehner 1985). Teti was Unas’ successor, and therefore the “natural” position for his pyramid would have been to the south-west of Unas. For the third time, however, (after Menkaure at Giza and Neferefre at Abusir), it proved impossible to place a new pyramid to the south west along an existing line, and a new idea was needed. Teti evidently elected to put his pyramid “at the beginning” of the line. Probably to respect the “dynastic” perspective of the pre-existing axis, it is the north-west corner of the pyramid which lies on the line.

At Teti’s death an obscure king called Userkare succeeded to the throne. We do not know where it was planned to position Userkare’s pyramid. His successors Pepi I, Merenre and Pepi II chose an area to the south of the Saqqara central field, where there stood only the pyramid of the 5th dynasty king Djedkare. The Merenre project was located to the south-west of Pepi I, in such a way as to place the pyramid along the diagonal of the latter. We thus have a new quarter-cardinal axis initiated at Saqqara south, oriented ~41° east of north and therefore roughly parallel to the Saqqara one. The monument of Pepi II does not lie on this axis, though. The “natural” position of his pyramid to the south-west of Merenre would actually have been in a wadi (dried river): building a pyramid there would have inadvisable. And so the king’s tomb was constructed to the immediate south of this area, near Shepsekaf’s monument. To sum up ,then, the “quarter-cardinal” family is made up of the Giza axis, the two Niuserre axes, the Saqqara axis and the Pepi I-Merenre diagonal alignment.

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Figure 7. A satellite image of Saqqara (numbering of the monuments is in chronological order; Shepsekaf’s Mastaba and Djedkare pyramid are not highlighted). 1- Djoser Step Pyramid, 2-Pyramid of Sekhemkhet 3-Pyramid of Userkaf, 4- Pyramid of Unas 5-pyramid of Teti 6-Pyramid of Pepi I 7-Pyramid of Merenre. The Saqqara axis (A) and the Pepi I-Merenre axis (B) are highlighted, as well as the three meridian alignments Pepi I-Userkaf, Merenre-Unas, Pepi II-Sekhemkhet. (Image courtesy of Google Earth, diagram by the author).

4. The Meridian Family

In the planning of the 6th dynasty pyramids a new kind of topographical pattern also emerges. In fact, the positions of the three monuments appear to have been selected according to “meridian” axes. Such lines run from south to north, in the sense that each new monument has been constructed due south of an existing one. To be precise, the apex of Pepi I aligns with that of Userkaf and the apex of Merenre aligns with that of Unas (Goyon 1977); furthermore, the apex of Pepi II aligns with the apex of the last pyramid of the Saqqara axis, that of Sekhemkhet. Curiously, the position in meridian alignment with the Djoser pyramid is vacant, and I have therefore proposed that the - unfinished - monument of Userkare might still be lying under the sand right there (Magli 2010c).

As discussed in the introduction, to interpret the meridian alignments it should be recalled that determination of true north is a key component of the architecture of the pyramids. It was probably carried out with nocturnal observations aimed at the transit of “imperishable” stars, i.e. those stars to which the “rebirth” of the pharaoh is closely connected by the Pyramid Texts. These invisible meridian lines crossing the desert and connecting pairs of monuments are therefore, and again, clearly conceived in such a way to harmonize the human-built landscape with the pre-existing one on the earth and with the sky above.

5. Discussion and Conclusions

The choice of the pyramid construction sites had to take various practical factors into consideration (Barta 2005). Nevertheless, at least in many cases, no one such practical factors can be deemed decisive. In particular, three clamorous examples can be cited, where a different mechanism, clearly of symbolic - as opposed to utilitarian - nature must have had a role. These are the three pyramids which were constructed “far in the desert” along south-west/north-east axes, namely Menkaure at Giza, Neferefre at Abusir, Unas at Saqqara. A clear willingness is also shown by the meridian alignments of the 6th dynasty pyramids with those of the Saqqara central field.

Of course, the problem of the interpretation of these evidences in absence of specific, written sources is actually doomed to remain, at least in part, at the speculative level. However, as discussed at length in previous works (see e.g. Magli 2009a, 2010a,b,c), it can be backed up by a series of clues pointing to the close relationship between astronomy and power during the Old Kingdom. A full discussion of this topic requires a careful chronological analysis king after king and monument after monument, and is given elsewhere (Magli 2010b,c). As a fundamental step, however, we can concur with the Egyptologist George Goyon who observed that alignments between new and previously constructed monuments where aimed to express connection to an ancestor or to sacred sites (Goyon 1977); a similar viewpoint inspired Goedicke (2001) analysis of Saqqara. Further, the connection with the cult of Ra, the Sun god, helps in explaining the fact that attention is called towards Heliopolis, starting with Giza and therefore with the first “solar” pharaoh, Khufu (Stadelmann 1991, Hawass 1993, Jeffreys 1998). Finally, it is worth mentioning again the fundamental role played by the northern stars in the rebirth “procedures” described in the Pyramid Texts, which were written in the funerary chambers starting from Unas and are present in all the 6th dynasty pyramids which are in meridian alignment with those of the Saqqara central field.

The alignments discussed here were plainly visible in antiquity: each king chose his site and planned his monument in accordance with pre-existing ones, with the aim of preserving the cosmic order - Maat - in the sacred landscape where his embalmed body was to rest for eternity. The pharaohs spelled out this message so plainly that, even though more than 4,300 years have passed, their burning desire to express their profound connection with their ancestors in stone, and their hope to live forever amid the imperishable stars, can still be clearly perceived today.

Appendix

The existence and willingness of the topographical alignments we have discussed in the present paper is attested beyond any doubt. Most of them were repeatedly noticed since the 19th century and then documented in the authoritative surveys made by Egyptologists Mark Lehner (1985), Miroslav Verner (2002) and George Goyon (1977) at Giza, Abusir and Saqqara respectively. Further, the present author has taken many direct measures, from which the data given in the text are taken. On field measures have been taken with a precision magnetic compass and corrected for magnetic declination. The nominal accuracy of the instrument is ½ °; magnetic anomalies have not to be expected in Egypt, however it is perhaps safer to assume a precision of ±1°. All data have also been cross-checked with topographical maps whenever available, and by using the Google-earth program. The satellite mapping of Egypt and Nubia provided by this program is quite accurate, to the point that a comprehensive archaeoastronomical research on the Egyptian monuments of Sudan has been recently carried out using this program (Belmonte, Fekri, Abdel-hadi, Shaltout and García 2010). Further, 3D rendering distortion effects, which are the major source of errors for this program, are negligible in the case of the flat-desert pyramids plateaus.

The possible astronomical alignments to Heliopolis proposed at the end of section 2 requires instead a delicate discussion. First of all, it involves the problem of dating the monuments. Indeed, of course, stellar alignments depend strongly on precession, while the precise dates of construction are unknown. Actually, different chronologies may differ for as much as 80 years. What has been done here is to take as a working framework one reliable chronology for the Old Kingdom, that given by Baines and Malek (2000). From such a chronology the dates of accession of the king who “inaugurated” the alignment were extracted, since pyramid construction likely commenced immediately after accession (the king Nebka is not documented in the royal annals, and therefore as a reference date 2500 BC has been assumed).

Then, the sky in correspondence of the alignments’ azimuths were investigated around such dates, searching for the setting of bright stars. Several effects have to be taken into account here. First of all, the horizon, which is however flat from Abu Roash down to the azimuth of Abu Gorab/Abusir, where the Cairo citadel blocks the view but also defines the last line of visibility of interest here. Second, the atmospheric effects have to be taken into account to estimate the minimal altitude of visibility. Refraction is negligible at Cairo latitude, while extinction may have a considerable effect. This effect may vary in dependance of the value of the visual extinction coefficient (Schaefer 1986). In optimal conditions however, and considering only very bright stars, extinction is negligible for stars with negative magnitudes and can be assumed equal to 1° for stars with magnitude around 1. Proceeding in this way, the following results are obtained: Djedefre at Abu Roash (2528 BC, ~26° south of west) Sirius; Khufu at Giza (2551 BC, ~45° south of west) Rigil; Nebka at Zawiet el Arian (2500 BC, ~54° south of west) Fomalhaut; Sahure at Abusir (2458 BC, ~70° south of west) Canopus. These results are valid within 1° or less, provided that the dates are valid as well.

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