Introduction

In the previous article (Stonehenge the Calendar) I explained how neither the summer or winter solstice, for which Stonehenge is famous cannot be used to work out the date and how instead a date toward or at the spring or autumn equinox (equal day and night) would be used. I then suggested that some barrows to the east of Stonehenge might be a way to calibrate a calendar to the equinox. These are recorded as being bronze age, but that could be a possible reuse of earlier features.

Now I want to explore another way to calibrate a "calendar".

Theory

 

Because the earth rotates at an angle compared to its orbit around the sun, from the point of view of an observer on the earth, the sun appears to move up toward the north pole by 23.5 degree in the northern summer and down toward the southern pole by 23.5 degree in the northern winter.

This is shown on the diagram to the left.

 

 

 

Plain of cows

Therefore from the point of view of an observer on the earth, the sun appears to move up toward the north pole by 23.5 degree in the northern summer and down toward the southern pole by 23.5 degree in the northern winter and most of the year the path of the rays of light falling on the earth form part of a cone.

 However at the equinox, from the point of view of someone observing on the earth's surface, the sun travels across the sky from east to west in an arc with the observer at the centre. So, on this day, the sun's rays travel along a plain so that if we had a slab angled so as to be in the same plain, the sun would shine across the plain throughout the day. Or to be more exact, at the point of equinox, when the such is exactly perpendicular to the earth's axis, the sun would shine directly along the plain. And throughout the rest of the day it would be slightly above of below this plain. But as the sun is about 0.5degrees wide and it moves about 0.4degrees each day, it does shine more or less directly along this plain for one day.

 

The Great Pyramid of Gaza

Great Pyramid at Gaza with various images placed
in day of year order showing how the north face is
completely in shadow for part of the year.

For all that has been written about the pyramids, one of the least mentioned aspects, is that which is most obvious: that part of it is in shadow. And whilst many mention the great accuracy of its alignment north-west and how accurate the angles are, few seem to realise that this means the North face is a very precisely aligned plain at an angle of 51.8444. The pyramid is at:

29.979175°N, 31.134358°E

At equinox the height oft the sun at this site will be:

(90° - 29.98°) =60.02°

So that at equinox the angle of the sun above the north slope will be:

60.02° - 51.84° = 8.18°

This is fairly close to the required angle so that for example a 10m long object protruding from the surface would have a shadow 70m long. And because the sun is moving east to west the end of the shadow would move along a straight horizontal line. We've no means of knowing if such a device existed because the surface stone was removed long ago. But even today we get a pronounced change from sun bathed to shadow as the images to the left show. And we can work out when this happens . As the sun moves 23.5 degrees from Equinox to solstice, the day the  sun will be shining down the slope is given approximately by: 

365.25/360 * asin (8.18 / 23.5) = 36.7 days.

 Which means that the midday sun should be shining down the slope of the pyramid 20.7 days before spring equinox or around 27th February 2015.

Bent Pyramid (Wikipedia)

Obviously, if the angle of the pyramid had been 60° (less a bit to account for size of sun) rather than 51.84°, the sun would have travelled around an arc keeping the north side of the pyramid just in shadow for a whole day. Although, as the sun is moving northwards during the day, one might even be able to see the precise hour of solstice!

And if the pyramid had been so aligned, then one could tell the day of equinox if the sun shone at any time.

But the pyramid was not built with the 60degree slope because from the evidence of the "Bent Pyramid" which has a marked change in slope from 54° at the bottom to 43°  at the top, it appears the pyramid was not structurally sound at steep angles.

 

 

 

 


OS map of Glastonbury Tor with North area where slope runs east-west 
highlighted in pink.

Glastonbury Tor

Could this type of effect have been used in the UK? Egypt is known for its sunshine, but Britain is not. That is why a single observation, particularly near the horizon where cloud is densest  cannot be used to reliably calibrate a calendar date. But if we have a plain, even a few minutes sunshine can tell us whether a suitably inclined plain is in shadow or not and so whether we are before or after the equinox. Because the cloud is densest at the horizon, a few minutes sunshine at any point during the day is far far more likely than a good view of the sun at the exact time it hits the horizon.

Obviously there's a huge problem in Egypt creating a plain at the required 60 degree angle, however as we travel further north the sun drops in the sky and so the required slope of the plane drops considerably. Take for example Glastonbury Tory as a possible candidate as an instrument to determine the day of equinox. Glastonbury Tor certainly has a nice north side which has the required "flat" which could serve the function. Or at least it has a fairly flattish area running W-E. Here the hill rises 40m (110m to 150m)86 over a distance measured on the map as 87m. The angle from horizontal is therefore

Slope angle = atan(40/86) = 24.7°.

The Tor is at

51.1444° N, 2.6986° W,

At equinox the height oft the sun at this site will be:

(90° - 51.14°) =38.86°

So that at equinox the angle of the sun above the slope will be:

38.86° - 24.7 = 13.856°

This is rather more than the great pyramid, but as the photo below shows, there are some strong ridges that might work in some way to bring this angle close to that required for the equinox. But using the figure we have, the sun moves 23.5 degrees from Equinox to solstice, the day the  sun will be shining down the slope is given approximately by: 

365.25/360 * asin (13.856 / 23.5) = 36.7 days.

Which means that the sun should be making an arc so that the rays of the sun are just parallel to this slope on the 12th February 2015 and 6th November 2015.

More

View of Glastonbury Tor showing the North face of the Tor which is in shadow from around 6th November
till 12th February. The date of the photo was not given, but is estimated to be late September
(shortly before the equinox)

Could it be the equinox calibration machine?

Note how the tor of the tower is close to the bottom of the fence at equinox! This tower effectively raises the angle of the slop so that the shadow of the tower runs along the fence at the bottom of Glastonbury Tor at the equinox. This site could provide a suitable observatory for the equinox allowing the date to be confirmed from a single short period of sunshine any time during the middle of the day. Indeed, perhaps the ridges might enable the same observation to be made on successive days meaning that even a few minutes of sunshine in the days before and after the calibration date would be enough.

However, why would the ridges continue around the hill? It could work, but there is nothing that is essential if and only if it had this function.

 

For next article in this series see: Stonehenge Lintel Ring