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nature 16 November 2000 Articles Nature 408, 320 - 324 (2000) ©
Macmillan Publishers Ltd. Ancient Egyptian chronology and the
astronomical orientation of pyramids KATE SPENCE Faculty of Oriental
Studies, University of Cambridge, Sidgwick Avenue, Cambridge CB3 9DA,
UK Correspondence should be addressed to K.S. (e-mail:
kes1004 at cam.ac.uk). The ancient Egyptian pyramids at Giza have never
been accurately dated, although we know that they were built
approximately around the middle of the third millennium BC. The
chronologies of this period have been reconstructed from surviving
lists of kings and the lengths of their reigns, but the lists are
rare, seldom complete and contain known inconsistencies and errors. As
a result, the existing chronologies for that period (the Old Kingdom)
can be considered accurate only to about 100 years, a figure that
radiocarbon dating cannot at present improve. Here I use trends in the
orientation of Old Kingdom pyramids to demonstrate that the Egyptians
aligned them to north by using the simultaneous transit of two
circumpolar stars. Modelling the precession of these stars yields a
date for the start of construction of the Great Pyramid that is
accurate to 5 yr, thereby providing an anchor for the Old Kingdom
chronologies. The pyramids of the middle of the third millennium in
Egypt (the Old Kingdom), built as tombs for the kings of the period,
were oriented to the cardinal points with extraordinary precision. The
most accurately aligned is the Pyramid of Khufu (Cheops) at Giza, also
known as the Great Pyramid, the sides of which deviate from true north
by an average of less than 3 minutes of arc1. Ever since modern survey
techniques revealed this achievement in the late nineteenth century2,
the question of how the ancient Egyptians achieved such accuracy has
been widely debated. The absence of contemporary source material
accounts for the range of possible orientation methods that have been
proposed over the years. There are no relevant texts or
representations from this period and discussions have therefore relied
either on much later textual or representational evidence or on
considerations of potential accuracy3. Although for many years it has
been accepted on the grounds of accuracy that a stellar method was
used3, 4, recent research has revived the possibility of solar
alignment5. Until now, discussions of ancient Egyptian orientation
methods have overlooked the evidence provided by the alignments of the
pyramids themselves. Researchers have made the implicit assumption
that the ancient method used for orientation had the potential to
produce the same degree of accuracy at any period3 but this assumption
is not supported by the evidence. Lists of measurements of the
alignment of pyramids (refs 3, 6) show that the alignment of the
pyramid of Khufu represented a peak of accuracy which was not
maintained in subsequent reigns. In fact, after Khufu's reign the
alignment of pyramids became increasingly inaccurate. If the Egyptians
had mastered a method of exceptionally accurate orientation, they
should have been able to reproduce the results in subsequent
generations. Nor can the accuracy of the Khufu alignment be considered
coincidental when overall trends in pyramid orientation are examined
in detail. Table 1 lists the pyramids for which accurate measurements
of orientation are available together with the accession dates of the
kings for whom they were constructed. As a result of differences in
reconstructions of the historical data, several chronologies of the
period are available7; here I follow the lower range of dates given in
von Beckerath's recent chronology8, with the exception of the reign of
Snofru. Stadelmann's proposed 46-year reign of Snofru is followed
here9, and the start dates for Snofru's construction of Meidum and the
Bent and Red pyramids also follow his chronology for the reign10. I
assume here that the pyramid alignment ceremony occurred in year 2 of
each king's reign (with the exception of those for the later pyramids
of Snofru), after the burial of his predecessor, the choice of a
suitable location, and preparation and levelling of the site. This
accords with the fact that even kings with short reigns are known to
have started construction of their own tombs. The dates and
measurements of alignment for each pyramid are plotted in Fig. 1a. The
figure shows that of the eight pyramids dating from 2600-2400 BC, six
lie approximately in a straight line. The other two, the pyramids of
Khafre and Sahure, lie close to this group. There is no clear
relationship between this group of pyramids and those pre- and
post-dating it: the pyramid of Djoser predates the first attempts to
orient structures accurately to the cardinal points, whereas for the
period from 2400-1800 BC we have only three structures for which
measurements are available, too few to assess whether they form a
pattern amongst themselves. Figure 1 Deviation of pyramid alignments
from true north over time. Full legend High resolution image and
legend (44k) The eight pyramids constructed between the reigns of
Snofru and Neferirkare are re-plotted in Fig. 1b. Researchers
proposing stellar methods agree that the Egyptians used northern or
circumpolar stars for orientation1, 3, 4, which suggests that the
alignment ceremony was carried out for either the east or west side of
the pyramid (the central axis was probably never levelled, ruling out
its orientation by this method). Where available, measurements of both
east and west sides are marked. In some of the earlier pyramids there
is considerable variation in the alignment of the different sides but
this appears to be the result of difficulties in constructing right
angles while laying out or extending the base. The graph suggests that
only one side was accurately aligned and that it was the west side of
the structure. Figure 1b shows that if the pyramids of Khafre (number
5 in Fig. 1b) and Sahure (number 7) are temporarily ignored, the
remaining six pyramids constructed between the reigns of Snofru and
Neferirkare lie close to a straight line plotted through four of the
points as a guide to the eye (line a). From this we can deduce that
the pyramids were oriented by a method that varied in accuracy over
time, becoming increasingly accurate until the reign of Khufu and then
decreasing in accuracy at a steady rate. The fact that these six
points converge closely on the line shows that the orientation
technique could be applied with great precision despite the fact that
the method itself was not accurate relative to true north. Methods of
orientation These results are incompatible with any of the methods of
orientation considered probable in current literature, solar or
stellar, all of which involve the bisection of angles produced by
measuring either sun shadows or two equivalent positions on the
trajectory of a northern or circumpolar star (isolated at equal height
or in its most easterly and westerly positions)3-5. These methods
would have maintained a level of accuracy over time: graphically, all
the measurements of alignment would lie in a band centred on true
north. The width of the band would vary depending on the potential
accuracy of the particular method and the points would be randomly
scattered within this band. Experimental work has shown that a precise
method of bisecting the angle between the most easterly and westerly
positions of a northern star could potentially achieve an accuracy of
within 3 arcminutes (J. Dorner, personal communication); however, only
one measurement of actual pyramid alignment falls within a band of
this width. Some of the more inaccurate methods proposed are likely to
require error margins of more than 60 arcminutes. In Fig. 1b, the
apparent precision of the alignment method (shown by the proximity of
the six points to line a) strongly suggests stellar orientation, as
solar methods would be unlikely to produce such accurate results. This
conclusion is supported by the progressive deviation of the alignments
from true north, which could not be achieved using a solar orientation
method. The most likely explanation of this deviation from north is
that a stellar orientation method was used which became increasingly
inaccurate as a result of the effects of precession. The north
celestial pole appears from the earth to be a point on the celestial
sphere around which the stars rotate. This point is directly aligned
with the axis of rotation of the earth. However, the revolving axis of
the earth is itself unstable and rotates slowly, like a gyroscope.
This is precession and, as a result, the north celestial pole appears
to trace out a large circle on the northern sky, with each cycle
taking around 26,000 years. This movement is extremely slow; without a
system of recorded measurements it would be unnoticeable to observers,
even over periods of hundreds of years. Today, the position of the
north celestial pole is marked approximately by the star alpha -Ursae
Minoris (Polaris) which lies within one degree of the pole. However,
during the period of pyramid construction there was no star accurately
marking the pole. The closest star was alpha -Draconis but this lay
nearly two degrees from the celestial pole at the beginning of the
reign of Khufu. In any case, sightings taken toward a single star
could not have achieved the results seen in Fig. 1b as, without a
method of isolating culminations (the positions of greatest or least
altitude of a star, which are also the points at which it crosses the
meridian), the measurements would become increasingly random as the
star moved away from the pole. The method of orientation I propose is
that the pole was considered to be located on an invisible chord
linking two circumpolar stars on opposite sides of the pole. These two
stars rotate around the pole, and when they are vertically aligned
above the north horizon (one at its upper culmination and the other at
its lower) an alignment made toward these stars with a plumb-line will
be exactly oriented to true north, as long as the chord itself passes
precisely through the pole. With the exception of the date when the
chord between the stars lies exactly on the precessional trajectory of
the pole, this method will produce alignments that become increasingly
inaccurate at a steady rate over time. This method therefore has the
potential to correspond with the results seen in Fig. 1b. This will be
referred to as the simultaneous transit method because it uses two
stars which cross (transit) the meridian simultaneously to establish
true north. Modelling the simultaneous transit method A period from
2750 to 2350 BC (2550 BC 200 years, double the maximum error margin
conventionally estimated for the relative chronologies of this
period)7 was examined for pairs of bright stars within 15 degrees from
the pole which could have been used in the simultaneous transit
method. Using SkyMap Pro 6 (ref. 17) it was established that only two
pairs of stars were joined by chords which crossed the celestial pole
during this period: zeta -Ursae Majoris and beta -Ursae Minoris
(around 2467 BC), and epsilon -Ursae Majoris and gamma -Ursae Minoris
(around 2443 BC). Figure 2a shows the circumpolar stars in 2467 BC,
when a chord between zeta -Ursae Majoris and beta -Ursae Minoris
crossed the pole (the discrepancy between this date and the date of
greatest precision of pyramid alignment shown in Fig. 1b will be
discussed below). Figure 2b shows a view of the north horizon at Giza
for the same date, showing the stars when they are vertically aligned
(in simultaneous transit). A measurement of alignment taken with a
plumb-line toward the stars at this time would be oriented exactly to
true north. Figure 2 Modelling the simultaneous transit method for
Giza, 2467 BC. Full legend High resolution image and legend (142k) The
Khafre and Sahure alignments The simultaneous transit method of
alignment can also be used to explain the anomalous orientations of
the pyramids of Khafre and Sahure, the two pyramids which do not
conform with the trend set by the six other pyramids of the period.
From Fig. 1b it is clear that although the deviation of these
pyramids' alignment (numbers 5 and 7) lies west rather than east of
north, they are approximately of the magnitude to be expected for
their dates. The simultaneous transit method involves making an
alignment toward two stars when they are vertically aligned. The
alignment can be taken when either of the stars is in the upper
position. Because the upper culminations of the two stars fall
approximately twelve hours apart, with the time of culmination of each
star moving slowly through 24 hours in the course of a year, for about
half the year the vertical alignment that falls within the hours of
darkness will have one of the stars always above, and for the other
half of the year the second star will be in the position of upper
culmination when the two stars are vertically aligned during the
course of the night. When the chord between these two stars passes
precisely through the celestial pole, an alignment taken toward the
stars when they are in simultaneous transit will be exact with either
star at its upper culmination. However, as the pole moves away from
the chord between the stars as a result of precession, the chord
itself begins to rotate around the pole. Alignments made using the
simultaneous transit method will deviate from true north at a rate
which increases steadily over time, regardless of which star is at its
upper culmination when the alignment was made. However, as the chord
itself is rotating around the pole, alignments made with a particular
star at its upper culmination will be the opposite side of the north
pole to alignments taken when the same star is at its lower
culmination. This is illustrated in Fig. 3. Figure 3 Deviation of
alignments from true north resulting from use of the simultaneous
transit method of orientation. Full legend High resolution image and
legend (145k) A graph of alignments made using the simultaneous
transit method should therefore take the form of two lines of equal
gradient, one positive and one negative, crossing at true north. In
Fig. 1b, the gradient of line a is used to generate a second line, b,
of equal but negative gradient, crossing line a at zero on the y-axis.
This line passes close to the points plotted for the pyramids of
Khafre and Sahure. The alignment of Khafre's and Sahure's pyramids can
therefore be shown to have been generated by the same method of
alignment as the other six pyramids of the period, the only difference
being the time of year at which the orientation ceremony was carried
out, and therefore the star which was uppermost. To show this
graphically, the pyramids of Khafre and Sahure can be re-plotted on
the opposite side of true north (Fig. 4). Line a passes through all
four points for which recent accurate measurements are available
(numbers 2-5), through the error bars of the three later points and
close to the point for number 1. Figure 4 Astronomical modelling of
the simultaneous transit method of orientation. Full legend High
resolution image and legend (25k) Modelling the results In order to
test further the theory that the simultaneous transit method was used
to orient this group of pyramids, the method was modelled
mathematically. F. R. Stephenson (personal communication) calculated
the distance from the pole of a chord running between the stars zeta
-Ursae Majoris and beta -Ursae Minoris. He confirmed that the chord
ran precisely through the pole in 2467 BC (astronomical date -2466) by
computing the date when the right ascension of the two stars differed
by exactly 180 degrees. The same procedure was repeated for the pair
of stars epsilon -Ursae Majoris and gamma -Ursae Minoris which
produced the date 2443 BC (astronomical date -2442). He then computed
the minimum angular distance between the north celestial pole and the
great circle passing through the pairs of stars at 25-year intervals
around these dates. The results are plotted in Fig. 4 (lines b and c)
alongside the graph derived from archaeological data (line a). Figure
4 shows that measurements of the angular distance of the pole from a
chord running between stars zeta -Ursae Majoris and beta -Ursae
Minoris produce a line (b) of very similar gradient to that implied by
the archaeological data. Stars epsilon -Ursae Majoris and gamma -Ursae
Minoris produce a significantly steeper gradient (line c) which,
crucially, cannot be accommodated to the three Giza pyramids (numbers
4-6) which form the most accurately fixed group temporally and
spatially. These results strongly support the hypothesis that the
pyramids were aligned using the simultaneous transit method, which was
carried out using stars zeta -Ursae Majoris and beta -Ursae Minoris.
The only major discrepancy between the results produced by the two
independent data sets is time: the line generated by the astronomical
modelling (line b) is over 70 years later than that derived from the
archaeological results (line a). Anchoring existing chronologies The
dating discrepancy between the two sets of results is caused by the
fact that while stellar positioning at a given time can be predicted
with great precision, existing Egyptian chronologies of this period
based primarily on cumulative reign lengths can only be considered
accurate to about 100 years7. In Fig. 4, although the chronology of
line b generated by astronomical data can be considered fixed, the
chronology according to which the archaeological data are plotted
(line a) is not anchored in time. However, the point at which line a
crosses zero on the y-axis can now be fixed at 2467 BC from the
results of the astronomical modelling. This gives a date of 2478 BC
for the alignment of Khufu's pyramid which would require the lowering
of von Beckerath's lower estimate of chronology by a further 74 years.
In reconstructing accession dates from dates of pyramid alignment
ceremonies, potential for error theoretically exists in the assumption
made here that this ceremony was held in the second year of each
reign. However, it is exceptionally unlikely in this period that the
error involved is more than 1 year. At present, a total of 5 years can
be considered an adequate error allowance for the reigns of Khufu and
Khafre (F. R. Stephenson and T. van Albada, personal communications)
given the accuracy of the archaeological data available for these
reigns and the precision of the astronomical modelling. Future
research The ability to fix the reigns of Khufu and Khafre to 5 years
represents an advance in establishing a reliable absolute chronology
for the second half of the third millennium BC in Egypt, but it does
not solve all the problems. It is not possible simply to shift
existing chronologies forward by the requisite number of years as
fixed astronomical dates soon after 2000 BC mean that these existing
chronologies will also have to be compressed. To achieve this, a
process of careful reanalysis of the historical data will be necessary
to make suitable adjustments. For this reason, the recalibrated
accession dates given in the last column of Table 1 show error margins
which increase over time as the possibility of numerous minor errors
in cumulative reign lengths is compounded. I intend to undertake
fieldwork to collect more accurate data for those pyramids that have
not been recently and reliably surveyed. From this and through more
detailed mathematical modelling I hope to refine the error margin for
dating the pyramids of Khufu and Khafre to 1-2 years. More accurate
data for the period around the reigns of Sahure and Neferirkare will
reduce the error margins for the dates of these later kings and will
assist in the process of refining the overall chronology of the
period. Received 17 July 2000; accepted 19 September 2000
------------------ References 1. Dorner, J. Die Absteckung und
astronomische Orientierung ägyptisher Pyramiden PhD thesis, Univ.
Innsbruck (1981). 2. Petrie, W. M. F. The Pyramids and Temples of
Gizeh (Field & Tuer, London, 1883). 3. Z caron ába, Z. L'orientation
astronomique dans l'ancienne Egypte et la précession de l'axe du monde
(Editions de l'académie Tchécoslovaque des Sciences, Prague, 1953). 4.
Edwards, I. E. S. The Pyramids of Egypt 3rd edn (Penguin,
Harmondsworth, 1993). 5. Isler, M. An ancient method of finding and
extending direction. J. Am. Res. Center Egypt 26, 191-206 (1989). 6.
Arnold, D. Building in Egypt: Pharaonic Stone Masonry (Oxford Univ.
Press, Oxford, 1991). 7. Kitchen, K. The chronology of ancient Egypt.
World Archaeol. 23, 201-208 (1991). | ISI | 8. von Beckerath, J.
Chronologie des pharonischen Ägypten (von Zabern, Mainz, 1997). 9.
Stadelmann, R. Die gro beta en Pyramiden von Giza (Akademische Druck-
und Verlangsanstalt, Graz, 1990). 10. Stadelmann, R. Beiträge zur
Geschichte des Alten Reiches. Die Länge der Regierung des Snofru.
Mitt. Deutsch. Archäologisch. Inst. Abteilung Kairo 43, 229-240
(1986). 11. Petrie, W. M. F. Medum (Nutt, London, 1892). 12. Dorner,
J. Form und Ausmasse der Knickpyramide. Neue Beobachtungen und
Messungen. Mitt. Deutsch. Archäologisch. Inst. Abteilung Kairo 42,
43-58 (1986). 13. Arnold, D. The Pyramid of Senwosret I (Metropolitan
Museum of Art, New York, 1988). 14. Arnold, D. Der Pyramidenbezirk des
Konigs Amenemhet III. in Dahschur (von Zabern, Mainz, 1987). 15.
Krauss, R. The length of Sneferu's reign. J. Egypt. Archaeol. 82,
43-50 (1996). | ISI | 16. Baines, J. & Málek, J. Atlas of Ancient
Egypt (Phaidon, Oxford, 1980). 17. Marriott, C. SkyMap Pro Version 6
(Thompson Partnership, Uttoxeter, 1999). Acknowledgements. For
research funding I acknowledge the British Academy, the Wingate
Foundation and the Lady Wallis Budge Fund, Christ's College,
Cambridge. I thank all those who discussed this project with me, in
particular B. Kemp; J. Dorner for allowing me to use measurements of
orientation from his PhD thesis; F. R. Stephenson for astronomical
calculations; T. van Albada and A. Egberts for their comments. I also
thank N. Gay for technical assistance.
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