1. How Accurately Did the Great Pyramid Point North? An Error of Under 9 Centimeters at 100 Meters
Let us convert the angle of error into distance. The orientation of pyramids from the Old Kingdom period was very precise, with the Great Pyramid of Khufu being the most accurate. The average amount that the four sides deviate from true north is reported to be less than three minutes of arc [1]. A minute of arc is one-sixtieth of a degree, so three minutes of arc is one-twentieth of a degree. Another report describes the accuracy as "better than four minutes of arc" [2].
If we convert this to distance, one-twentieth of a degree is approximately 0.05 degrees. Assuming the error is exactly three minutes of arc, the sideways distance from the intended line at 100 meters would be about 8.7 centimeters (100 times the tangent of 0.05 degrees). Since the actual average error is smaller than three minutes of arc, 8.7 centimeters serves as an upper limit estimate for this calculation. However, there are no surviving documents or diagrams from this era that record how orientation was determined. Therefore, discussions rely on materials from much later periods or infer from the precision of the finished structures [1]. Are there clues other than the size of the error?
2. Why Did Pyramid Alignment Errors Grow Larger After King Khufu?
The precision of pyramid orientation peaked during the reign of Khufu. In the eras of subsequent kings, the alignment gradually became less accurate [1]. According to an introduction to Dash’s paper, the pyramid of Khafre has a deviation of about six minutes of arc [5]. This is larger than Khufu’s "better than four minutes of arc."
Researcher Spence noticed this change. He reasoned that if a single fixed method had been used every time, the pattern of error would not change this much. Based on this thought, Spence proposed a method using stars [1]. However, this is a proposed hypothesis and has not been proven. Criticisms exist.
3. Could Egyptians Find North by Watching Two Stars with a String?
In those days, there was no star pointing north like the current North Star. Spence focused on two circumpolar stars that circle without setting below the northern horizon: Kochab in the Little Bear constellation and Mizar in the Great Bear constellation. His proposal was that if you align a plumb line with these two stars at the moment they line up one above the other in the northern sky, that direction is true north [1].
Because Earth’s axis slowly changes direction (precession), the alignment of these two stars also shifts over time. Spence suggested that the changes in error for each pyramid could estimate the start date of the Great Pyramid’s construction within a range of about five years [1].
Another star-based idea comes from Belmonte of the Canary Islands Astrophysics Institute. He reviewed Spence’s theory and offered an alternative. His method involves observing when two stars in the Great Bear constellation cross the true south line to determine the position of Thuban, which was then close to the north celestial pole. According to this method, the orientation dates to around 2562 BCE, which is the beginning of Khufu’s reign, requiring no date adjustment like Spence’s [3]. Even within "star theories," methods differ among researchers.
4. How Does Marking a Stick’s Shadow Tip Draw an East-West Line?
The method using the sun’s shadow involves standing a stick (gnomon) on the ground and marking the tip of its shadow at several points during the day. You mark points in the morning and evening where the distance from the base of the stick to the shadow tip is the same. Connecting these two marks produces an east-west line [4].
Dash actually tried this method on the autumn equinox of September 22, 2016. The resulting accuracy was reported to be about the same as the error in the pyramids [4].
However, there is no evidence that this method was used in ancient times. Dash himself states that because other methods could achieve similar results, it cannot be said that this specific method was used [4]. The astronomy magazine *Astronomy* notes that among researchers, the view that ancient engineers used the sun’s movement is accepted, but star theories remain. The issue is not settled [6].
5. Why Is the Theory That the Three Giza Pyramids Mirror Orion’s Belt Weak?
There is a theory that the three great pyramids of Giza mirror the pattern of Orion’s Belt stars (Alnitak, Alnilam, and Mintaka). Robert Bauval announced this in 1989 and popularized it in a 1994 book [7]. It links the arrangement of stars in the night sky with the layout on the ground.
There are three main criticisms from mainstream researchers. First is the angle. The alignment of the three pyramids is about 38 degrees, but calculations by astronomers like Krupp show that the orientation of the Belt stars around 10,500 BCE (the date claimed by the theory) was about 47 to 50 degrees, which does not match. Critics also point out that the map is flipped upside down when making the comparison [7].
Second is the date. The Giza pyramids were built in the Fourth Dynasty (third millennium BCE), which is far from the date claimed by the theory [7]. Third, there are no Egyptian documents or physical evidence showing that this design was intended. The Menkaure pyramid appears to have been added later, which makes the theory harder to support [6].
The narrow ventilation shafts inside the Great Pyramid have also been claimed to point toward stars. However, they only point roughly in those directions, and horizontal sections and large stones at the exits make them unsuitable for observing stars [6]. The true purpose of the shafts remains unknown.
6. How Can You Draw an East-West Line with a Stick Yourself?
You can try this on a sunny day in a schoolyard or garden with an adult. With an adult’s help, place a blunt stick upright on soft ground so it does not fall. In the morning, mark the tip of the shadow and measure the length from the base of the stick to the mark with a string. In the evening, find the spot where the shadow tip is the same length as the string from the base of the stick, and make a second mark.
Connecting the two marks creates an east-west line. If you do this on another day and compare how much the lines overlap, you can feel the difficulty of determining orientation precisely.
SAFETY NOTE: Please do not look directly at the sun. Wear a hat and bring water.
If you want to read more, try Spence’s paper [1], Dash’s own site [5], or the introduction in the astronomy magazine [6].