Hi Alex,

Regarding the 45 degree contention here are a couple of pictures. First the alignments to Heliopolis (H) and Djedefre (D) from Giza (G) -

[freeimage.host]

- you'll notice I propose a geometrical scheme for these alignments but for the moment ignore this.

The second picture shows the root two 45 degree construction in Khufu, defining the floorline of the King's burial chamber (and also the vertical axis point common to Gantenbrink's scheme, if you believe in it) -

[freeimage.host]

For more information on 45 degree alignments please see - Magli,G. 2013. 'Architecture, Astronomy and Sacred Landscape in Ancient Egypt'. Cambridge.

You write -

"If you examine in Stellarium (and I urge you to open Stellarium in order to see clearly what I will be talking about) the starry sky visible from the Giza plateau in 2560BC, you can see that at the moment of the culmination of Kochab, Orion's belt appears on the eastern horizon and the altitude of the lower of three belt's stars (Alnitak) is 0° 15'. Can we assume that the Orion's belt was visible to the observer under such conditions? No, the Alnitak's altitude is insufficient for observations, because firstly, to observe such a low located star, an ideally flat relief is needed, and secondly, the atmosphere significantly affects the stars near the horizon (Alnitak's brightness at this altitude was reduced by atmosphere from 1.85m to 5.65m and this can be seen in Stellarium).
It should also be remembered that speaking about the king's rebirth in the sky, we are talking about the heliacal rise of Sah (heliacal rise is the rise of asterism in the rays of the rising Sun, when asterism is first time seen before sunrise after a long period of invisibility), therefore the stars rise in the brightening sky, what also noticeably interferes to observation.
Summarizing what has been said, we can unequivocally conclude that under these conditions, at the moment of the culmination of Kochab in 2560 BC, the Orion's belt could not be fully visible. The connection between the culmination of Kochab and the rebirth of the king did not exist at that time.
If we move back in time, then because of the precession of the stars, the Orion's belt would have the greater altitude at the moment of Kochab's culmination, the more we recede into the past.
For clarity, I compiled a table of dates and the corresponding altitudes of Alnitak as the lowest of the three stars of the belt. Since the azimuth of the QCN shaft is unknown to me, we can take it equal to the average azimuth of the sides of the pyramid's core masonry (since the pyramid is not oriented exactly along the meridian, strictly speaking through the shaft one can "observe" not the culmination of Kochab but the trajectory point along the azimuth of -5' 30"; data in the third column).
Which of the dates thus can be considered correct so that the observer could see Kochab's culmination at the same time with the full visibility of heliacal rise of Sah?
In this article [articles.adsabs.harvard.edu], the author calculates the visibility conditions for the heliacal rise of Sirius, and we can use his data: “For those few researchers who consider the question (such as Aveni and Lockyer), Sirius is always taken to be visible to the horizon at heliacal rise. But this is easily disproven since the extinction (0.35 magnitudes per air mass) at the horizon (with the equivalent of roughly 40 air masses) will dim Sirius by 14 magnitudes. Even one degree above the horizon (with 26 air masses) and a good extinction (0.26 magnitudes per air mass), Sirius will still only be barely visible even under a dark night sky. In general, the altitude of best visibility will be a trade-off between sky brightness and extinction. For the particular case of Sirius, the altitude of Sirius at the heliacal rise will be around 6° while the altitude of the Sun will be around —5°.”
Even if we consider only 3° (and not 6°) as the necessary altitude of Alnitak as a condition for its visibility during a heliacal rise, then this corresponds to dates older than 2700BC, which is significantly older than historical expectations for the dates of Khufu's reign.
What you think about this?"


These facts are undoubtedly correct and allow you to conclude that Khufu was built at the earlier date.

I came across the Kochab/Alnitak correlation in 1994 using Skyglobe (but of course using too early a date). When I checked it using Stellarium I was gobsmacked by the precision of the alignment with Alnitak (with 0 degrees altitude). I suppose you are right but we know vanishingly little about Old Kingdom concepts of the sky. For all I know the ceaseless observations of the stars over hundreds of years might have allowed astronomer priests to infer some kind of model whereby they could estimate when a key star was sitting on the real horizon, but I admit it's a long shot. Of course it could have been the other way around - Egyptians were hopelessly superstitious, mummifying everything in sight. (I still can't understand why Joanne Conman is villified so much - her view that Egyptians were more astrologers than astronomers is surely something we might expect).

You further write - "my hypothesis is supported by images and descriptions of the stretching of the cord ceremony, while the “simultaneous transit” method does not have any ancient documentary support and therefore completely hypothetical."

Your novel reconstruction of the 'stretching of the cord' and identification of the'Aq' of Meskhetiu as three stars horizontally aligned at the upper culmination of the constellation is a most impressive hypothesis. In this position at 2780 BC Thuban was virtually at the pole. Since stars were gods this conjunction likely would have been considered the mandate of heaven. If the pyramid was built at the conventional date Thuban might have retained its special significance. When Alnitak culminates in the south at the conventional date, it is vertically below Betelgeuse or in simultaneous transit, but perhaps this is another coincidence?

By the way, KC north shaft, in plan, is fairly straight but is aimed a few degrees to the east. This does not appear to be sloppy work but intentional - should this not be taken into account when investigating the target of the shaft?

Meanwhile I continue my quest for hard data on the shafts. One scholar sent me right back to Brabin and said he 'thought' Gantenbrink is correct. Luca Miatello also forwarded a paper by one Jeremy Potter (GM.183 (2001) p. 87. linked as attachment). Potter's own site is here -
[www.seedofenergy.com]

I sent the illustration below comparing Petrie's and M and R's Khufu shaft layout to Miatello , which to me seemed to me to be essentially the same -
[freeimage.host]

In response I was told that the blue level I added to the drawing signifying 154 cubits above base is incorrect, that M and R corrected an error by Petrie (their drawings look essentially the same to me), that the plan of the exit points contains errors, and that Gantenbrink confirmed that the shaft exits are at the same level. But I can find no trace of any such statements by Gantenbrink in print.

Ah well, keep pressing on.

Robin