Willy de Rop of the Royal Observatory of Belgium wrote a paper entitled ‘A tidal period of 1800 years’ in 1971 about tides and the motion of the Moon. It generated some interest and was referred to in at least one other paper, but on closer consideration leads to some ideas we can put forward here.
The opening paragraph states:
‘The Swedish oceanographer O. Pettersson
has presented evidence indicating that the last
maximum of oceanic tides occurred about 1433.
He pointed out that there is a coincidence
between a tidal period of 1800 years and climatic
changes of the same period. We think we
can explain this period as follows.’
De Rop’s basic premise is that there’s a correlation between the so-called ‘lunar wobble’ period and the anomalistic year.
His paper contains a geometric proof, and the final numbers are:
300 lunar wobbles in 1799 anomalistic* years (the lunar wobble is known to repeat in just under 6 years).
Update: *this should be tropical years – see numbers chart below re. the eventual one year difference between tropical and anomalistic years.
What do we make of this? Several things, all interlinked.
A few months ago the Talkshop featured a thesis by Ralph Ellis based on his concept of the Great Year, namely the perihelion precession cycle.
Ellis said: ‘The Seasonal Great Year of 21,700 years in length is the reason for the variability in Interglacial spacings.’
Update 6/1/16: New science paper from Ralph Ellis:
Modulation of Ice Ages via Precession and Dust-Albedo Feedbacks
Several sources quote a period of 21,600 years including this one which says:
‘For the Earth we have an approximately 41,000-year axis tilt period plus the 100,000-year and 400,000-year cycles of variation in the Earth’s orbit shape. Add in the 21,600-year cycle of precession of the Earth’s perihelion date, you will find the net effect to be quite complex to predict.’
Wikipedia is less precise, saying: ‘it takes about 21000 years for the ellipse to revolve once relative to the vernal equinox’
If we apply the concept of the Great Year to de Rop’s lunar cycle, we find his period looking a lot like a ‘Great Month’ (noting that the word ‘month’ itself derives from ‘Moon’).
In numbers: 1799 anomalistic years(AY) x 12 = 21588 AY
Correction: we find 1799 tropical years(TY) x 12 = 21588 TY = ~21587 AY (see chart).
Obviously this fits closely with the estimated 21,600 year period quoted fairly widely on websites, and close to the 21,700 years used by Ralph Ellis.
If we have a Great Month and a Great Year, is there anything else? In a word: yes.
It turns out that 1799
AY TY x 3 is equivalent to whole numbers of lunar apsidal cycles (610) and lunar nodal cycles (290), so that would be the Great Season (3 Great Months x 4 = 12 = Great Year).
That would be 900 lunar wobbles (300 x 3, also 610 + 290), so in a Great Year there would be 3600 wobbles. Since perihelion precession means a full revolution of the perihelion precession date (currently early January), there are 10 wobbles per degree of movement of the perihelion (10 x 360 = 3600).
After the Great Month, Season and Year, the other period we can look for is the Great Day. If we say there are 30 Great Days in a Great Month of 300 wobbles, there will be 10 wobbles in a Great Day. The period will be 1799
AY TY / 30 = 59.9666~ AY TY, which looks a lot like the 60-year climate period often referred to in science papers and elsewhere, e.g.:
‘Given that records of solar activity are accurate, solar activity may have contributed to part of the modern warming that peaked in the 1930s, in addition to the 60-year temperature cycles that result in roughly 0.5 °C of warming during the increasing temperature phase.’ – Wikipedia
So de Rop may have provided a foundation for the period of the perihelion precession and the (controversial in some quarters) 60-year climate period.
For a geometric description of the lunar wobble, see de Rop’s paper (shorter version – only 2 pages) and in particular Figure 3, showing the interaction of the apsidal and nodal cycles in a ‘half-wobble’ or 180 degrees of movement (=~3 years). Once the meaning of Figure 3 is clear, everything should start falling into place (hopefully).
Note: Keeling and Whorf also found the same tidal cycle in their paper entitled:
‘The 1,800-year oceanic tidal cycle: A possible cause of rapid climate change’