Mathematical Archaeoastronomical Theories

(A) Calculation of declination with the Stonehenge

Geometry accounts for the well-known alignment of Stonehenge. As mentioned, the Sun rises over the Heel Stone, as viewed from the center of the site, at the summer solstice. This can easily verified, referring to the above figure, a protractor, and the equation: sin delta = cos phi cos A.

  1. With the protractor, measure the azimuth of the Heel Stone. With the direction of geographic North indicated in the diagram, it should be about A = 50 degrees. 

  2. Look up the latitude of Stonehenge on a map. It should be about phi = 51.2 degrees. 

  3. By substituting A and phi into the equation, find the declination. Delta is approximately 23.5 degrees, the declination of the summer solstice position at the time Stonehenge was built.

This method has led some astronomers to debate that Stonehenge was not an observatory but rather just a ceremonial center. This mathematical expression demonstrates that this sighting cannot determine the exact time of the solstice. The sighting is of low precision. Because the Sun's path moves slowly at this time of year, there are dozens of days when the positions of the Sun are indistinguishable, from which solstice cannot be exactly determined.

(B) The Megalithic yard and  Stonehenge's possible geographical significance

Astronomers have well established, because it is objectively true, that the axis of Stonehenge aligns approximately to the midsummer rising sun azimuth. In addition, the station stone rectangle is constructed perpendicular to the axis and has a ratio of 5:12 (note this is only a ratio). In Megalithic yards, this is 40:96, i.e. the units of the rectangle's ratio are expressed in 8 MY 'quanta'.

A rectangular structure may align to extreme sunrises (for example, most northwest of the sunrise) and opposite extreme moonrise azimuths (the 'lunstices') only within half a degree of the latitude of Stonehenge. Also, rectangular structure further aligns to the quarter day sunrises and sets - those days lying between the two solstices. (Figure 4.3)




The secret of the calendar (and eclipse prediction) is to be able to find the exact number of lunar months in the solar year. (which is 12.368, almost 7/19ths). The over-run is 0.368 of a lunation, which is 10.875 days, meaning that in the whole year, the moon is 10 days ahead, if we take 12 ‘moon months’. The two main features of Stonehenge are built to the ratio 7/19 (0.368). The Aubrey circle is 104 MY in diameter (283 feet), whilst the Sarsen circle has an outer diameter of 104 feet. The fraction is 0.367 (104/283).


Looking aside from the ‘big’ picture of the Sarsen and Aubrey circles of stones, we focus on the dimensions of the stones themselves. This same fraction may be found from a rope marked with 30 equal divisions. Peg out a 5:12:13 triangle, divide the‘5' side into‘3' and‘2'. At this 3:2 point, a constructed hypotenuse to the apex has a length of 153, which, is 12.369 units (by Pythagoras’ theorem). One could even use the station stone rectangle, where the divisions are eight Megalithic yards. It has been called the construction the Lunation Triangle, as it appears not to have been discovered and named previously by modern culture.


When using this triangle with units as Megalithic yards or multiples thereof, the 0.368 fractional component will automatically fall out as one foot (12") or multiples thereof. Thus it is true that the Megalithic yard splits into a foot and a Royal cubit (20.64 inches). If the Megalithic yard is understood to represent the time elapsing between 12 and 13 lunations (full moons), i.e. between 354.367 days and 383.89 days, then where the foot meets the cubit is found to be 365.2 days - the solar year, or 12.368 lunations. (Table 5.1)

Astronomers like Robin Heath have, for years, used Stonehenge to calibrate ropes whereby he can subsequently derive a lunisolar calendar for years in advance and predict eclipses. He has termed 0.368 (very nearly 7/19) the Silver Fraction. Of course, astronomically, 12.368 is the metonic cycle expressed as an annual figure. [Metonic cycle: In nineteen years there are exactly 235 lunations. 235/19 is 12.368. Named after a 4th century AD astronomer, it appears that the phenomenon was known about by the builders of Stonehenge, i.e. before 2500 BC]

Why Stonehenge is WHERE it is??

The large Lunation Triangle, shown incorporated into a huge cardinally aligned 5:12 rectangle (refer to the above Triangle 1), includes the location of the bluestone site, and the exact north-south and east-west lines complete a right angled triangle via Lundy and Caldey Island. In Old Welsh, Lundy is called Ynys Elen, the 'island of the elbow, or right angle'. This suggests that this may be the reason why Stonehenge is located where it is. (See below)