Stonehenge Visitors Guide – under ‘Eclipse Cycles’ – says:
‘Now, it’s widely accepted that Stonehenge was used to predict eclipses. The inner “horseshoe” of 19 stones at the very heart of Stonehenge actually acted as a long-term calculator that could predict lunar eclipses. By moving one of Stonehenge’s markers along the 30 markers of the outer circle, it’s discovered that the cycle of the moon can be predicted. Moving this marker one lunar month at a time – as opposed to one lunar day the others were moved – made it possible for them to mark when a lunar eclipse was going to occur in the typical 47-month lunar eclipse cycle. The marker would go around the circle 38 times [2 x 19] and halfway through its next circle, on the 47th full moon, a lunar eclipse would occur.’
We’ll start by noting that 47 is a Lucas number, which are closely related to Fibonacci numbers. There are 235 synodic months (SM) in the 19-year Metonic cycle, which is 47 x 5. The next Lucas number after 47 is 76, which is 4 x 19. Therefore in a given 76 year period there will be 4 Metonic cycles and 47 x 5 x 4 synodic months including 20 (5 x 4) eclipses.
Although we’ve said the Metonic cycle = 235 synodic months (47 SM x 5), closer study shows one SM is ‘lost’ every quarter precession, which accounts for the approx. 2 hour time difference between 235 SM and 19 tropical years (TY).
Wikipedia says: ‘Nineteen tropical years are about two hours shorter than 235 synodic months.’
In 6441 TY (see Why Phi quarter precession post) we get 79,664 SM = 339 x 5 x 47, -1
The ‘-1’ tells us it’s the end of the period, which consists of 339 Metonic cycles.
So each Metonic cycle in fact falls short by 1/339th of 235 synodic months:
(29.530589d x 24) / 339 = 2.09~ hours
After one quarter of the precession period one whole synodic month is ‘lost’.
Returning to our 76-year period, and noting that Phi = 1.6180339~:
76 TY/47 = 1.6170213~ TY (=99.93742~% of Phi, or 99.96132% of 55/34 in Fibonacci numbers)
In 76 TY there are almost 940 (47 x 20) synodic months.
20 SM = 590.61178 days = 1.6170415~ TY
The difference between the two 1.617~ numbers is due to the 2.09 hour period explained above.
There will be 20 eclipses per 76 TY period, but see footnote (Singapore University text) for more re. overlapping eclipse cycles. They say ‘more than one lunar eclipse would have been visible from Stonehenge every 47 months’. But:
‘No matter how often eclipses are seen within a 47-month cycle, the eclipses that are separated by 47 months are all related to each other and form a family.’
In the full precession cycle we in fact get 339 x 76 TY = 25764 TY (339 x 47 x 1.6170213~ TY)
All the above links lunar eclipses, Metonic cycles and Phi to Stonehenge.
Singapore University’s Department of Mathematics has a web page: PREDICTING ECLIPSES WITH THE STONEHENGE
Section (C): Using the Bluestone Horseshoe ( Lunar Eclipses )
‘The Bluestone Horseshoe, consisting of 19 upright columns at the monument’s center, could predict successive lunar eclipses. This was done by placing a stone marker on top of a pillar at one end of the horseshoe during a lunar eclipse, and moving it to the adjacent pillar every full moon.
Moving the rock this way every lunar month, the marker would stand at the center of the horseshoe after two-and-a-half trips around the row – 47 months after the original eclipse. The full moon that rose that month would fall into Earth’s shadow during the night. That stone could then be taken down and moved to the beginning of the horseshoe again.’
[Talkshop note: months = lunar synodic months (SM) in this context]
‘It predicts all lunar eclipses occurring at Stonehenge without predicting a lot of eclipses that wouldn’t be visible from the site.’
‘Stonehenge builders could have kept track of lunar eclipses by moving rocks around the monuments inner curve of 19 columns called the Bluestone Horseshoe. Placing a rock on top of one of the horseshoe’s outermost columns during an eclipse and moving it over one column every full moon, the marker would stand atop the center column during a full moon 47 months later, a moon that would be eclipsed.
The trick that complicates this explanation, however, is that more than one lunar eclipse would have been visible from Stonehenge every 47 months. The keepers of the stones could have had more than one rock traveling around the Bluestone Horseshoe at once, In fact, there may have been as many as six, depending on the frequency of eclipses.
No matter how often eclipses are seen within a 47-month cycle, the eclipses that are separated by 47 months are all related to each other and form a family. A family begins as a partial, or penumbral eclipse and it recurs every 47 months. Each time it would be a little closer to a total eclipse. There might be a dozen or so total eclipses in the family, and then the eclipses would grow more partial, eclipsing a smaller part of the moon every 47 months until the eclipse failed to appear. That family would then be finished, and the stone that marked it could be retired.’