The topic is one well suited to a planetarium. Based on lectures that I had given to our local Egyptian Society in the planetarium in Cape Town, I designed and scripted a prerecorded presentation (that opened in December 1998). I had found the Bauval argument ingenious, but somewhat unconvincing. However, further checks revealed further holes, as I shall report below.
The pyramids have a strong astronomical association. The four faces of an Egyptian pyramid are precisely aligned with the four cardinal points of the compass. Given that the Egyptians never recognised a North pole on the Earth, they could have only done this by means of the rotation of the sky about the North Celestial Pole. The most obvious way of fixing azimuthal North would be by the symmetry of the rising and setting points of stars. The great pyramid of Khufu is level to a centimetre and aligned to a twentieth of a degree, a tribute to the accuracy of ancient surveying skills.
Khufu's pyramid also contains four "star shafts", aimed towards the meridian in the sky. When the pyramid was built (c. 2500 BC), these shafts aimed at the transitpoints of Thuban (Alpha Draconis - then pole star), Orion's Belt, Sirius and Kochab (Beta Ursa Minoris), clearly intentionally and not coincidentally. The shafts apparently served to direct the ka, or spirit, of the dead pharaoh towards these key stars. Thuban and Kochab were circumpolar "Imperishable ones" (stars that never die), Orion represented the deity Osiris, and Sirius his consort, Isis. Precession has since changed the transit points, so the shafts no longer function in this manner.
Khufu's pyramid is the largest of a line of three - together with that of Khafre and the much smaller pyramid of Menkaure. Given the surveying skills of the Egyptians, many have wondered why the line of the three pyramids is slightly crooked. One possibility is that the design would allow for the smaller pyramid to be later enlarged (retaining its south and east faces) to form a straight line of three almost identical pyramids. Another is that the deviation of the line closely matches that of the three stars of Orion's Belt - which are also slightly crooked. This has suggested that the lay out at Giza may be an attempt to portray Orion's Belt. If so, the orientation of the line, with respect to the cardinal points, is wrong - for 2500 BC. Precession, however, changes the angle that the Belt makes in the sky. Bauval claims that going back to 10500 BC gives "a perfect match".
Or does it? My own investigation showed that, while the line of the two outer pyramids is set 38 degrees from north, the angle of Orion's Belt to north in 10500 BC is close on 50 degrees! Hardy an exact match. I calculate that circular precessional motion would give 47 degrees, whereas including nutational terms makes it slightly higher. Measurements in the planetarium agree. Bauval, on the other hand appears to have used computer programmes. He implies that only with modern sophisticated computers can we examine the ancient skies! I wonder if he also made the mistake of measuring angles off a flat screen.
Bauval's choice of 10500 BC (when Orion is furthest south in its precessional cycle) also supposedly fits with the Milky Way aligning with the Nile. But the course of the Nile is variable, and we do not now know where it ran in 10500 BC with any accuracy.
A parallel assertion of Hancock and Bauval is to say that 10500 BC would be during the astrological "Age of the Lion" - a connoctation they seek with the sphinx. However the Vernal Equinox of 10500 BC would lie at 2000: 11h40m, +2.2 degress, which though close to the star pattern we now know as Leo, still lies decidedly in Virgo. Again, not a perfect match.
Finally, as my colleague in the planetarium world, Ed Krupp, has pointed out, the otherwise straight line of the pyramids is deformed towards the north, but the line of Orion's Belt is deformed towards the south.
The astronomical basis for arguing that the layout at Giza goes back to 10500BC is therefore very thin. It would be well if more could be done to counter the publicity of books, put out to the public, that base so much conjecture upon such flimsy science.