This page last modified 2012 January 17
The Pyramidiocy of Prof. A.N. dos Santos
All images generated by Project Pluto's GUIDE v7.
In the Jun 1996 to Oct 1996 issues of the deservedly defunct publication, Amateur Astronomy and Earth Sciences, Professor A.N.dos Santos (Adjunct Professor of Nuclear Physics at the Federal University of Minas Gerais, Brazil) wrote a series of articles entitled Rethink at Giza. In these articles he attempted to demonstrate that the Great Pyramid was intended to align to the star Vega (α Lyrae) in 11,917 BCE.
The argument is difficult to follow in places; this is at least partly a consequence of the poor English language translation; but it is absolutely riddled with speculation, unsubstantiated assertion, fallacious reasoning and error of fact1, much of which is irrelevant to the argument. From an astronomical perspective, the testable hypothesis is that the Entrance Gallery of the Great Pyramid would have aligned on Vega at the time of sunrise on the summer solstice of 11,917 BCE. Dos Santos' calculations are given in the last instalment of the series (AA&ES Oct 1996, pp30-33). They boil down to this:
|Altitude of Vega at epoch (precessed position) from Cairo:||25° 12' 00"|
|Correction due to latitude:||00° 04' 09"|
|Correction due to nutation in obliquity2:||00° 08' 21"|
|Correction due to proper motion3:||01° 05' 10"|
|Correction due to atmospheric refraction4:||00° 01' 30"|
|Total correction:||01° 19' 10"|
|Apparent altitude of Vega at epoch:||26° 31' 10"|
|Inclination of Entrance Gallery:||26° 31' 23" (Petrie's measurement)|
If this was correct, this would be a remarkable coincidence (but still no
more than a coincidence unless there was corroborative evidence). However, as we
shall see, the calculation is flawed. Using Guide to simulate the sky at sunrise
on the solstice of -11,916 (11,917 BCE), we get:
Clicking on this image
The altitude of Vega is 31.42° (31° 25'). It is corrected for precession5, nutation in obliquity, and proper motion, but not for atmospheric refraction. (The altitude of Vega given in the screen shot is slightly erroneous as the cursor was not exactly over the centre of the disc of the star image.) This is approximately 5° higher than dos Santos' calculation.
The Sun is shown at the lower right of the diagram, just below the horizon (the green line). This is the true position of the Sun; however, atmospheric refraction will cause it to appear on the horizon; this is the time of observed sunrise.
Dos Santos' sources of error include:
- The calculation for the obliquity of the ecliptic2. In 11,917 BCE it was 24° 3.3' ±1', nearly half a degree greater than dos Santos' figure of 23° 35' 29".
- The value for the proper motion of Vega. He does not say how he calculated this3, but the true figure is 1° 22' away from the celestial pole of 11,917 BCE, or nearly 2.5 degrees different from dos Santos' figure.
- The assertions that Vega was at lower culmination at the time of Sunrise6,7. Here the altitude is 25° 34'. Assuming a mean atmospheric refraction of 2', the altitude of lower culmination is only 25° 36', almost a degree less than dos Santos' calculation.
Given that dos Santos asserts that "the Egyptians were capable of precisions of better than 1' " (I contend that they could not systematically achieve this), I suggest that he must accept that his hypothesis about the alignment of the Entrance Gallery with Vega is now thoroughly debunked.
1. Examples include:
"[June 24] corresponds to the Summer Solstice (Midsummer or St John's Day)"(AA&ES Jun 1996, p58.)
The solstice is never on St John's Day.
"Earth's libration has not been directly observed by positional astronomers, who generally disregard its existence."(AA&ES Jun 1996, p60.)
'Libration' in this context is another term for 'nutation in obliquity'. If you think that astronomers 'generally disregard its existence', look in any decent text on astronomy or astrophysics.
"It seems that Pyramid mystics and astrologers such as Piazzi Smyth and Sir Herschel..."(AA&ES Jun 1996, p61.)
'Sir Herschel' refers to Sir John Herschel; good Sir John was a 19th Century astronomer, not an astrologer.
"The Great Pyramid is in reality a sort of supercomputer..."(AA&ES Jun 1996, p61.)
"...the ancients were in possession of superior Science. And this Science could only come from Atlantis, as is obvious in hindsight."(AA&ES Aug/Sep 1996, p60.)
2. Nutation in Obliquity (dos Santos uses the alternative term 'libration') is the change in inclination of Earth's axis with respect to the plane of the ecliptic. This change has a period of approx. 41,000 years and the angle measured is that between the plane of the equator and the ecliptic plane. Dos Santos uses a formula, e = 22.965 + 1.16 * sin(8.80 (t + 2.825)), which is insufficiently precise for long periods. A good source of astronomical formulae is in Jean Meeus' Astronomical Algorithms.
3. Proper Motion
is the motion of stars across the line of sight as measured against an inertial
frame of reference. The star with the greatest proper motion is Barnard's Star
(10".31 per annum). Vega's proper motion is more typical of close stars, 0".346
per annum. More distant stars generally have smaller proper motions. The effect
is shown in this image of part of the constellation of Lyra. The largest
(brightest) star is Vega:
I suspect that dos Santos calculated the proper motion of Vega in declination by doing so with respect to the present day celestial pole, not that of 11,917 BCE.
4. Atmospheric Refraction. The earth's atmosphere refracts incoming starlight, causing the star to appear slightly higher than its true altitude. For an object with an apparent altitude of 25°, refraction is 2' 03"; for an apparent altitude of 30° the refraction is 1' 40".
5. Precession is a wobble of the Earth's axis of rotation as a consequence of the gravitational attraction of the Sun and Moon on the Earth's equatorial bulge. It has a period of approx 25,800 years, during which time the spring equinox (and hence the imaginary grid of celestial co-ordinates) makes a full circle of the ecliptic. Hence it is called Precession of the Equinoxes. A consequence is that the axis of Earth's rotation points to different parts of the sky, making a full circle in the processional period. At different times, different bright stars are near the celestial pole. For more information on positional astronomy and the system of celestial co-ordinates, see my book AstroFAQs.
6. Dos Santos used the planetarium program Skyglobe v3.6 for a lot of his astronomical data. Whilst Skyglobe was an admirable piece of shareware for its day (1993), the data sets and algorithms that it uses are not reliable for astrometry, nor for periods 14,000 years away from the present. Curiously, the screen shots from Skyglobe in dos Santos' AA&ES articles are for 11549 BCE, Jul 22!!! (AA&ES Jun 1996, p60.)
7. Dos Santos' uses the incorrect date of Jun 21 or 24 (Gregorian) for the date of the solstice in 11,917 BCE. It is unclear from the text which he is using, but his argument is incorrect for both; it is also incorrect if he was accidentally using the Julian calendar. The solstice was actually Jun 11 (Gregorian) or Sep 11 (Julian). For more information about Julian and Gregorian calendars, see the Calendar FAQ