A proof of De Rop’s long-term lunar cycle (1799 anomalistic years)

Posted: May 10, 2020 by oldbrew in Maths, moon, Tides

Credit: NASA

The idea is to validate Belgian astronomer Willy de Rop’s 1971 calculations, which can be found here.

From our 2016 post discussing his paper, De Rop’s long-term lunar cycle:

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).

To see what the lunar wobble is, refer to the paper. Essentially it’s when the number of lunar apsidal and nodal cycles in the period sums to 1. For more information, please refer to that post.

Three pairs of periods align (with a difference of exactly 1 in each case) at the quasi-6-year lunar wobble period:
— Lunar Evections in longitude and latitude
— Draconic Year and Full Moon Cycle
— Draconic Month and Anomalistic Year

Therefore after 300 such periods the difference should also be 300.

[Note: this is from a pocket calculator so decimal places are limited, but OK.]
Convert 1799 anomalistic years into days:
1799 * 365.25964 = 657102.09 days

Taking each in turn:
Evections in longitude = 31.81194 days
Evections in latitude = 32.280777 days
657102.09 / 31.81194 = 20655.832
657102.09 / 32.280777 = 20355.832
Difference = 300.000

Draconic Year = 346.62008 days
Full Moon Cycle = 411.78443 days
657102.09 / 346.62008 = 1895.7415
657102.09 / 411.78443 = 1595.7429
Difference = 299.9986

Draconic Month = 27.21222 days
Anomalistic Year = 27.554549 days
657102.09 / 27.21222 = 24147.316
657102.09 / 27.554549 = 23847.317
Difference = 299.999

And that’s the proof.

Footnote: the sum of nodal and apsidal cycles in the period should also be 300, as described in de Rop’s paper.

Draconic Years per nodal cycle = Tropical Years plus 1
Full Moon Cycles per apsidal cycle = Tropical Years minus 1

  1. Paul Vaughan says:

    5.99685290323073 = (0.0754402464065708)*(0.0745030006844627) / (0.0754402464065708 – 0.0745030006844627)
    ⌊ 5.99685290323073 / 1.00002638193018 ⌉ = ⌊5.99669469884984⌉ = 6
    5.99685290323073 / 6 = 0.999475483871788
    i.e. harmonic of 5.99685290323073 nearest 1.00002638193018 is 5.99685290323073 / 6 = 0.999475483871788
    1814.31362251033 = (1.00002638193018)*(0.999475483871788) / (1.00002638193018 – 0.999475483871788)

  2. Paul Vaughan says:

    Pleas Can. EU phi UN D-US the ream Mayan D-or?

    0.0748026830551271 = (1.00002638193018)*(0.0808503463381246) / (1.00002638193018 + 0.0808503463381246)
    8.85109350901809 = (0.0754402464065708)*(0.0748026830551271) / (0.0754402464065708 – 0.0748026830551271)

    Sure Can. do…..

    — –
    4.42585697034808 = (6.40939079526111)*(2.61803398874989) / (6.40939079526111 – 2.61803398874989)
    8.85171394069616 = 2*4.42585697034808

    4.42543810026188 = (1.61803398874989)*(1.18483367770519) / (1.61803398874989 – 1.18483367770519)
    8.85087620052376 = 2*4.42543810026188
    – —

    harmonic mean:
    8.85129505078776 = (8.85171394069616)*(8.85087620052376)/((8.85171394069616+8.85087620052376)/2)

    beat with LAC:
    19865.084604843 = (8.85129505078776)*(8.84735293159855) / (8.85129505078776 – 8.84735293159855)

    There’s the savage “London call UN” fear fact tor again: 10 times UN dread.
    The Clash = 0.000244240081 = %error.

    For QUICK reference:
    8.84735293159855 = (0.0754402464065708)*(0.0748024157783867) / (0.0754402464065708 – 0.0748024157783867)
    19.8650360864628 = (29.4474984673838)*(11.8626151546089) / (29.4474984673838 – 11.8626151546089)
    ‘or’ = french for gold

    UN O-Thor UN dread EU May recall:

    ⌊ 5.99685290323073 / 0.999978614647502 ⌉ = ⌊5.99698115078656⌉ = 6
    5.99685290323073 / 6 = 0.999475483871788
    i.e. harmonic of 5.99685290323073 nearest 0.999978614647502 is 5.99685290323073 / 6 = 0.999475483871788
    1986.46983643213 = (0.999978614647502)*(0.999475483871788) / (0.999978614647502 – 0.999475483871788)

    Con clues ya in:
    to the upscale reach of J-S.

  3. oldbrew says:

    Keeling and Whorf found the same period…

    The 1,800-year oceanic tidal cycle: A possible cause of rapid climate change

    ‘The greatest possible astronomical tide raising forces would
    occur if the moon and the sun were to come into exact mutual
    alignment with the earth at their closest respective distances (7).’


    Over 30,000 views of the K&W paper and/or its abstract.

  4. oldbrew says:

    ‘The extreme weather events of 535–536 were the most severe and protracted short-term episodes of cooling in the Northern Hemisphere in the last 2,000 years’


    De Rop quotes 1433 as a maximum, and this is about 1799/2 years earlier = the minimum.

  5. Paul Vaughan says:

    Cue Borg UN eyes: Cube bey’O

    So win samurai we’11 earn phine a11y from Chandealer QBO poll hear mow shh!UN:
    1000*((Φ^3)/4-D+Y+57T/4-A) ~= JS

    “If you look up into the eastern sky during the early morning of May 12, you’ll see Jupiter and Saturn lined up in the sky close enough to look like eyes over a wide, open-mouthed smile of the moon”

    A free ca11ed from “Obey UN” to say: Rush ya relief freely O-pen to “God’s will” homing in on the job: I’m not mice elf I don’t DO this….May kin a fuel love me”

    O-Bei’satUN comm.and UNjoy Hawaii.

    the total number of hours worked has plummeted to approximately 30 per cent. […] the pandemic is disproportionately impacting hourly workers compared to those on a salary.

    “It’s very unequally distributed. When you compare that to previous recessions like the 2008 financial crisis… that isn’t true in other recessions. [Job losses] weren’t as concentrated at the bottom end of the labour market”

    tr.ippi.n up hinterland voyeur US haunters on mount for ever rest:

    0.999978614638874 = 1 / (4/57*((J-S)/1000-(Φ^3)/4+D-Y+A))
    365.242188996849 = 1 / (365.25*4/57*((J-S)/1000-(Φ^3)/4+D-Y+A))

    “Eur. the right kind of dream R to fulfill my yen ‘or’ fan to C” — Put. Ban O Tar “Heart BRI car: don’t EU mess SAR own-D”

    -0.000000000863 = %error

    Free Will

    “The right “eye” will be the brighter Jupiter, and the left will be Saturn”

    Sew mill UN kneels my yen “don’t fee like $atUN bot tie ’em to dem.” We’R left with the right wei to comm.UN:nigh.gate BRI tor-bees at turn IT up hi dim ill UN knee AI high mile lion tug ever non-C ENSO R-shhippi kneel young “key pawn ROCkin in the free world”.

    “won’t look D-own
    won’t O-pen my eyes
    swing from the Chandler
    1 2 3 won too free dr.ink” — See ya

  6. Paul Vaughan says:

    Putin’ J-S in to well V-E T-DAY Mayphine a11y — Cure Act shh!UN

    0.999978614638874 = 1 / (4/57*((J-S)/1000+D+A-Y-(Φ^3)/4))
    0.999978614647502 = 1 / T

    365.242188996849 = 365.25 / (4/57*((J-S)/1000+D+A-Y-(Φ^3)/4))
    365.242189 = 365.25 / T

    -0.000000000863 = %error

  7. Paul Vaughan says:

    980: Land Sight

    ⌊ 19865.084604843 / 980.01081610826 ⌉ = ⌊20.2702707748978⌉ = 20
    19865.084604843 / 20 = 993.254230242151
    i.e. harmonic of 19865.084604843 nearest 980.01081610826 is 19865.084604843 / 20 = 993.254230242151
    73500.6758031973 = (993.254230242151)*(980.01081610826) / (993.254230242151 – 980.01081610826)

    ⌊ 19865.0360864628 / 980.00845444919 ⌉ = ⌊20.2702701147899⌉ = 20
    19865.0360864628 / 20 = 993.251804323141
    i.e. harmonic of 19865.0360864628 nearest 980.00845444919 is 19865.0360864628 / 20 = 993.251804323141
    73500.675803198 = (993.251804323141)*(980.00845444919) / (993.251804323141 – 980.00845444919)

  8. tallbloke says:


    A new turn for Earth’s rotation
    Andy Jackson
    Nature volume 465, pages39–40(2010)

    Earth’s spin rate varies with time. A six-year periodic signal in the planet’s core is partly responsible, and increases the interior magnetic-field strength to much higher levels than previously thought.

    The conservation of angular momentum is a powerful factor on a planet such as Earth. We can demonstrate the constant interchange of angular momentum between component parts, such as the liquid core, ocean, atmosphere and Moon, on a wide range of timescales. The interchange manifests itself to an observer on Earth’s surface as tiny variations in the planet’s rotation, or spin rate. At the two extremes of the measurable time periods — centuries and days — the oceanic tides and atmospheric winds, respectively, are the processes clearly mediating the interchange of angular momentum. However, on some medium timescales, outstanding questions remain. Not least is the origin of a strange peak in the spectrum of spin-rate variations at around 5–8 years1 — a feature that cannot be accounted for by atmospheric motions or by the ocean.

    An explanation of this signal is now presented by Gillet et al.2 (page 74 of this issue), and it involves intercommunication of angular momentum between Earth’s deep interior (the fluid core) and the overlying solid mantle. By identifying this process, the authors are able to determine a value for the strength of the magnetic field in the core that is much higher than previously thought.

  9. oldbrew says:

    Another oddity perhaps is that for every 14 nodal cycles, the difference between the numbers of apsidal and Saros cycles in the period is exactly 15.
    – – –
    Re 980: it’s 2/3rds of 1470.

  10. oldmanK says:

    Re the ‘Keeling and Whorf’ paper: Page1 col1 subject ‘Ice-Rafted Debris (IRD) Cycle’ , the source is VM29-191 from (b) Hematite-stained grains (HSG) identified in core MC52-VM29-191 interpreted to indicate ice-rafting events (Bond et al., 1997). This may also be found in the paper Glacier response to North Atlantic climate variability during the Holocene N. L. Balascio1,2, W. J. D’Andrea1, and R. S. Bradley3 link https://www.geo.umass.edu/climate/papers2/Balascio_ClimateofPast_2015.pdf

    What that proxy correlates to is something very different, and together correlate with several other sources of evidence. Especially the other proxy -C/N ratio. Here: https://melitamegalithic.wordpress.com/2018/06/29/searching-evidence-3/
    The three small peaks at 4375, 3550, and 2345bce, are not coincidence – several correlating proxies each.

  11. oldbrew says:

    Open Access
    Published: 08 May 2020
    Intradecadal variations in length of day and their correspondence with geomagnetic jerks

    Pengshuo Duan & Chengli Huang
    Nature Communications volume 11, Article number: 2273 (2020)

    ‘Here we report that the intradecadal variations present a significant 8.6-year harmonic component with an unexpected increasing phenomenon, besides a 6-year decreasing oscillation. More importantly, we find that there is a very good correspondence between the extremes of the 8.6-year oscillation with geomagnetic jerks.’


  12. oldbrew says:

    TB – 5.9 years is 2/3rds of the apsidal cycle of 8.85 years.

    1/3rd of a nodal cycle is about 6.2 years and they meet in the middle so to speak at 5.9967~ anomalistic years as per de Rop, when the sum of their two portions in the period is 1.

    Earth’s 6 year period or cycle linked to angular momentum (see link) does look a lot like that ‘lunar wobble’.

    ‘What is not yet understood is the source of the excitation of the torsional waves and the cause of the 6-year periodicity.’

  13. oldbrew says:

    Earth’s rotation variations: a wavelet analysis (2014)

    ‘The length‐of‐day for the period 1962–2012 confirms the presence of a prominent, robust 6‐year periodicity’


  14. oldbrew says:

    APRIL 21, 2015 FEATURE
    Why do measurements of the gravitational constant vary so much?

    (Phys.org)—Newton’s gravitational constant, G, has been measured about a dozen times over the last 40 years, but the results have varied by much more than would be expected due to random and systematic errors. Now scientists have found that the measured G values oscillate over time like a sine wave with a period of 5.9 years. It’s not G itself that is varying by this much, they propose, but more likely something else is affecting the measurements.

    As a clue to what this “something else” is, the scientists note that the 5.9-year oscillatory period of the measured G values correlates almost perfectly with the 5.9-year oscillatory period of Earth’s rotation rate, as determined by recent Length of Day (LOD) measurements. Although the scientists do not claim to know what causes the G/LOD correlation, they cautiously suggest that the “least unlikely” explanation may involve circulating currents in the Earth’s core. The changing currents may modify Earth’s rotational inertia, affecting LOD, and be accompanied by density variations, affecting G. [bold added]

    – – –
    Again, 5.9 years is 2/3rds of the lunar apsidal cycle of 8.85 years.
    5.9*1.5 = 8.85

  15. oldmanK says:

    Quote: “—and be accompanied by density variations, affecting G. ” But should not that effect equatorial but not polar. If I recall correctly from a previous look into this, the centrifugal effect was very small.

  16. oldbrew says:

    the “least unlikely” explanation

    Seems to suggest that any actual explanation would be deemed unlikely?

  17. Paul Vaughan says:

    23 UN dread?

    1149.63848537955 = (5.93130757730447)*(5.90086336719184) / (5.93130757730447 – 5.90086336719184)

    2299.27697075909 = (11.8626151546089)*(11.8017267343837) / (11.8626151546089 – 11.8017267343837)

    [R]Just spe11 it out bro. Get clear rants.

    from the double a11y harmonic means give UN AB11ove:
    5.90086336719184 = 2/3*8.85129505078776
    11.8017267343837 = 4/3*8.85129505078776

    D-rope’s ki11UN US with XRaise nightmare.