Trimble was given the wrong angle of incline for the upper south shaft.


In 1954, Badawy gave the angle of incline of the upper southern shaft as 45 degs, but Trimble used a 44.5 degree angle in her calculations. (this same incorrect angle is repeated by Edwards and Cornell, and also by Badawy in his 1964 paper).

Discussing the upper shafts, Petrie was careful to point out that: "It is striking that the slope of both passages continuously increases up to the outside (except just at the mouth of the S. channel); hence these quantities, which only extend over a part of either passage, cannot give the true mean slope; probably on the whole length the means would not be greater angles than 31 degs and 44.5 degs respectively."

Perhaps it was this odd mention (scribal error) by Petrie of 44.5 degs that confused the issue, as he should have written, not greater than 45.5 degs, which is consistent with his survey data.

According to Gantenbrink the overall angle for the 42m (138ft) section of the shaft from it's last change of angle in the lower section, to the top end of the shaft, is 45 degs.

If it was intended by the designers that the upper southern shaft should target Orion's 'belt', then as Virginia Trimble in principle demonstrated, an approximate date for its construction can be calculated.

At the latitude of Giza, and allowing for a 6 arc min tolerance, Alnitak in Orion's 'belt' was at 45.1 - 44.9 degs altitude due south between c.2470 - c.2520, Alnilam, the middle star, at the same altitude between c.2530 - c.2580, and Mintaka between c.2630 - c.2670 BC.

c.2570 BC, is midway between the earliest and latest dates, and fits well within the estimated 2589 - 2566 BC (+- 50 years) for the reign of Khufu.


The top of the upper northern shaft's final 11m (36ft) section (the only section of the shaft apart from the initial horizontal section that is parallel with the N/S axis of the pyramid), was facing an area of the sky where the North or Pole Star, Thuban, reached its highest point in the sky due north as it circled the NCP c.2570 BC, the same era when Orion's 'belt' aligned with the southern shaft when it reached its highest point in the sky due south

Although stars are points of light in the sky, the top ends of the shafts are not 'facing' points, but small areas of the sky. Immediately after a series of niches (these may have once held a closure stone), and 8.1m down the shaft from the original exterior face of the pyramid, the upper southern shaft has a square cross section of 22.5 x 22.5cm (3 x 3 AE palms). Although the shafts were not designed for observing the sky, the small square area of the sky 'seen' from these niches is about 1.6 arc degrees square. This means that a star crossed the 'field of view' of the shaft for approximately seven minutes each day, and from 45.35m down the shaft where the long straight section begins, for about one and a half minutes each day.

The c.2570 BC date for the two upper shafts alignments with Orion's 'belt' in the southern sky and Thuban in the northern sky fits the archeological evidence for the era of Khufu's reign. The question of intent can be debated in the context of what is known about the royal funerary ideology of the Old Kingdom that was strongly influenced by celestial phenomena, making the royal funerary complexes suitable candidates for investigation into possible deliberate architectural / celestial links. Badawy's 1964 paper, 'The Stellar Destiny of Pharoah and the So-Called Air-Shafts of Cheops' Pyramid' (in MIOAVB, band X, 1964: 189-206), examines the ancient Egyptian Old Kingdom cultural context for possible stellar links.



SC: "However, this raises the following interesting question: if the three other shafts supposedly pick out individual stars in the night sky, then surely by logical extension, the KC south shaft should also point to one star - a star within Orion's Belt. Question is - which one? As can be seen from the data, it seems that within 100 years or thereabouts, both Al Nitak and Mintaka reach altitude of 45*."



Its not possible to determine which areas of the sky the top end of the lower shafts were facing with any confidence, as survey data for the top sections is not available.


It might be better to think of the shafts 'targeting' specific areas of the sky, 'Enclosures / Mansions' - associated with significant stars or star patterns when they reached their highest point in the sky - for example there are references to the 'Enclosure / Mansion of Sah' (CT 469).

In the PTs there is one mention of Sah (sAH, 'Orion') that has the O49 'town' det.: "I have gone up on the ladder, with my foot on Sah (sAH, 'Orion' with O49 'town det) and my arm is in elevation. I have grabbed onto Thighs-Forward's rope and my arm has been received at the great place. (Nt 272b)


Another example from the PTs, specifically associates a northern celestial 'enclosure' with the the king: "Pepi is an Imperishable Star, son of the great sky that is in the midst of Selket's enclosure.....Pepi is a star. The Sun's aegis is over this Pepi..... (P 511) We know from later depictions that Selket was in the northern sky near the large distinctive asterism, the Plough / 'Big Dipper' (msxtiw).


Horus the god of kingship had an 'Enclosure / Mansion' in the sky:

"Any god who will take this Pepi to the sky, alive and stable - he is the one who will become esteemed, he is the one who will become ba, he is the one who will smell a wafer, he is the one who will go up to Horus's enclosure that belongs to the sky." P 337


He who shall give his finger against this pyramid and this god's enclosure of Pepi and of his ka, he has given his finger against Horus's enclosure (Hwt Hrw) in the Cool Waters (qbHw, the sky) P 483


Perhaps the king in his celestial realm, would then 'visit' these 'Enclosures / Mansions' from his 'House of Eternity' at the appropriate season. The king could accompany Sah across the southern sky (P 38, N 9), and as Dual King he also had his place as an Imperishable Star in the 'Marsh / Field of Rest / Offerings' in the northern sky.

CT