My thanks to Astrophysicist Ian Wilson who has left a long comment which I’m reposting here for further discussion, because it contains findings which are as Ian says, amazing (and Ian isn’t a man of hyperbole) . The summary below is further explained in Ian’s new paper which I’ll be putting up a further post on soon:
Are Changes in the Earth’s Rotation Rate Externally Driven and Do They Affect Climate?
which is available from this link. This is a stupendous work, containing many exact period matches, rather than being dominated by tenuous statistical derivations like so many other climate papers are. Top quality science on the talkshop. In the meantime, to whet your appetite:
Ian Wilson:
We know that the strongest planetary tidal forces acting on the lunar orbit come from
the planets Venus, Mars and Jupiter, in order of the size of their respective tidal
influences. In addition, we known that, over the last 4.6 billion years, the Moon has
slowly receded from the Earth. During the course of this lunar recession, there have been
times when the orbital periods of Venus, Mars and Jupiter have been in resonance(s) with
the precession rates for the line-of-nodes and line-of-apse of the lunar orbit. When these resonances have occurred, they would have greatly amplified the effects of the planetary tidal forces upon the shape and tilt of lunar orbit. Hence, the observed synchronization between the precession rates of the line-of-nodes and line-of-apse of the lunar orbit and the orbital periods of Venus, Earth, Mars and Jupiter, could simply be a cumulative fossil record left behind by these historical resonances.
In addition:
The synchronicities of the four Jovian planets have effectively determined the relative position of the three largest Terrestrial planets. The combined synchronicities of the Terrestrial and Jovian planets (principallyJupiter and Venus) have then determined the properties of ellipticity and tilt of the lunar orbit (e.g. the precession rates of the line-of-nodes (18.6/9.3 years) and line-of-apse
(8.85 years)). Hence, cumulative influence of the planets upon the shape and tilt of the lunar orbit over more than 4 billion years has indirectly set the properties of the lunar tides and these in turn have influenced the properties of the Earth/ocean/atmosphere system.
The dominant cycle for the four Jovian planets is the ~ 179 year Jose Cycle:
9 × SJS = 9 × 19.858 yrs = 178.72 yrs_____________SJS = synodic period Jupiter & Saturn
14 × SJN = 14 × 12.782 yrs = 178.95 yrs___________SJN = synodic period Jupiter & Neptune
13 × SJU = 13 × 13.812 yrs = 179.56 yrs___________SJU = synodic period Jupiter & Uranus
5 × SSN = 5 × 35.871 yrs = 179.36 yrs_____________SSN = synodic period Saturn & Neptune
4 × SSU = 4 × 45.368 yrs = 181.47 yrs_____________SSU = synodic period Saturn & Uranus
The 179 year Jose cycle also appears to be embedded within the relative sidereal orbital periods of Venus, Earth, Mars and Jupiter as well, with:
28 × SVE = 7 x (6.3946 yrs) = 44.763 yrs
69 × SVJ = 44.770 yrs _________________________SVJ = synodic period of Venus & Jupiter
41 × SEJ = 44.774 yrs _________________________SEJ = synodic period of Earth & Jupiter
20 × SMJ = 44.704 yrs _________________________SMJ = synodic period of Mars & Jupiter
since 44.75 years x 4 = 179 years
This is accompanied by a remarkable near-resonance condition that exists between the orbital motions of the three largest terrestrial planets with:
4 x SVE = 6.3946 years_______________________SVE = synodic period of Venus and Earth
3 x SEM = 6.4059 years_______________________SEM = synodic period of Earth and Mars
7 x SVM = 6.3995 years_______________________SVM = synodic period of Venus and Mars
[Note: This means that these three planets return to the same relative orbital configuration once
every ~ 6.40 years]
[Note: 6.4 years = 12.8/2 years = Synodic period of Jupiter-Neptune]
This in turn leads to another remarkable near resonance condition between the orbital period of the Jupiter/Terrestrial planets and the lunar orbit such that:
The line of nodes of the lunar orbit appears to rotate around the Earth, with respect to
the Sun, once every Draconitic Year (TD = 346.620 075 883 days). This means that the
Earth experiences a transition from a maximum to a minimum in the meridional components of its tidal stress, at times separated by:
¼ TD = 86.65002 days_______________________________ 1st tidal harmonic
5 x ¼ TD = 1 ¼ TD = 433.275095 days = 1.18622 years_____ 2nd tidal harmonic
5 x 1 ¼ TD = 6 ¼ TD = 2166.375474 days = 5.93111 years ___3rd tidal harmonic
[Note: Amazingly, the point in the Earth’s orbit where the 2nd tidal harmonic occurs (i.e. 1 ¼ TD), rotates around the Sun (with respect to the stars) once every 6.3699 years. This is just over three hundredths of year less than the time required for the realignment of the positions of the
three largest terrestrial planets.]
The first point that needs to be made about this is that there appears to be an almost
perfect synchronization between the three tidal harmonic intervals and sub-multiples of
the sidereal orbital period of Jupiter (TJ = 4332.82 days = 11.8624 sidereal years):
1/50 * TJ = 86.6564 days
1/10 * TJ = 433.282 days = 1.18624 years
1/2 * TJ = 5.93120 years
There is also a connection with the Chandler wobble:
The side-lobe period that is produced by the modulation of the Earth’s sidereal year with a cycle that is only two or three hundredths of year shorter than the iconic 6.40 year period, almost perfectly matches the 2nd harmonic time interval over which there are the greatest changes in the meridional tidal stresses acting upon the Earth:
(6.370 yrs × 1.00 yrs)/(6.370 yrs – 1.00 yrs) = 433.2743 days = 1.18622 years
the possibility is that the source of excitation for the Chandler Wobble has an extra-terrestrial origin. It is possible that the 6.40 year realignment period for the terrestrial planets has interacted with the sidereal orbital period of the Earth/Moon system over the eons, to produce a side-lobe modulation that it has slowly nudged the precession rate of the line-of-nodes of the lunar orbit towards its current value. Hence, we now have a precession rate that produces a 2nd harmonic for the maximal changes in tidal stresses that varies on a time scale of 1 ¼ TD = 433.2751 days = 1.18622 years.
The fact that 2nd tidal harmonic is so close to the nominal 433 day period of the
Chandler Wobble, suggests that the variations in lunar tides produced by the precession
of the line-of-nodes of the lunar orbit could, in fact, be the source of the ocean-bottom
pressure fluctuations that are thought to be responsible for the excitation of the Chandler
Wobble.
Finally, the period of the Chandler Wobble (TCW) is ~ 433.26 mean solar days
Connection to Inner planets
TCW = 1 / [ 1 − [(1/SVE) − (1/SEM)] ] = 1.186249 sidereal years = 433.285(1) days
where the following values have been used:
Synodic_VE = 1.5987 = 1.599 (3 dp) sidereal years using TV = 224.70069 days
Synodic_EM = 2.1354 = 2.135 (3 dp) sidereal years using TM = 686.9600 days
Connection to Jupiter
Sidereal period Jupiter’s orbital period from GSFC Ephemeris:
TJ = 4332.80 days
10 x TCW = 4332.6 days
TJ = 10 * TCW = 10 / [ 1 − [(1/SVE) − (1/SEM)] ]
Beat Period of the Chandler Wobble with the Earth Year
TCW / (TCW – 1.0) = 1.186249 / 0.186249 = 6.369(2) years
1.0 / [(1/SVE) − (1/SEM)] = 6.369(1) years
AMAZING!!
Tallbloke's Talkshop 
Congratulations Ian, as you say, AMAZING. Now the question of ‘why phi?’ becomes more interesting, and urgent.
‘This means that these three planets return to the same relative orbital configuration once
every ~ 6.40 years’
Which is roughly the difference between minimum and maximum solar cycle lengths.
Fantastic wealth of information Ian, thanks.
Can you elaborate a bit on the “…realignment time for orbits of the planets Venus, Earth and Mars…”, my Solex/v11 finds e.g. three Mars-centric conjunctions with Earth and Venus in 2010 😦 TIA
Also worth noting that the (square root of 179.7) divided by 2 equals the square root of 44.77 = 6.685
6.685 x Phi = 10.81, which is the central solar ‘dynamo’ period also derived from the harmonic of the Jupiter and Saturn related periods I found in Bart’s Power Spectral Density analysis of sunspot numbers.
tallbloke says:
March 5, 2013 at 11:51 am
………
Sun appears to change its rate of oscillation about every 105 years or so
http://www.vukcevic.talktalk.net/SSN-Vfspec.htm
Next change over somewhere mid 2020s
(if you divide 105 with Phi you get the AMO’s 64 year cycle (1880-2011)
Chaeremon says:
March 5, 2013 at 11:44 am
Fantastic wealth of information Ian, thanks.
Can you elaborate a bit on the “…realignment time for orbits of the planets Venus, Earth and Mars…”, my Solex/v11 finds e.g. three Mars-centric conjunctions with Earth and Venus in 2010 😦 TIA
Ian is referring to the period that sees the return of all three planets to the same configuration with respect to each other.
This paper by Nils-Axel Mörner might be of interest for the discussion of the Earth’s Rotation Rate taking place here?
ARCTIC ENVIRONMENT BY THE MIDDLE OF THIS CENTURY;
In ENERGY & ENVIRONMENT; VOLUME 22 No. 3 2011
ABSTRACT:
At around 2040-2050 we will be in a new major Solar Minimum. It is to be expected that we will then have a new “Little Ice Age” over the Arctic and NW Europe. THE PAST SOLAR MINIMA WERE LINKED TO A GENERAL SPEEDING-UP OF THE EARTH’S RATE OF ROTATION. This affected the surface currents and southward penetration of Arctic water in the North Atlantic causing “Little Ice Ages” over northwestern Europe and the Arctic
…
In 1984, I launched the theory that angular momentum might be transferred back and forth between the solid Earth and hydrosphere; affecting primarily the surface circulation of the main ocean currents, and especially the Gulf Stream and Kuro Siwo Current which bring oceanic water masses from low to high latitudes (Mörner, 1984a, 1984b). This was followed up in a series of papers (Mörner, e.g. 1988, 1995, 1996a,1996b). I THEN REALIZED THAT THE SOLAR WIND MIGHT AFFECT THE ROTATION OF THE ENTIRE TERRESTRIAL SYSTEM (Mörner, 1996b, 1999). The Solar minima were found to correspond to periods of speeding-up of the Earth rate of rotation (Mörner, 2010)
…
Click to access Moerner_Science_environm_sea_level_3_11_Paper_534.pdf
Chaeremon,
If you have access to an solar system orrey try looking at the terrestrial planets [i.e. Mars, Earth and Venus] on these dates when Venus and the Earth align:
Aug 17th 2007
Jan 11th 2014
Jun 3rd 2020
Oct 20th 2026
Mar 20th 2033
Aug 5th 2039
Dec 30th 2045
May 26th 2052
This is a 44. 8 year sequence with each date separated by 6.4 years from the other.
You should see Mars consistently about 56 degrees ahead of the alignment of Venus and the Earth, although this angle can vary from 44.1 to 67.9 degrees over this time period because of the relatively high ellipticity of Mar’s orbit.
I wonder whether there is somewhere within this a way of determining when the ENSO cycle “locks on” to the annual cycle. Whenever this happens additional ENSO cycles follow at intervals of 2 or 3 years before reaching a hiatus. It has become apparent that there are important connections between this behavior and climate. The 60 year cycle shows a general tendency, but a way of forecasting ENSO behavior on a decadal scale would be invaluable.
Rog,
I have some interesting ideas about the FB sequence and planetary distances which I will discuss with you in private at this stage. We live in interesting times. Sorry for my limited comments but I am very busy right now.
Hi Ian, thanks for finding the time to put together your comment and for dropping by now. I’ll look forward to hearing from you about the FB sequence, and will try not to distract this thread with too much speculation.
Pochas, I agree that being able to forecast ENSO would be invaluable. In fact, if I work out how to do it, I might go into the forecasting for cash business. 😉
Landscheidt was working on this right up to his death. His cycle based system was difficult to understand, but contains some insights. I hope we’ll find the key in the motion of the system, though I suspect the subharmonics of waves interacting with Earth’s physical surface affect the outcome, so it won’t be a simple answer.
Thanks to Ninderthana and tallbloke for chiming in on my “…realignment time for orbits of the planets Venus, Earth and Mars…” question to Ian.
But there are “… 3 Mars-centric conjunctions with Earth and Venus in 2010” and I’m too blind to see the 6.4 years cycle, by Solex numerical integration.
Would it be possible that Ian explains to me the 6.4 math (any ref or base equ’s would be just Okay), this I want to learn and reproduce for my spreadsheet. TIA.
Chaeremon, by ‘mars centric’ do you mean, as seen from Mars? If so, the conjunctions are a product of retrograde apparent motion. Try heliocentric for an easier life. 😉
tallbloke said: “Try heliocentric…” nice try 🙂 but I do not want (nor do we need) that the Sun also lines-up.
B.t.w. “apparent” happens just to us earthlings, it is just our view and not the (by fictitious coordinates tamed for us) physics (e.g.Venus doesn’t switch to retrograde direction around the Sun). W.o.w. the line-up happens regardless of us assuming the Venus-centric, Mars-centric or geocentric observer.
B.t.w[2]: I do not object to Ian’s 6.4 years cycles, I only want (while we are here) to get their math base all together; the cycles could be hypotrochoidial so that many of them can start in one-and-the-same of Earth’s year. This I’d like to reproduce.
Chaeremon: In general, planets reach closest approach at inferior conjunction when they are in line with the Sun. The idea of synodic periods is based on a reference point being used. The Sun and the planet pair’s alignment with it is the only sensible reference point to use, as far as I can see.
tallbloke, I cannot disagree with your comment, except that the line-up of e.g. 3 planets shall also see the Sun (see below). The cycle math has input from each independent synodic, each has used e.g. its own star for “start/stop” reference.
But after multiplication (etc) of the independently obtained base figures, there is only the one cycle numeric result and no reference coordinate was handed down (by cycle arithmetic) to the result.
Example for 3 occurrences in one year (there are other years with more than 1 occurrence), time in TT:
2010/10/03 21:30:13, 2010/08/20 19:43:13, 2010/01/27 05:33:11
It can be that I appear to be nitpicking, but my attempt was to “just” reproduce the 3 planet’s cycle with “ordinary ephemerides and numerical integration” and make a nice diagram for years 1600-2100.
Earth-Venus heliocentric oppositions are currently meeting up with Mars every second Venus synod (3.197yrs), there is one later this month. Mars goes in and out of phase with the Ea-Ve syzygies over a 299yr cycle, which also is resonant for Ceres (13*23yrs). So around 150yrs ago, Mars was lining up with the Ea-Ve conjunctions instead, but only every 6.394yrs.
In the current Ea-Ve-Ma phase, the tightest alignments are from 1958 to 2048, so the last analogue of this 299yr cycle was right on the Maunder minimum.
oops correction, ~150yrs ago Mars does line up with The Ea-Ve syzygies every 3.197yrs, alternating between conjunct and opposing Ea-Ve. The current configurations are Ea opposite Ve+Ma, alternating with Ea+Ma opposite Ve every 3.197yrs.
Ulric, thank you for clarifying “… syzygies, … conjunct and opposing …”
I suppose that syzygies (has Sun as common reference) is precisely what tallbloke suggested.
And then the 3.197 you mentioned seem halves of the 6.4 cycle. Yet when, during syzygy, 2 of the here discussed bodies are in opposition, then one of the 3 is behind the Sun.
TB says: ‘Now the question of ‘why phi?’ becomes more interesting, and urgent.’
It’s the signature of magnetic flux.
https://tallbloke.wordpress.com/2013/02/20/a-remarkable-discovery-all-solar-system-periods-fit-the-fibonacci-series-and-the-golden-ratio/comment-page-2/#comment-45568
@Ian, the 299yr cycle (187 Venus synods) is in phase with Jupiter over 4 steps, see 9th Dec 619, and 13th Oct 1815.
Hello, I’ve now made data points for years 1600-2100 and plotted just solar “eclipses” syzygies with Mars to Earth or Venus (can send the .csv and diagram).
By this view on the data, Mars+Venus together they separate the terrestrial months into odd+even, twice a terrestrial year and with opposite odd+even.
And Mars+Earth seem to be falling in love during April (sparse)+May (dense) and October (sparse)+November (dense) 🙂 again with a (few) opposite dots.
What a surprise !
P.S. if I understand “Mars-centric ecliptic longitude° ” correctly, the diagram also shows the tight and narrow relation to the Mars-year “seasons” …
P.P.S. data points from numerical integration and DE421 ephemerides.
@ Kent 5 March, 1:47
Thanks for the great link.
Looks like we will get another “mini-Bond” event this time.
I would like to see some weight put on the different ocean surface elevations (Pacific vs Atlantic)for future predictions — if that would make a difference?
Kent Forssgren says:
“I THEN REALIZED THAT THE SOLAR WIND MIGHT AFFECT THE ROTATION OF THE ENTIRE TERRESTRIAL SYSTEM”
Well maybe more equatorial jet stream speeds up the rotation rate, aided by weaker easterly trade winds in the tropics, both effect sea water transport too. It would be more rational that weather and climate would alter the rotation, rather than a few milliseconds change of rotation rate causing the climatic variation.
Ulric,
I did a rough calc of the volume of cold water which would be upwelled due to the ocean piling up against the opposing continent when the LOD slowed by 3ms. It’s a significant volume. Add in the Chandler Wobble, where the Earth gets a tilt at the surface of around 40m and consider the inertial mass of the global ocean. There will be significant pressure waves and internal tidal mixing as a result.
tallbloke, sea level is higher in the east Pacific when there is less up-welling:
The exchange of angular momentum between zonal winds and solid Earth (and ocean) is a small signal on the back of longer term changes in LOD of much greater amplitude. The question is, are the changes in the wind driving the longer term changes in LOD, or are the longer term changes in LOD changing the ocean currents which are changing the longer term wind regimes.
Tricky to disentangle cause and effect here.
“The exchange of angular momentum between zonal winds and solid Earth (and ocean) is a small signal..”
The trade winds move a lot of water westwards, and it’s in the opposite direction to the effects of LOD reducing, in fact it moves in the right direction to cause the reduction in LOD.
Longer term changes if they are slow will not cause much acceleration, what scale do you mean by longer term?
Ulric, the inter-annual angular momentum exchange is around 1/8 of the multi-decadal ~60yr swings.
Adding10mph in one year will cause a lot more immediate slosh than adding 80mph in 60yrs. But the winds seem to be blowing it much stronger in the opposite direction anyway. Think about it, LIA type conditions, more El Nino episodes, shorter LOD, and the water is higher in the east Pacific. not in the west where your angular momentum slosh says it should be.
Ulric,
Which side of the ocean the slosh would occur on would depend on whether the Earth was speeding up or slowing down.
And if LOD is shorter that means acceleration so the slosh would be to the west not the east.
“The dominant cycle for the four Jovian planets is the ~ 179 year Jose Cycle”
It’s a pseudo cycle, it is constantly shifting because the orbital periods do not match that well. The only repeatable return of all four is at 4627yrs. Out of interest, did Desmond King-Hele note the 179yr period before Jose? I would have thought that astronomers many centuries back would clocked the rough harmony of 112 Venus synodic periods with Jupiter and Saturn.
“Thus all the days of Mahalalel were 895 years..” 179*5 !
Its been a while since I made a comment in here, got distracted by life. In regard to the LOD shifts and angular momentum shifts driving mechanisms, I think that the magnetic fields of the earth hold the ions in the atmosphere, oceans and solid earth semi locked together, so that the homopolar inductive effects of the changing strengths of the solar wind couplings between the planets, is the missing spin orbit interactions driver.
Thus the synod conjunctions speed up the planetary rotation via the increased magnet coupling, and expands the earths orbit for the outer planet conjunctions, to the point of closest approach then it all slows back down together, with very little slip between the atmosphere and oceans, relative to the solid earth, when the soluble ion content is higher, and a more relative shift in momentum for more neutral or deionized air masses, that have just lost large volumes of precipitation that takes the particles, aerosols, and soluble gases out with it.
In the oceans there would be an expected decrease of momentum transfer for the more densely concentrated sea water at depth, leading to the deep ocean current flows that drive the upwelling patterns, in sync with the trade wind shifts to drive the ENSO patterns. The combination of lunar declinational tides, perigee/apogee, and phase interactions thus giving rise to the QBO cycles with major El Ninos coinciding with multiple outer planet conjunctions, 1982-3 and 1997-8 as prime examples.
It is all a complex patterns of inter-modulation of the combination of effects that follows the above mentioned inner and outer planetary periods of synods. It is this pattern I have tried to tease apart to get the analog period of 6558 days I currently see as the best fit for forecasting the weather effect repeats.
The Saturn/Jupiter synods process ~120 degrees around the star field so every third or ~60 years their synod occurs closer to between the Earth and the center of the galaxy, causing an extra strength magnetic coupling effect, that weakens and strengthens as the every third alignment drifts off of optimal then shifts to a later synod cycle, giving rise to the coming and going of the strength of the ~60 year cycle that gives Lief S. such fits.
The cause of the “global warming” from the 1980’s till 2007 was a result of the Neptune Uranus synod occurring in mid northern hemisphere summer sky, about the same time as both Saturn and Jupiter were with in ~60 degrees of the same alignment, as the timing of when the earth passes the outer planets spreads out, and slips into the fall and winter seasons for the NH, the peak solar wind speeds from the extra CME’s associated with outer planet synods, that electro scavenged the upper level atmospheric ions and gave us clearer skies, that resulted in the “surface warming” are now occurring in late NH fall and winter.
Hence the Australian “heat wave” this year that will process later into their fall each year, just as the spring synod of earth and Saturn will move the spring outbreaks of severe weather and tornadoes in the USA later in the spring into summer in several more years then will start increasing hurricane intensities as the Earth/Saturn synod timing moves into July-August-September.
The reason for the 1976 step in ENSO and SST temps was the combination of these effects, the SST’s are starting to show the cooling as the extra CME effected electro scavenging decreases, cloud levels increase, and the temps drop globally. This and the SSB patterns due to the spreading out of the massive planets, is lowering the solar activity. Mainly because the greater magnetic fields of the galaxy that couple into the poles of the sun are more balanced/defused through the whole solar system, so there is less magnetic flux being pulled out the the internal containment fields of the solar furnace process, reducing the leakage of flux via sunspot production (visible leaks of containment fields).
Richard Holle said “…period of 6558 days I currently see as the best fit for forecasting the weather effect repeats.”
I’m in the middle of something with 1/3 of your period, ~2190.333 days, is there something you would explicitly point to for me to consider with this base period?
It’s a 6 years distance which returns to the same season close to the same day, from full-/new moon at start towards the quadrature 6yrs later at arrival and ahead of e.g. the neap/spring tides. Additionally, certain combinations of lunar line-of-apsides *and* line-of-nodes, when comparing at both ends of the interval, they dictate 2 very narrow bands at -1.0 day and +1.0 day offset to the day of quadrature median in e.g. 500 years. A bit more than 10% of the cases are in either band, all other combinations tend towards zero offset but with varying mileage; I’m not fully through that yet.
From your period I’d cautiously infer that odd multiples of my base period result in similar situations at arrival of quadrature, for however many multiples you’d like (to observe 😉
This is in contradistinction to wiki-wiki-pedia’s claim that *all* luni/solar cycles must be coincident for non-physical reasons, e.g. have no orbital resonance.
P.S. Thank you for pointing to years 1982-3 and 1997-8 as prime examples (gives me much to do for comparison with actual observations).
P.P.S. it’s quite possible that I’m effectively looking at artifacts from ephemerides, but who does not 😉
The 6558 day long period was chosen as it is 240 X 27.32 lunar declinational cycles, or just one 27.32 day period short of the Saros cycle length. The reason for this choice is to get a best fit of the weather pattern repeats, due to there being a four fold pattern of ebb and flow of where the mobile polar highs (MPH) inflow from across North America, ( the initial focus of the data base I had).
From one lunar declinational culmination at Max North to the next there runs four different regimes of storm tracks that when averaged together (as per standard Meteorological processes) swamps out the finer signal that works better, if used in sets of four cycles ~109.3 days long the cold air masses and the frontal patterns they drive holds together much better for the calculation of the position and characteristics of the resulting forecast composite frontal activity and precipitation.
6561 (cf. 6558 quoted above) is 3^8 so any cycles that have a relationship with 3 should readily fit into the overall cycle, in theory anyway.
For Saros cycles, Wikipedia notes:
A complication with the saros is that its period is not an integer number of days, but contains a multiple of ⅓ of a day. Thus, as a result of the Earth’s rotation, for each successive saros, an eclipse will occur about 8 hours later in the day.
http://en.wikipedia.org/wiki/Saros_%28astronomy%29#Description
@Richard Holle (March 9, 2013 at 4:32 pm)
Thanks for the info. There is a study of near-Saros cycles (in centuries and also geological time frames), the first 2 entries (part I and II) in this scholar.search result, it’s not behind paywall:
http://scholar.google.com/scholar?q=significant+high+number+commensurabilities+in+the+main+lunar+problem
and can be downloaded as .pdf (click Print this Article in the top frame, dragg that frame a bit down).
E Perozzi, AE Roy, BA Steves, GB Valsecchi (Celestial Mechanics) show that Sun+Earth+Moon are in sync (almost undisturbed) over more that just millennia. Besides of that their analysis is interesting “… the cycle is therefore the natural averaging period of time by which solar perturbations can be effectively removed in any search into the long term evolution …” emphasis mine.
There is a nice resonance at 20 Earth-Mars synods, with 36 Chandler’s and 45 eclipse years.
Working onwards to 400 Earth-Mars synods, at 720 Chandler’s and 900 eclipse years, is the 854yr Great cycle of Saturn and Jupiter, at 29 Saturn orbits and 72 Jupiter obits (72-29=43 synods).
[reply] so 720 Chandler = 72 Jupiter = 10:1