MARGINALIA
Astronomy and the Great Pyramid
J. Donald Fernie
Pyramidology! The very word produces groans and upturned eyes in an
audience of scientists, along with sighs of "here we go
again." As well it might. The rubbish written about pyramids
generally, and the Great Pyramid of Khufu (or Cheops) in particular,
is overwhelming. Bizarre theories about its construction and
supposed metaphysical properties have only multiplied over the
centuries. The Internet is filled with this nonsense.
Yet these age–old monuments are a marvel, and they do tether
our modern civilization to its origins. So there is a danger that
the baby of rigorous scholarship can all too easily be thrown out
with the bathwater of mystical blather, particularly by those
scientists or educators who are plied with questions from
well–meaning New Age disciples. But in fact, there are, and
long have been, serious scientists applying careful methods to the
study of ancient pyramids. Henry Petroski penned a thoughtful
analysis of the engineering challenges of pyramid construction in a
recent issue of American Scientist (May–June). Here I
look at some studies that examine the astronomy of the pyramid builders.
Anatomy of a Pyramid
Whatever the excesses of its advocates, the Great Pyramid is one of
the most remarkable structures ever made, if only in terms of sheer
workmanship: The fact that it is the only standing remnant of the
seven ancient wonders speaks for itself. Built roughly 4,500 years
ago, it towers over the Giza plain some 16 kilometers west of Cairo
amid several smaller pyramids, 60 or more of which stretch down the
western bank of the Nile. The base of the Great Pyramid covers 13
acres, or about seven midtown blocks in Manhattan. It rises in 201
stepped tiers comprised of more than two million pieces of limestone
and granite, averaging two or three tons apiece (with some a good
deal more), to the height of a modern 40–story building. It
was the tallest construction in the world until the Eiffel Tower was
erected in the 19th century.
For the first 3,000 years or so of its history, the Great Pyramid
was encased in brilliant polished limestone—about 22 acres of
it. The slabs were up to 2.5 meters thick and were fitted together
with joints so fine they could scarcely be seen, according to
Herodotus, who visited in 440 B.C. This must have been a dazzling
sight in the Egyptian sun! Unfortunately, the covering was stripped
in medieval times to build palaces and mosques in Cairo, and now we
can only see the rough building blocks.
Under this shining canopy lay the interior structure. Strabo, after
a visit in 24 B.C., described an entrance on the north face of the
pyramid made of a hinged stone that could be raised but was
otherwise indistinguishable from the stones around it. So
indistinguishable, in fact, that its location was lost during a
period of neglect in early Christian times. Much later, in the early
9th century, an Arab potentate named Al–Mamun, following
rumors of vast, hidden wealth, forced a new entrance near the base
of the north side. So impregnable was the structure that his
engineers could proceed only by building fires against each huge
stone in their path and, having heated it to a high temperature,
dousing it with cold vinegar to shatter it. The residue was cleared,
and they repeated the process on the next stone. Inching forward in
this way for some 30 meters, and almost at the point of giving up,
they broke through into a pre–existing tunnel, later termed
the Descending Passage because it started high on the north face and
sloped smoothly into the pyramid's depths below ground level. Unlike
the ragged tunnel gouged by Al–Mamun's men, the Descending
Passage, about a meter square, was astonishingly straight. It was so
exact that in 1881, Flinders Petrie, an experienced, professional
surveyor and skeptic, using the best equipment then available, found
that the average departure from a perfect line over the full length
of some 100 meters was less than 7 millimeters.
Of less interest was the discovery of another tunnel, the
so–called Ascending Passage, which led off of the Descending
Passage and headed up to what the potentate's henchmen called the
King's Chamber because it had a flat ceiling, which was an Arab
custom for male deceased. An offshoot of the Ascending Passage led
to the Queen's Chamber, so called for its gabled ceiling. The
dimensions of these rooms, along with the overall dimensions of the
pyramid itself, provoked endless discussion among luminaries such as
Isaac Newton and John Herschel, who speculated that the measurements
might hold the key to converting biblical units to their modern
equivalents. Although this numerical Rosetta Stone never emerged,
Newton did conclude that the builders must have employed more than
one unit of length.
Pointing at the Heavens
The first modern European astronomer on the scene was probably John
Greaves, a professor of geometry at Gresham College. In 1637,
Greaves suddenly abandoned the academy in order to undertake
measurements of the Great Pyramid. His work was thorough and
extensive, and Newton and others scrutinized the published results
for data to develop their theories. Upon his return to England in
1640, Greaves's reputation won him the Savilian Professorship of
Astronomy at Oxford. Unfortunately, he fell from this lofty position
after being fired for misappropriation of funds!
Some two centuries later, a much more famous astronomer named
Charles Piazzi Smyth, Astronomer Royal for Scotland, turned his
attention to the Pyramid. A curious figure, Smyth produced some
first–rate science in other fields, but he lost almost all
rationality when it came to this subject. For example, he attributed
great significance to the fact that the slope of the Pyramid is near
the ratio 10:9, and that its height of 484.9 feet (or 0.09184 mile)
multiplied by 109 equaled 91,840,000 miles.
Coincidentally, that number is close to the actual distance between
the Earth and the Sun. Smyth believed that the coincidence meant
that the Pyramid builders must have also known this distance. There
was much more along these lines, with liberal doses of religious and
prophetic conclusions. He published a three–volume,
1,600–page opus about his findings, which, needless to say,
was a great hit among the like–minded, but which was dismissed
by one reviewer as containing "more extraordinary
hallucinations than has appeared in any other three volumes of the
past century." Nevertheless, Smyth was not entirely without
redemption. Like a previous investigator, he was intrigued by the
extraordinary straightness of the Descending Passage and took care
to measure carefully its angle of descent, noting that a person
within the passage looking out through the surface opening would see
a patch of sky close to the celestial north pole. However, Polaris,
the current pole star, would not have been visible to the builders
because precession (the slow wobble of the earth's axis of spin)
would have placed the pole much farther from Polaris than it is now.
A possible (though not very likely) pole star for people of that era
is the magnitude 3.7 star Thuban (Alpha Draconis), which, Smyth
calculated, would have been visible in the opening at lower
culmination (the time of its lowest point in the sky) around the
years 2123 and 3440 B.C. He suggested that the Pyramid might have
been built near either of those dates, which despite the flimsiness
of his argument is not entirely ridiculous when compared to the
modern estimate at about 2500 B.C.
A long–standing problem relating not only to the Great
Pyramid but also its smaller cousins is the question of how the
builders managed to orient such colossal structures to the cardinal
points with surprisingly high accuracy. The eastern side of the
Great Pyramid, for example, points only three arcminutes away from a
true north–south line, and other pyramids in the group are not
much worse. This makes it virtually certain that some astronomical
method was used to establish the local meridian. At first thought
this does not seem too difficult a problem, even without a bright
star close to the north celestial pole during the millennia of
interest. (Even today, Polaris is some 43 arcminutes from the pole,
and during this time it was about 25 degrees away.)
Still, other possibilities spring to mind. An obvious method would
be to note the directions of sunrise and sunset on a given day and
bisect the angle between the two—the result marks the
meridian. But this, and other seemingly straightforward methods,
while fine in principle, turn out to be unsatisfactory in practice,
at least when accuracies of a small fraction of a degree are called
for. For instance, in this case the rising and setting sun must be
seen over an absolutely flat horizon, which Giza lacks. Then there
is refraction in the earth's atmosphere: When one sees the lower
edge of the setting sun just touching the horizon it has in fact
already set. The light rays are bent to produce an image above the
horizon, thereby shifting the direction in which the sun appears to
set. And since the amount of refraction depends on air temperature,
pressure and other factors, all of which can differ between morning
and evening, the effect may not be consistent between rising and
setting. Furthermore, the sun's celestial coordinates will change
during the course of the day, spoiling the symmetry of the method.
All in all, these practical hurdles have stymied modern astronomers
who tried to figure out just how the early Egyptians managed to
orient their pyramids as precisely as they did.
An Answer Written in the Stars
That an astronomical method was used to orient the pyramids received
strong, if unexpected, support in the 1980s when historians
discovered that among most of the Giza pyramids, the departure of a
pyramid's eastern edge from a true north–south line correlated
strongly with the accession date of the king for whom each was
constructed. Which is to say that the direction of north as
determined by the Egyptian method varied systematically as the
centuries went by. The ready explanation for this is once again
precession of the equinoxes: The early Egyptians must have applied
some method of using the stars to find the north celestial pole
without realizing that the pole is not fixed, but rather drifts
slowly through the heavens.
In November 2000, Kate Spence, an Egyptologist at the University of
Cambridge, published a seminal paper in Nature in which she
suggested a method by which the pyramid builders determined what
they thought was north. She also showed that the resulting
orientation errors varied as a function of time—just as
predicted by precession. Moreover, by fitting the time–linked
precession errors to the slight deviations of each pyramid, she
revised their building dates. Instead of 2554 B.C., her data suggest
the Great Pyramid was constructed between 2485 and 2475 B.C.
The method proposed by Spence involved two stars on opposite sides
of the celestial pole. She had to choose them by trial and error,
since the pole drifts into different star fields as millennia pass.
For the period of interest, Spence found that the stars named Mizar
(Zeta Ursa Majoris) and Kochab (Beta Ursa Minoris) would have
appeared to revolve around the pole on almost (but not exactly)
opposite sides, so that a line joining them would always pass very
nearly through the pole. When these two were aligned vertically, the
pyramid builders might have hoisted a long plumb line and fixed it
at the moment when the two stars both lay on the line. The point
where the vertical line touched the ground would indicate north.
One idiosyncrasy of this method was that because these two stars
were circumpolar (they never set), they could be seen from Egypt
year–round. Thus, at some date during the year Kochab would
have appeared above Mizar at meridian transit (when they would have
been vertically aligned), but six months later Mizar would have
topped Kochab. Early in the pyramid era, the pole was really
slightly west (or east, depending on which star was uppermost at the
time) of the line. Because of precession, the opposite was true late
in the era. Support for Spence's theory came from two pyramids whose
deviation from true north was of the expected magnitude but opposite
sign. The explanation was that all the pyramids except these two had
been set during the time of year when Kochab was above
Mizar—these two must have been set six months later (or
earlier), when Mizar surmounted Kochab.
Like many groundbreaking papers, this one quickly became the center
of arguments and proposed improvements. Spence accepted a small but
significant correction by extending the pole displacement to an
azimuthal displacement, but she seems not to have been enthused by
other proposals to use different stars in a different way. The
method still has some practical problems. For one, the plumb line
would have to be very long to reach high enough to be seen against
the upper star, especially because the observer would need to be far
away from the line to achieve sufficient accuracy. And it would have
been difficult to see the line at all against a dark sky.
Nevertheless, the explanation for the two pyramids with errors of
reversed sign supports the basic idea. As centuries went by and the
errors grew, later builders may have realized the problem and
abandoned the method or used different stars. Thus, the failure of
Spence's scheme among later pyramids is not necessarily a valid
critique. My own inexpert view is that whether she is proved right
or wrong, Spence's basic idea marks a major breakthrough in dating
these pyramids.