Hi Jeff,

Just to add to your list:


The accuracy of astronomically derived dates for the shafts, depends on at least three variables:

1. how accurately AE surveyors could measure the altitude of a star or asterism due south or north.

2. how accurately the builders could build the shafts according to the architect's design.

3. to what extent the angles of incline have been affected by subsidence over 4500 years


Its difficult to assess by how much these variables affect astronomically derived dates, but if they are taken into account, the uncertainty factor may be similar to the historically derived dates for the OK that according to the Oxford History of AE, edited by Ian Shaw, pub. 2000, are accurate to +- 50 years.


A few thoughts on the angles for the shafts:


Egyptologist Alexander Badawy's original proposal for the shafts aligning with a significant star, the North or Pole Star Thuban in the northern sky, and the distinctive 3-star asterism in Orion crossing the southern sky, used an unfortunate scribal error in Petrie's survey data (44.5 degs instead of the correct 45 degs for the upper southern shaft). According to Gantenbrink's survey, the angles of inclines for the upper shafts are 45 degs for the top end of the southern, and 31.2 degs for the top 11m / 36 ft of the northern shaft. Using these values, the resulting date is c. 2570 BC for both shafts, which is consistent with Khufu's reign. (2589 - 2566 +- 50 years)


The angle of incline at the top of the shafts is crucial because that tells us what small area of the sky the top ends of the shafts were actually facing.


The star alignment proposal is based on the ancient Egyptian idea of the ba (bA, 'soul') that used the shafts as 'model passageways' to ascend in "his bird-shape" straight from the sarcophagus chamber (perhaps corresponding to the Duat) through the superstructure of the pyramid ('Khufu's Akhet') and on up to his celestial destiny with dual options for the 'Dual King' of the Two Lands' - the northern or southern regions of the sky.


Assuming Khufu's ba left his pyramid through the shafts, what did he see as he exited from the top end? - in other words what areas of the sky were the top ends of the shafts facing - the crucial survey data from the top of the shafts allows us to determine which areas of the sky the top ends were facing.


The southern and northern regions of the sky were recognized, and associated with, among other celestial deities, Horus and Seth: ".....having expelled Horus from the sky's southern part, having expelled Seth from the sky's northern part....." (Nt 458) The dead king was to raise himself, clear away his dust, remove the shroud on his face, and he would wander the southern and northern mounds. (P 526; PT 553)


Although its not known what the angles of the top ends of the lower shafts are, if all four shafts are considered, then they may have something in common with inscriptions from Pepi's pyramid:


"These four paths of yours are those which are in front of the tomb (HA.t, with jA, 'ascension', det.) of Horus, on which the god has walked since the going down of the Sun. (Sethe Vol 2: 244; §1355ab).......the doors of the sky are opened for you....the doors of the tomb are opened for you, the doors of Nut are unbolted for you.....you ascend to the sky as a star, as the Morning Star" (PT 553)


The god walked these four paths after sunset, at night, and the 'doors' of the tomb and of the sky are plural.

CT