
A year after I wrote the original ‘Why Phi’ post explaining my discovery of the Fibonacci sequence links between solar system orbits and planetary synodic periods here at the Talkshop in 2013, my time and effort got diverted into politics. The majority of ongoing research into this important topic has been furthered by my co-blogger Stuart ‘Oldbrew’ Graham. Over the last eight years he has published many articles here using the ‘Why Phi’ tag looking at various subsystems of planetary and solar interaction periodicities, resonances, and their relationships with well known climatic periodicities such as the De Vries, Hallstatt, Hale and Jose cycles, as well as exoplanetary systems exhibiting the same Fibonacci-resonant arrangements.
Recently, Stuart contacted me with news of a major breakthrough in his investigations. In the space of a few hours spent making his calculator hot, major pieces of the giant jigsaw had all come together and brought ‘the big picture’ into focus. In fact, so much progress has been made that we’re not going to try to put it all into a single post. Instead, we’ll provide an overview here, and follow it up with further articles getting into greater detail.
One of the longest known climatic periods is the ~413,000 year cycle in the eccentricity of Earth’s orbit. This period has been found in various types of core sample data and discussed in many paleoclimatic science papers, along with cyclicities around 95, 112 and 124kyr, and shorter periods such as Earth’s obliquity variation, ~41Kyr and Earth’s equinoctial-precession periods of ~19 and ~23kyr. Stuart has discovered how all of these periods are related to each other and to the planetary orbits and their synodic conjunctions.
We’ve also been able to link these Earth Orientation Parameters and climatic periodicities to the planetary orbital and synodic conjunction periods which we believe are key to modulating solar activity. The basis for these were laid out in my 2011 post on Jupiter and Saturn’s motion and further developed with the valuable input of many Talkshop contributors, culminating in the solar variation models published by Rick Salvador and Ian Wilson in the 2013 special issue of Pattern Recognition in Physics.

Figure 1 below scratches the surface of what we have discovered. These relationships are all precise whole number ratios, not approximations. The red ‘Graham Cycle’ is a novel addition to previously known cyclic periods which connects the three areas of the figure; Solar-Planetary at the top, climatic periods bottom left, and Earth Orientation Parameters bottom right. Of note, are the ratios between the 60kyr Graham Cycle period and the periods in the three groups. They are mostly ratios of Fibonacci numbers or combinations of them. We know from a previous investigation that Fibonacci and phi (Golden Section) related periodicities tend to be stable and minimally resonant. It could be that the reason the 60kyr period hasn’t been found previously is due to it not showing up strongly in periodograms and other spectral analyses. Nonetheless, it’s an important period for our ‘Why Phi’ investigation and has a lot more connections than we wanted to clutter up Figure 1 with, as it already looks pretty busy!

Solar cycles
Starting with the upper ‘Solar planetary’ section of figure 1, Ian Wilson’s 2013 PRP paper noted that the Hale cycle and Jupiter-Saturn synodic (J-S) have a 193 year beat period, which is evident in Oxygen18 isotope data as well as Group Sunspot Numbers and 10Be ice core data. This was picked up by the Helmholtz Institute research lab and covered in our earlier post on the Solar Magnetic cycle. What they didn’t pick up on is the fact that the same 193year beat period can also be derived from the 178.8yr Jose cycle and the 2403yr Solar Inertial Motion (SIM) period.
This second route to the 193 year solar magnetic cycle is a novel result revealed in this post. Using the beat period formula of (A*B)/(A-B) = period, the solar inertial motion cycle (A) proposed by Charvatova of ~2403 tropical years and the Jose cycle (B) produces the same 193 year result. It was then possible to tie all this together in the 60 kyr cycle shown in the diagram.
There are 336 Jose and 25 SIM in 60 kyr which means the beat period produces 336-25 = 311 solar magnetic cycles of 193 years each. The number of Hale cycles in 60 kyr is given by the number of J-S minus the number of solar magnetic cycles. i.e. 3024-311 = 2713. It’s notable that 311 and 2713 are both prime numbers. Coupled with the fact that the number of J-S in 60Kyr is the Fibonacci multiple 144×21, we think this is a strong indicator that both 193yr and 60kyr periods are significant solar-planetary cyclic periods.
Support for the 60kyr period comes from Russia, where in 2017 A. S. Perminov and E. D. Kuznetsov produced a paper at at Ural Federal University, Yekaterinburg, entitled ‘Orbital Evolution of the Sun–Jupiter–Saturn–Uranus–Neptune Four-Planet System on Long-Time Scales’. This paper shows inter-related variations in the orbital parameters of the gas giants including antiphase changes in the eccentricities and orbital inclinations of Jupiter and Saturn at ~60kyr and in-phase changes in those parameters at ~400kyr, antiphase to Uranus. These ~400kyr variations are likely to be drivers of Earth’s 413kyr eccentricity cycle.

Original Russian Text © A.S. Perminov, E.D. Kuznetsov, 2018, published in Astronomicheskii Vestnik, 2018, Vol. 52, No. 3, pp. 239–259.
Planetary-climatic cycles
Moving on to the lower left ‘climatic and planetary cycles’ section of Figure 1,
The de Vries cycle is half of 21 J-S and is a prominent climatic cycle. It also links to other cycles through resonant harmonics: Hallstatt = 11 de Vries, J-S synodic precession cycle = 12 de Vries. 6 de Vries is 7 Jose cycles. 33 de Vries is 7 Eddy cycles. See also Why Phi? – Jupiter, Saturn and the de Vries cycle.
The lunar-terrestrial year (L-T) is 13 lunar months. Earth’s tropical year is used throughout this post. Whole numbers of both occur at 353 tropical years and 363 lunar years, forming 10 beats (363-353) of 35.3 years. An important period is 13 L-T, which is 2 Hallstatts and 11 de Vries cycle pairs (22 de Vries). This is 1/9th of the obliquity cycle. It is also 3x7x11 J-S. It follows that the 41kyr obliquity cycle is 3x7x11 Jose cycles, because the Jose cycle is 9 J-S. 3,7 and 11 are all Lucas numbers. We will post a separate article on the inter-relation of the Fibonacci and Lucas series, as they relate to orbital resonance. See also Sidorenkov and the lunar or tidal year (2016)
An explanation for the effect of the motion of the gas giants on these and other climatic periods is found in Nicola Scafetta’s 2020 paper ‘Solar Oscillations and the Orbital Invariant Inequalities of the Solar System’ discussed here at the talkshop.
EOP
At the lower right of Figure 1 we find Earth orientation parameters and associated cycles. To understand how these link to planetary periods we need to look at the motions of Jupiter and Saturn in particular. Kepler gives us this useful graphic in his book De Stella Nova (1606).

From an earlier post: ‘As successive great conjunctions occur nearly 120° apart, their appearances form a triangular pattern. In a series every fourth conjunction returns after some 59.8 years to the vicinity of the first. These returns are observed to be shifted by some 7–8°’. Wikipedia. [2019 version]. After 3 J-S the conjunctions have nearly described an exact triangle, but the start position has moved (precessed) slightly, by 60/7 degrees of precession of the J-S conjunction axis. It takes 42 of those (42*3 J-S) to complete the precession cycle in 2503 years. (41×61.051 y = 41×360 degrees movement of the axis).
The 413kyr eccentricity cycle is equivalent to 55*3 of these J-S synodic precession periods, and 6765 or 55×123 (Fibonacci and Lucas numbers) of the 61.051 360 degree periods. Additionally 413 kyr = 10 obliquity periods.
In the brown triangle: the 19 kyr and 23 kyr periods have a beat period of the 112kyr perihelion precession.
23 kyr is 10 Hallstatt cycles.
In the blue triangle: the 95 kyr (5×19 kyr) and 124 kyr (3 obliquities) have a beat period of 413 kyr i.e. Earth’s eccentricity cycle (mentioned in various research papers). Since our 95 kyr = 353×270 and our 124 kyr = 353×351, we find: (351×270) / (351-270) = 1170, and 1170*353 = 413010 years (the obliquity period).
Discussion
The 95 and 124kyr eccentricity cycles are linked with glacial periods. From Park and Maarsch (1993) paper ‘Plio—Pleistocene time evolution of the 100-kyr cycle in marine paleoclimate records’: “The DSDP 607 time scale is more favorable to an abrupt jump in amplitude for the 95-kyr δ18O envelope, but not in the 124-kyr envelope. Rather, long-period δ18O fluctuations appear phase-locked with the 124-kyr eccentricity cycle some 300-400 kyr prior to its growth in amplitude and phase-lock with the 95-kyr eccentricity cycle in the late Pleistocene.” Because the 124kyr period is 3x41kyr (obliquity period), this may help explain the change from glacial periods around 41kyr to around 100kyr.
The bi-modality of glacial cycles and the 95 and 124kyr cycles is one of the modes of variation mirrored between celestial cyclic motion and Earth climatic events. There are also many periods which are ‘quasi-cyclic’ and vary in length within bounds whose attractor nodes fit our phi-Fibonacci scheme. We are not claiming to have elucidated a deterministic and predictable system with our precise whole-number orbitally resonant ratios. We are offering this scheme as a potentially useful roadmap for further investigations into the intriguing numerical links between planetary orbits, synodic timings, planar inclinations, eccentricities, energy transfers and other celestial mechanical and orientation data.
As an example of how our scheme links shorter to longer term cycles, there are exactly 9 Jupiter Saturn conjunctions in the period of the Jose cycle of 178.8 years. There are 55x21x2 Jose cycles in the 413kyr eccentricity period. Experienced researchers like Paul Vaughan will immediately see that this product of multiple Fibonacci numbers resolves to the product of the first 6 prime numbers 1,2,3,5,7,11.
The solar system is organised by the forces of gravity and electro-magnetism into a log-normal distribution of which the Fibonacci series and Lucas series are examples which maintain the stability of the system. Resonance is minimised, but also utilised to transfer energy between orbits in order to resolve inequalities through resonance-forced changes to the eccentricity and inclination of orbits. These changes give rise to the cyclic changes in climatic factors on Earth observed at all timescales from the ~22yr Hale and ~60yr J-S trigon to the ~100kyr and 413kyr glaciation in core sample data and other indices.
Data sources and acknowledgements
Planetary data used is from NASA JPL which gives the Seidelmann values for orbital periods. Our thanks to Paul Vaughan for insisting on their use.
The periods we have calculated can all be reproduced using the ratios we have provided on Figure 1 and the NASA JPL values for the Jupiter, Saturn and Uranus orbital periods.
2317.99883398204 = 80*(√28+√163+√43+√19) ~= 2318
4635.99766796409 = 160*(√28+√163+√43+√19) ~= 2318 * 2
2384035.65182465 = beat(4635.99766796409,4627)
2384110.34604552 = beat(74626.0277273697,72361.0252351259) = 360*60*60 / 0.543599
La2011 Table 5
moderators: calculations caught in filter
_
easy hindsight:
https://tallbloke.wordpress.com/2013/01/09/tim-cullen-solar-system-holocene-lawler-events/
algebraic review
4270.51884168654 = 2/(1/11.8627021700857-3/29.4701958106261+1/84.0331316671926+1/164.793624044745)
49962.9015304794 = 1/(2/11.8627021700857-2/29.4701958106261-2/11.8619993833167+2/29.4571726091513)
4669.65169718707 = 2/(-3/11.8627021700857+1/29.4701958106261+1/84.0331316671926+1/164.793624044745+4/11.8619993833167-4/29.4571726091513)
simple alternate perspective
anomalistic
19.8549641949401 = 1/(1/11.8627021700857-1/29.4701958106261)
13.8125825263028 = 1/(1/11.8627021700857-1/84.0331316671926)
12.7828803855253 = 1/(1/11.8627021700857-1/164.793624044745)
9.95061383963391 = 2/(3/11.8627021700857-1/29.4701958106261-1/84.0331316671926-1/164.793624044745)
synodic
9.92945505108639 = 2/(+4/11.8619993833167-4/29.4571726091513)
4669.65169718707 = 2/(-3/11.8627021700857+1/29.4701958106261+1/84.0331316671926+1/164.793624044745+4/11.8619993833167-4/29.4571726091513)
link to net search result for perihelion 4670
_
moderators: other calculations caught in filter
4670 years
This is a test comment.
3 comments have vanished. Cause unknown
headin’ up the mountain now.
[mod] nothing in the WP spam filter now
Mayan 36750
15009.1608487337 = 5482096 / 365.25
36135.2404360745 = beat(25672.5169367299,15009.1608487337)
anomalistic
171.471519050756 = beat(164.793624044745,84.0331316671926) — Standish
tropical
171.444289533663 = beat(163.7232045,83.74740682) — Seidelmann
171.444286952825 = beat(163.723203285421,83.7474058863792) — ‘factsheet’
1079630.33859387 = beat(171.471519050756,171.444289533663) ; * 2 = 2159260.67718775
1079528.00372651 = beat(171.471519050756,171.444286952825) ; * 2 = 2159056.00745301
36750.2561948093 = beat(2159260.67718775,36135.2404360745)
36750.3154881725 = beat(2159056.00745301,36135.2404360745)
compare
Berger 1988 Table 4 (based on Berger 1978)
2166101.14285714 = beat(75259,72732)
36748.2810485504 = beat(2166101.14285714,36135.2404360745)
supplementary
lunisolar with general precession
13374613.0030966 = beat(25771.4533429313,25721.8900031954)
25672.5169367299 = axial(13374613.0030966,25721.8900031954)
no mystery left here
36135.2438440821 = axial(2159056.00745389,36750.3190131859)
15009.1614366987 = axial(36135.2438440821,25672.5169367299) = 5482096.21475421 / 365.25
bias hindsight “120k orbital solutions” tunes with round-off a typo f(UN)code’n’PRrhymesnot:
30031.0042303539 = beat(36750.3190131859,16526.3120307908)
15009.1624987455 = axial(36135.25,25672.5169367299) = 5482096.6026668 / 365.25
weather influence campaign or entertainment: unknown
Seidelmann short-model sidereal UJS bias clarification
30031 = 59*509 (lowest primorial+1 that’s not prime)
33052.4924754047 = harmean(36750,30031) ~= 33052.5
36750.0186045651 = beat(30031,16526.25)
36750.0196670027 — La(2004a,2010a)average
systematic bias review
19.8650360864628 = beat(29.4474984673838,11.8626151546089)
16.9122914926352 = harmean(29.4474984673838,11.8626151546089)
21.1746788367349 = beat(84.016845922161,16.9122914926352)
321.183589283115 = slip(21.1746788367349,19.8650360864628)
1908.55545325512 = slip(321.183589283115,19.8650360864628)
33052.6240615815 = slip(1908.55545325512,321.183589283115)
compare
15009.1608487337 = 5482096 / 365.25
36135.2404360745 = beat(25672.5169367299,15009.1608487337)
36750.3154881723 = beat(2159056.00745389,36135.2404360745)
33052.6200736723 = harmean(36750.3154881723,30031)
again: the bias in the short-duration models is systematic
it could easily be corrected by experts before publication
it isn’t
why?
unknown
supplementary
30031 = 13*11*7*5*3*2 + 1 = 13# + 1 = 59 * 509
36750.3253483715 = beat( 30031 , 33052.6240615815 / 2)
36135.2499689834 = axial(2159056.00745389,36750.3253483715) ~= 36135.25
15009.1624933944 = axial(36135.2499689834,25672.5169367299) = 5482096.6007123 / 365.25
recall:
33053√Φ/8 ~= 5256; 5256√Φ/8 ~= 836
typo: “/√Φ” not “√Φ”
serpent no. anomalistic UN guidance
Lunisolar Bias
general & lunisolar precession
25746.6478202264 = harmean(25771.4533429313,25721.8900031954)
NASA ‘factsheet’ tropical
11.8619854620833 = beat(25746.6478202264,11.8565229295003)
29.4571820908507 = beat(25746.6478202264,29.4235181382615)
19.858866774147 = beat(29.4571820908507,11.8619854620833)
60.9467636123559 = slip(29.4571820908507,11.8619854620833)
883.349939238609 = slip(60.9467636123559,19.858866774147) ; / 2 = 441.674969619304
600.349139225674 = harmean(936.955612197409,441.674969619304) ; * 4 = 2401.3965569027
835.54616509501 = beat(936.955612197409,441.674969619304)
biased (short-duration) Seidelmann sidereal model:
19.8650360864628 = beat(29.4474984673838,11.8626151546089)
61.0464822565173 = slip(29.4474984673838,11.8626151546089)
835.546575435631 = slip(61.0464822565173,19.8650360864628)
2401.00140862743 = harmean(2401.3965569027,2400.60639037357)
2401.00140862743 = 7.00000102669615 ^ 4
supplementary anomalistic (Standish 1992 Table 2a) review
936.955612197409 = 1/(-2/11.8627021700857+5/29.4701958106261)
4270.51884168654 = 2/(1/11.8627021700857-3/29.4701958106261+1/84.0331316671926+1/164.793624044745)
1536.74746987137 = harmean(4270.51884168654,936.955612197409)
2400.60639037357 = beat(1536.74746987137,936.955612197409)
Why aren’t the biased models unbiased before publication?
Unknown.
25770.0359146014 = 360*60*60/50.290966 — widely cited general precession rate
25722.1631216381 = 360*60*60/50.38456501 — W94 lunisolar precession
25746.0772642216 = harmean(25770.0359146014,25722.1631216381)
13846300.2974074 = beat(25770.0359146014,25722.1631216381)
25674.4678646892 = axial(13846300.2974074,25722.1631216381)
36131.3759941719 = beat(25674.4678646892,15009.1608487337) — spicy whether
15009.1608487337 = 5482096 / 365.25
11.8619855831937 = beat(25746.0772642216,11.8565229295003)
29.4571828377274 = beat(25746.0772642216,29.4235181382615)
19.858866774147 = beat(29.4571828377274,11.8619855831937)
60.9467604151707 = slip(29.4571828377274,11.8619855831937)
883.351954142505 = slip(60.9467604151707,19.858866774147)
835.54977055391 = beat(936.955612197409,441.675977071252)
36130.8944646852 = beat(29.447498973306,29.4235181382615) — Sidorenkov
36131.2752839187 = harmean(36131.65611118,36130.8944646852) —- or
36131.65611118 = beat(29.4474984673838,29.4235181382615) — Seidelmann
29.447499867163 = beat(36131.3759941719,29.42351935)
11.862615400484 = 2 * beat( 835.54977055391 , 29.447499867163 / 5 )
blur 64k mixmmod11sample
23093.6961437637 = beat(11.862615400484,11.85652502)
63999.6554631887 = beat(36131.3759941719,23093.6961437637) ~= 64k
un weather seidelenkov or sidormann
11.8626149080812 = 2 * beat( 835.54977055391 , 29.4474986534485 / 5 )
29.4474986534485 = beat(36131.3759941719,29.4235181382615)
Bound 2401 = 7^4 with surely enough error = 0.000014667% J-aims.
2362 notes
comparing systematically biased models
(which can be systematically unbiased)
Seidelmann (1992) & Sidorenkov (2017) share superficial similarity
however, lots of detail differences are noteworthy
here’s one to start with
Seidelmann (1992) sidereal review
=
Jovian V-E 5256 Ratio Summary
J:U:S:N = 1:2:16:31
J: 1 = ⌊0.999878363433384⌉ = ⌊5256 / 5256.6393995685⌉
S: 16 = ⌊16.0035845857963⌉ = ⌊5256 / 328.426420457382⌉
U: 2 = ⌊1.99911615294986⌉ = ⌊5256 / 2629.16188848974⌉
N: 31 = ⌊31.0045597971227⌉ = ⌊5256 / 169.52345185329⌉
J: 5256.6393995685 = 1 * 5256.6393995685
S: 5254.8227273181 = 16 * 328.426420457382
U: 5258.32377697949 = 2 * 2629.16188848974
N: 5255.227007452 = 31 * 169.52345185329
=
Sidorenkov analogs:
5256 / x =
1.11245625125401
16.039288833368
1.98119882107214
31.0141327829003
4724.68017872629 = 1 * 4724.68017872629 — carefully take note of something about this one
5243.12523289982 = 16 * 327.695327056239
5305.87838443763 = 2 * 2652.93919221881
5253.60490137049 = 31 * 169.471125850661
even more perfect jupiter-saturn framing — part i
19.8650352019356 = beat(29.447498973306,11.8626149212868)
9.9325176009678 = 19.8650352019356 / 2
4.9662588004839 = 19.8650352019356 / 4
16.9122913389518 = harmean(29.447498973306,11.8626149212868)
8.4561456694759 = axial(29.447498973306,11.8626149212868)
4.22807283473795 = 8.4561456694759 / 2
2.11403641736897 = 8.4561456694759 / 4
6.56961469713012 = axial(14.723749486653,11.8626149212868)
10.7425999661684 = beat(16.9122913389518,6.56961469713012)
5.3712999830842 = 10.7425999661684 / 2
2.6856499915421 = 10.7425999661684 / 4
4.73161069513687 = axial(16.9122913389518,6.56961469713012)
2.36580534756843 = 4.73161069513687 / 2
1.18290267378422 = 4.73161069513687 / 4
131.716314078385 = slip(19.8650352019356,10.7425999661684)
65.8581570391927 = slip(19.8650352019356,5.3712999830842)
50.0715810605726 = slip(19.8650352019356,2.6856499915421)
100.143162121145 = slip(19.8650352019356,4.73161069513687)
50.0715810605727 = slip(19.8650352019356,2.36580534756843)
96.1826326350372 = slip(19.8650352019356,1.18290267378422)
supplementary
61.0464717290582 = slip(29.447498973306,11.8626149212868)
835.550927105133 = slip(61.0464717290582,19.8650352019356)
even more perfect jupiter-saturn framing — part ii
basic
2432.00637869116 = slip(100.143162121145,19.8650352019356)
1216.00318934558 = slip(100.143162121145,9.9325176009678)
1216.00318934592 = slip(50.0715810605726,9.9325176009678)
608.00159467279 = slip(100.143162121145,4.9662588004839)
608.00159467296 = slip(50.0715810605726,4.9662588004839)
608.001594672738 = slip(96.1826326350372,19.8650352019356)
304.000797336369 = slip(96.1826326350372,9.9325176009678)
compound
1216.00318934576 = slip(356.529955086161,131.716314078385)
1216.00318934575 = slip(208.887731776281,65.8581570391927)
1216.00318934571 = slip(208.887731776281,50.0715810605726)
1216.00318934591 = slip(104.44386588814,50.0715810605726)
608.00159467288 = slip(178.26497754308,65.8581570391927)
1216.00318934554 = slip(104.443865888141,50.0715810605726)
–
a little more wholesome than “perfect jupiter-saturn framing”
2432.00637869017 = 2/(27/11.8626149212868-67/29.447498973306)
608.001594672542 = 1/(54/11.8626149212868-134/29.447498973306)
19.0000498335169 = 1/(1728/11.8626149212868-4288/29.447498973306)
19 ~= 1/(1728/j-4288/s)
431 ~= 1/(-89/j+221/s)
431.004429758615 = 1/(-89/11.8626149212868+221/29.447498973306)
862.008859517229 = 2/(-89/11.8626149212868+221/29.447498973306)
basic
862.008859517104 = slip(131.716314078385,4.22807283473795)
431.004429758552 = slip(131.716314078385,2.11403641736897)
431.004429758552 = slip(65.8581570391927,2.11403641736897)
compound
862.008859517073 = slip(356.529955086161,65.8581570391927)
862.008859517088 = slip(310.94560772299,131.716314078385)
862.008859517088 = slip(155.472803861495,131.716314078385)
431.004429758544 = slip(155.472803861495,65.8581570391927)
Theorrery Skeptic
Doubtful weather there’s a trustworthy political party (or orrery).
JEV ingredients (Bollinger 1952 method)
1.59868960469858 = beat(1.00001741273101,0.615197262149213)
0.799344802349289 = 1.59868960469858 / 2
0.399672401174645 = 1.59868960469858 / 4
0.761766202327597 = harmean(1.00001741273101,0.615197262149213)
0.380883101163799 = axial(1.00001741273101,0.615197262149213)
0.190441550581899 = 0.380883101163799 / 2
0.0952207752909496 = 0.380883101163799 / 4
0.814040380789063 = beat(11.8626149212868,0.761766202327597)
0.407020190394532 = 0.814040380789063 / 2
0.203510095197266 = 0.814040380789063 / 4
0.715800563194352 = axial(11.8626149212868,0.761766202327597)
0.357900281597176 = 0.715800563194352 / 2
0.178950140798588 = 0.715800563194352 / 4
44.2785528962259 = slip(1.59868960469858,0.814040380789063)
22.1392764481129 = slip(1.59868960469858,0.407020190394532)
11.0696382240565 = slip(1.59868960469858,0.203510095197266)
6.84872428662588 = slip(1.59868960469858,0.715800563194352)
3.42436214331294 = slip(1.59868960469858,0.357900281597176)
24.1185188101801 = slip(1.59868960469858,0.178950140798588)
thus:
350.939503542819 = slip(22.1392764481129,0.761766202327597)
207.994354394449 = slip(44.2785528962259,0.399672401174645)
207.994354394443 = slip(73.0136987128728,44.2785528962259)
146.027397425746 = slip(44.2785528962259,1.59868960469858)
73.0136987128728 = slip(22.1392764481129,0.799344802349289)
89.3948929753992 = slip(44.2785528962259,0.190441550581899)
88.5571057924501 = harmean(89.3948929753992,87.7348758857048) ; 44.2785528962251 = axial
87.7348758857048 = slip(22.1392764481129,0.190441550581899)
4724.68017871817 = beat(89.3948929753992,87.7348758857048)
4724.68017872629 = slip(44.2785528962259,0.0952207752909496)
4724.68017870897 = slip(350.939503542819,44.2785528962259)
4724.68017872737 = slip(89.3948929753992,44.2785528962259)
4724.68017870897 = slip(87.7348758857048,44.2785528962259)
2362.34008935448 = slip(350.939503542819,22.1392764481129) ——— 700,44
2362.34008936368 = slip(89.3948929753992,22.1392764481129) ——— notice
2362.34008935448 = slip(87.7348758857048,22.1392764481129) ——— anything
1181.17004467724 = slip(350.939503542819,11.0696382240565)
1181.17004468184 = slip(89.3948929753992,11.0696382240565)
1181.17004467724 = slip(87.7348758857048,11.0696382240565)
980.292586153988 = slip(292.054794851491,88.5571057924518) ; 292 = 163+67+43+19
490.146293076994 = slip(146.027397425746,44.2785528962259)
245.073146538497 = slip(73.0136987128728,22.1392764481129)
with NASA Horizons 1929.72222222222 sidereal
JSUN orbital invariant (long-run wide-guassian central limit)
2320.40158057186 = axial(130705.116382548,2362.3400894)
compare (Horizons 1929.72222222222 JSUN orbital invariants only — without Sidorenkov JEV)
2320.22208286955 = axial(130705.116382548,2362.15404490606)
notin’ a few interresstin’ properties not shared by Seidelmann & Sidorenkov
˚Knot f(eel)in’PRsure’22DC(44)ide weather appearance orrery’a11 IT
/a typo h/tM11
130704.452624679 = beat(173901.37537739,74619.9907876555)
73: lowest prime congruent to 1 mod 24
73 = average(19,43,67,163) ; 19 = x mod 24 for x = 19, 43, 67, 163
5256 = 7920 – 2400 – 240 – 24
Perfect Contrusst?
Simple Reason: Center Unknown
Here’s the backstory on how the lunisolar bias stood out distinctly.
One – and only one – of the many parameter lists fits the criterion.
“[…] the largest known number not of the form a^2+s with s a semiprime”
883.339228237648 = harmean( 936.716909730743 , 835.716909730743 )
883.339228237648 = harmean ( 101 + C√φ , C√φ ) = 2 / ( 1/(101+C√φ) + 1/(C√φ) )
101: lowest odd prime Mertens zero-crossing
_____________
supplementary
1/(
5/beat( harmean(general,lunisolar precession) , Saturn tropical) –
2/beat( harmean(general,lunisolar precession) , Jupiter tropical)
)
low
Seidelmann (1992) tropical
883.332192747065 — LLR
883.334207569974
~Center:
883.342073334256 = grand harmonic mean
high
NASA ‘factsheet’ tropical
883.349939238609 — LLR
883.351954142505
Diversifying Bidecadal Chandler Resonance Diagnostics
Seidelmann (1992) short-duration (biased) sidereal
6.46811773461345 = beat(1.18290267954072,1.00001743371442)
Standish (1992) nodal
19.8630730877524 = beat(29.4511026866654,11.862499899747)
bias diagnostics
280.076577904465 = slip(19.8630730877524,6.46811773461345)
2790.5838772567 = slip(280.076577904465,19.8630730877524)
Standish (1992) anomalistic orbital invariant (0=-2+5+3-6)
2790.83682251396 = 1/(-2/11.8627021700857+5/29.4701958106261+3/84.0331316671926-6/164.793624044745)
reverse-engineering sidereal earth estimate from jovian anomalistic:
1.00001743139444 = 14/(2/11.8627021700857-5/29.4701958106261-3/84.0331316671926+6/164.793624044745+84/11.8626151546089+140/29.4474984673838+43/11.862499899747-43/29.4511026866654)
Experts failed us severely more than a decade ago.
They harassed us viciously and relentlessly without ever volunteering the most important information.
Why? Unknown.
compare – using Standish (1992) short-duration (biased) sidereal earth
6.46811767349981 = beat(1.18290267954072,1.0000174322536)
280.076463317364 = slip(19.8630730877524,6.46811767349981)
2790.74314407649 = slip(280.076463317364,19.8630730877524)
Anomalistic QBO Halstatt
19.8549641949401 = beat(29.4701958106261,11.8627021700857) —– Standish (1992) anomalistic
16.9161211952138 = harmean(29.4701958106261,11.8627021700857)
8.45806059760692 = axial(29.4701958106261,11.8627021700857)
6.57189983390616 = axial(14.735097905313,11.8627021700857)
9.46619163320184 = harmean(16.9161211952138,6.57189983390616)
4.73309581660092 = axial(16.9161211952138,6.57189983390616)
2.36654790830046 = 4.73309581660092 / 2
1.18327395415023 = 4.73309581660092 / 4
203.72293652095 = slip(19.8549641949401,9.46619163320184)
50.9307341302375 = slip(19.8549641949401,2.36654790830046) ——————–
4724.17556802657 = slip(203.72293652095,16.9161211952138)
2362.08778401328 = slip(203.72293652095,8.45806059760692)
4724.17556802739 = slip(50.9307341302375,16.9161211952138)
2362.0877840137 = slip(50.9307341302375,8.45806059760692) ——————– 2362
_
2320.15794438421 = axial(130704.452624679,2362.0877840137)
2320.15815353613 = axial(130705.116382548,2362.0877840137)
anomalistic JEV intro
0.761769224080824 = harmean(1.0000262476142,0.615197860179071)
0.715803548953639 = axial(11.8627021700857,0.761769224080824)
6.84967828238651 = slip(1.59867106414771,0.715803548953639)
835.563824740778 = slip(6.84967828238651,0.761769224080824)
1.59867106414771 = beat(1.0000262476142,0.615197860179071)
24.0670906604158 = slip(6.84967828238651,1.59867106414771)
24.067904774739 = ⌊(e^√7π)^(1/p)⌉^p – e^√7π for p=2,3,4,6,12
Anomalistic “4670 years”
19.8549641949401 = beat(29.4701958106261,11.8627021700857)
16.9161211952138 = harmean(29.4701958106261,11.8627021700857)
111.307357343015 = harmean(164.793624044745,84.0331316671926)
19.9477072615632 = beat(111.307357343015,16.9161211952138) ; / 2 = 9.97385363078158
4270.51884168622 = slip(19.9477072615632,19.8549641949401)
8.45806059760692 = axial(29.4701958106261,11.8627021700857)
55.6536786715076 = axial(164.793624044745,84.0331316671926)
9.97385363078158 = beat(55.6536786715076,8.45806059760692)
2135.25942084311 = slip(19.8549641949401,9.97385363078158)
4670.79911370059 = slip(2135.25942084311,19.8549641949401)
invariant 0=1-3+1+1
2135.25942084327 = 1/(1/11.8627021700857-3/29.4701958106261+1/84.0331316671926+1/164.793624044745)
What’s in anomalistic “mode 11”? by US Diss Cover:
16.9161211952138 = harmean(29.4701958106261,11.8627021700857)
19.8549641949401 = beat(29.4701958106261,11.8627021700857) ; / 2 = 9.92748209747005
60.8544553085225 = slip(29.4701958106261,11.8627021700857)
thus base what follows with Standish (1992) anomalistic
_
compare & contrast
—-
1.
Seidelmann (1992) short-duration sidereal
11.8626151546089
29.4474984673838
84.016845922161
164.791315640078
29.3625733662893 = harmonic mean
19.8060547427555 = axial(60.8544553085225,29.3625733662892)
66.1523612443866 = slip(28.3699051701599,19.8549641949401)
8040.33760745923 = slip(19.8549641949401,19.8060547427555)
172978.748617708 = slip(8040.33760745923,19.8549641949401) —– further notes be low
86489.3743088542 = slip(8040.33760745923,9.92748209747005)
56.7398103403199 = beat(60.8544553085225,29.3625733662892) ; / 2 = 28.3699051701599
1182607.44767058 = slip(172978.748617708,66.1523612443866) ; * 2 = 2365214.89534115
202615.037187354 = slip(86489.3743088542,66.1523612443866) ; * 2 = 405230.074374708
—-
2.
Sidorenkov (2017)
11.8626149212868
29.447498973306
84.0168377823409
164.791321013005
29.3625729287642 = harmonic mean
analogUS (to 1. above) calculations rightly left as an exercise in undersstandin’ 4 those curryUS’n’willin’ (who’ll thus ‘no. who’ tune$ what – CO[$] ITsnot what y/n0boughtWHOyen owe…)
—-
supplementary
2364963.50364963 = beat(74619.9907876555,72337.575351641)
1182481.75182481 = beat(73001.7461837436,68756.9632341238)
405629.613215262 = beat(304406.35241565,173901.37537739)
172826.54615749 = beat(68756.9632341238,49188.0779029847)
173901.37537739 = 1 / g_2
—
in agree mint with us?
Weather 5256 & 4724 are (no. doubt?) in agree mean T.
JPLat0˚Know? Anomalistic weather variant. Mnemonic in-put taxicab:
Seidelmann (1992) tropical
4.72860952101702 = 2/(3/11.85652502+5/29.42351935) = 1727.12462755147 d ~= 1727
2.36430476050851 = 1/(3/11.85652502+5/29.42351935) = 863.562313775734 d
1.18215238025426 = 1/(6/11.85652502+10/29.42351935) = 431.781156887867 d
0.591076190127128 = 1/(12/11.85652502+20/29.42351935) = 215.890578443933 d
“Euler started to use the letter e for the constant in 1727 or 1728 […]”
Sidorenkov (2017)
4.73161069513687 = 2/(3/11.8626149212868+5/29.447498973306) = 1728.22080639874 d
2.36580534756843 = 1/(3/11.8626149212868+5/29.447498973306) = 864.110403199371 d
1.18290267378422 = 1/(6/11.8626149212868+10/29.447498973306) = 432.055201599685 d
0.591451336892109 = 1/(12/11.8626149212868+20/29.447498973306) = 216.027600799843 d
Seidelmann (1992) sidereal short-duration model
4.73161071816289 = 2/(3/11.8626151546089+5/29.4474984673838) = 1728.220814809 d
2.36580535908144 = 1/(3/11.8626151546089+5/29.4474984673838) = 864.110407404498 d
1.18290267954072 = 1/(6/11.8626151546089+10/29.4474984673838) = 432.055203702249 d
0.591451339770361 = 1/(12/11.8626151546089+20/29.4474984673838) = 216.027601851124 d
Seidelmann (1992) synodic
4.73208801967701 = 2/(3/11.8619993833167+5/29.4571726091513) = 1728.39514918703 d
2.36604400983851 = 1/(3/11.8619993833167+5/29.4571726091513) = 864.197574593514 d
1.18302200491925 = 1/(6/11.8619993833167+10/29.4571726091513) = 432.098787296757 d
0.591511002459627 = 1/(12/11.8619993833167+20/29.4571726091513) = 216.049393648379 d
Horizons 1929.72222222222 sidereal (wide-Guassian sample-center)
4.73208337117502 = 2/(3/11.8619848807702+5/29.4571542179636) = 1728.39345132168 d
2.36604168558751 = 1/(3/11.8619848807702+5/29.4571542179636) = 864.196725660838 d
1.18302084279375 = 1/(6/11.8619848807702+10/29.4571542179636) = 432.098362830419 d
0.591510421396877 = 1/(12/11.8619848807702+20/29.4571542179636) = 216.049181415209 d
Standish (1992) nodal
4.73181582715489 = 2/(3/11.862499899747+5/29.4511026866654) = 1728.29573086832 d
2.36590791357745 = 1/(3/11.862499899747+5/29.4511026866654) = 864.147865434162 d
1.18295395678872 = 1/(6/11.862499899747+10/29.4511026866654) = 432.073932717081 d
0.591476978394361 = 1/(12/11.862499899747+20/29.4511026866654) = 216.03696635854 d
Standish (1992) anomalistic
4.73309581660092 = 2/(3/11.8627021700857+5/29.4701958106261) = 1728.76324701349 d ~= 1729
2.36654790830046 = 1/(3/11.8627021700857+5/29.4701958106261) = 864.381623506743 d
1.18327395415023 = 1/(6/11.8627021700857+10/29.4701958106261) = 432.190811753372 d
0.591636977075115 = 1/(12/11.8627021700857+20/29.4701958106261) = 216.095405876686 d
Solves Longstanding Curiosity
This is highly technical but precise.
26256.8112288057 = slip(8040.33760745923,16.9161211952138)
306006.586378586 = slip(26256.8112288057,66.1523612443866)
The original curiosity? Systematically be low.
397906.462823915 = beat(306006.586378586,172978.748617708) ; / 4 =
99476.6157059787
99476.8155050052 = beat(16.9161211952138,16.9132450828034)
16.9132450828034 = harmean(29.4571309198874,11.861990807677) —- Standish (1992) sidereal
(further) clarifies lunisolar bias; well-paid technicians “No!” managers can unbias (hierarchically nested) models for clean, simple public presentation
_
supplementary
398.773134809729 = slip(56.7398103403199,19.8549641949401)
935.113131399583 = slip(398.773134809729,16.9161211952138)
936.033465118244 = harmean(936.955612197393,935.113131399583) ~= 936.0
for future reference
2365.09305036237 = slip(398.773134809729,9.92748209747005)
4730.18610072473 = slip(398.773134809729,19.8549641949401)
Adjust Sidorenkov (2017) earth sidereal year estimate (which looks like a long-duration estimate) to 1.00001743390371 = (1-(1/240)^1)^(0/1)/(1-(1/240)^2)^(2/2)/(1-(1/240)^3)^(3/3)/(1-(1/240)^4)^(2/4)/(1-(1/240)^5)^(5/5)/(1-(1/240)^6)^(1/6) to match SUNEV 5256 (but not JEV 5256) more closely than Seidelmann (1992).
At this point a very large volume of calculations needs to be presented to crystallize the lunisolar bias in detail. Presently this isn’t feasible.
To complete the transformation:
11.862615918328 = 2/(1/((φ^22+1/11)^(e/11+1/22))+5/((1-(1/240)^1)^(0/1)/(1-(1/240)^2)^(2/2)/(1-(1/240)^3)^(3/3)/(1-(1/240)^4)^(2/4)/(1-(1/240)^5)^(5/5)/(1-(1/240)^6)^(1/6))-3/0.615197262149213)
0.761766208470514 = harmean(1.00001743390371,0.615197262149213)
0.814040383108898 = beat(11.862615918328,0.761766208470514)
1.59868955058708 = beat(1.00001743390371,0.615197262149213)
44.2784630136991 = slip(1.59868955058708,0.814040383108898)
351.268593378986 = slip(44.2784630136991,0.761766208470514)
5256.18499467858 = slip(351.268593378986,44.2784630136991)
alternately:
0.380883104235257 = axial(1.00001743390371,0.615197262149213) ; / 4 = 0.0952207760588143
5256.18499465625 = slip(44.2784630136991,0.0952207760588143)
100ka note
19.8549641949401 = beat(29.4701958106261,11.8627021700857) —- Standish (1992) anomalistic
19.8589101021728 = beat(29.4571726091513,11.8619993833167) —– Seidelmann (1992) synodic
99925.8030607636 = beat(19.8589101021728,19.8549641949401)
99972.391587704 = harmean(100019.023576957,99925.8030607636) ———— v ————–
100019.023576957 = beat(16.9161211952138,16.9132606717144)
16.9132606717144 = harmean(29.4571726091513,11.8619993833167) —- Seidelmann (1992) synodic
16.9161211952138 = harmean(29.4701958106261,11.8627021700857) — Standish (1992) anomalistic
8.45806059760692 = axial(29.4701958106261,11.8627021700857) —– Standish (1992) anomalistic
_
55.6536786715076 = axial(164.793624044745,84.0331316671926) —– Standish (1992) anomalistic
111.307357343015 = harmean(164.793624044745,84.0331316671926) — Standish (1992) anomalistic
171.471519050756 = beat(164.793624044745,84.0331316671926)
19.9477072615632 = beat(111.307357343015,16.9161211952138) —– Bollinger (1952) method
9.97385363078158 = beat(55.6536786715076,8.45806059760692)
4270.51884168622 = slip(19.9477072615632,19.8549641949401) —- orbital invariant
2135.25942084311 = slip(19.8549641949401,9.97385363078158) —- orbital invariant
49831.9228185121 = slip(4270.51884168622,19.8549641949401)
4670.79911370059 = slip(2135.25942084311,19.8549641949401) —- “4670 years” (review)
45051.2652209889 = slip(4270.51884168622,8.45806059760692)
99973.0172242633 = slip(45051.2652209889,4270.51884168622) —————- ^ ————-
Selected Algebra
Seidelmann (1992) synodic:
11.8619993833167, 29.4571726091513
Standish (1992) anomalistic:
11.8627021700857, 29.4701958106261, 84.0331316671926, 164.793624044745
_
“4670 years”
4669.65169718707 = 2/(-3/11.8627021700857+1/29.4701958106261+1/84.0331316671926+1/164.793624044745+4/11.8619993833167-4/29.4571726091513)
4670.79911381622 = 1/(107/11.8627021700857-323/29.4701958106261+108/84.0331316671926+108/164.793624044745)
_
“100 kiloyears”
99972.3915878471 = 4/(1/11.8627021700857-3/29.4701958106261-1/11.8619993833167+3/29.4571726091513)
99973.0183503139 = 1/(2766/11.8627021700857-8342/29.4701958106261+2777/84.0331316671926+2777/164.793624044745)
_
“41 kiloyears”
derivation
8.45806059760692 = axial(29.4701958106261,11.8627021700857) ; / 4 =
2.11451514940173
45051.2652209889 = slip(4270.51884168622,8.45806059760692) ; / 4 =
11262.8163052472 = slip(4270.51884168622,2.11451514940173)
41002.979235297 = slip(11262.8163052472,2135.25942084311)
summary:
41002.9789528914 = 1/(-5029/11.8627021700857+15167/29.4701958106261-5049/84.0331316671926-5049/164.793624044745)
_
4724 years &
2362 years
derivations
14.6844304038441 = axial(111.307357343015,16.9161211952138) ; / 4 =
3.67110760096102
48.6117359109827 = slip(19.8549641949401,3.67110760096102)
384.86912152873 = slip(48.6117359109827,16.9161211952138)
4724.17556801612 = slip(2135.25942084311,384.86912152873)
19.9477072615632 = beat(111.307357343015,16.9161211952138) ; / 4 =
4.98692681539079
1067.62971042156 = slip(19.8549641949401,4.98692681539079)
4724.17556801612 = slip(1067.62971042156,384.86912152873)
192.434560764365 = slip(48.6117359109827,8.45806059760692)
2362.08778400806 = slip(1067.62971042156,192.434560764365)
algebra:
2362.08778401334 = 1/(31/11.8627021700857-77/29.4701958106261)
4724.17556802668 = 2/(31/11.8627021700857-77/29.4701958106261)
tropical
4724 years &
2362 years (orbital invariant: 0=-2+5+3-6)
Seidelmann (1992) tropical
2361.92512664087 = 1/(-2/11.85652502+5/29.42351935+3/83.74740682-6/163.7232045)
4723.85025328173 = 2/(-2/11.85652502+5/29.42351935+3/83.74740682-6/163.7232045)
NASA ‘factsheet’ tropical
2362.05130068208 = 1/(-2/11.8565229295003+5/29.4235181382615+3/83.7474058863792-6/163.723203285421)
4724.10260136417 = 2/(-2/11.8565229295003+5/29.4235181382615+3/83.7474058863792-6/163.723203285421)
adjusting Seidelmann (1992) short-duration sidereal earth to a long-duration 4724 year tuning:
4723.99999667307 = 1/(-693.5/0.615197263396975+1166.5/1.00001741532595-465/11.8626151546089)
1.00001741532595 = 365.256360947803 days ; compare:
1.0000174152119 = 365.256360906146 days —- Standish (1992) sidereal
easy hindsight
supplementary notes on geophysical 64 year structure previously illustrated & explored
Standish nodal with day
3.93839482956483 = slip(1.00001071395229,0.0027378507871321)
63.8858575898369 = slip(3.93839482956483,1.00001071395229) ~= 64 year
Meeus & Savoie tropical with day
4.12891838459878 = slip(0.999978614647502,0.0027378507871321)
32.0054607170862 = slip(4.12891838459878,0.999978614647502) ~= 32 year
supplementary note on 26 (& 52) year geophysical structure(s) previously noted
Standish anomalistic with day
3.85237502099482 = slip(1.0000262476142,0.0027378507871321)
26.077823955957 = slip(3.85237502099482,1.0000262476142) ~= 26 year
JSEV tropical (Seidelmann 1992)
1.59868953279706 = beat(0.99997862,0.61518257)
0.799344766398529 = 1.59868953279706 / 2
0.399672383199264 = 1.59868953279706 / 4
0.761743683794994 = harmean(0.99997862,0.61518257)
0.380871841897497 = axial(0.99997862,0.61518257)
0.190435920948749 = 0.380871841897497 / 2
0.0952179604743743 = 0.380871841897497 / 4
61.0914225103732 = slip(29.42351935,11.85652502)
0.771361726706669 = beat(61.0914225103732,0.761743683794994)
0.385680863353334 = 0.771361726706669 / 2
0.192840431676667 = 0.771361726706669 / 4
1.50472508020829 = harmean(61.0914225103732,0.761743683794994)
0.752362540104143 = axial(61.0914225103732,0.761743683794994)
0.376181270052072 = 0.752362540104143 / 2
0.188090635026036 = 0.752362540104143 / 4
12.800522799798 = slip(1.59868953279706,0.752362540104143)
6.40026139989901 = slip(1.59868953279706,0.376181270052072)
3.2001306999495 = slip(1.59868953279706,0.188090635026036)
1859.26427454788 = slip(12.800522799798,1.59868953279706)
1859.26427454788 = slip(6.40026139989901,1.59868953279706)
1859.26427454788 = slip(3.2001306999495,1.59868953279706)
929.632137273939 = slip(12.800522799798,0.799344766398529)
929.632137273939 = slip(6.40026139989901,0.799344766398529)
929.632137273939 = slip(3.2001306999495,0.799344766398529)
59.0007181299284 = slip(12.800522799798,0.190435920948749)
29.5003590649642 = slip(12.800522799798,0.0952179604743743)
29.5003590649642 = slip(6.40026139989901,0.0952179604743743)
JSUN tropical (Seidelmann 1992) 1470 year & 2402 year
8.45107360405992 = axial(29.42351935,11.85652502)
16.9021472081198 = harmean(29.42351935,11.85652502)
19.8588720868409 = beat(29.42351935,11.85652502)
3635.42278750964 = slip(163.7232045,83.74740682)
17760.7407596846 = slip(3635.42278750964,171.444289533663)
16.9182475901445 = beat(17760.7407596846,16.9021472081198)
8.45912379507225 = 16.9182475901445 / 2
4.22956189753613 = 16.9182475901445 / 4
33.7721548821359 = harmean(17760.7407596846,16.9021472081198)
16.886077441068 = axial(17760.7407596846,16.9021472081198)
8.44303872053399 = 16.886077441068 / 2
4.22151936026699 = 16.886077441068 / 4
114.253729166588 = slip(19.8588720868409,16.9182475901445)
57.1268645832942 = slip(19.8588720868409,8.45912379507225)
67.1361846326796 = slip(19.8588720868409,4.22151936026699)
475.496204649037 = slip(114.253729166588,16.9021472081198)
237.748102324519 = slip(114.253729166588,8.45107360405992)
118.874051162259 = slip(57.1268645832942,4.22553680202996)
2939.57946202776 = slip(114.253729166588,4.22553680202996) ~= 2940
2939.57946202744 = slip(475.496204649037,114.253729166588)
2939.57946202744 = slip(237.748102324519,114.253729166588)
2939.57946202744 = slip(118.874051162259,114.253729166588)
1469.78973101388 = slip(114.253729166588,2.11276840101498) ~= 1470
1469.78973101372 = slip(475.496204649037,57.1268645832942)
1469.78973101372 = slip(237.748102324519,57.1268645832942)
1469.78973101372 = slip(118.874051162259,57.1268645832942)
2402.06517243955 = slip(67.1361846326796,16.9021472081198) ~= 2402
Amicable Bonds (tropical version)
“consensus” of Seidelmann (1992) & NASA ‘factsheet’
29.4235187441307 = harmean(29.42351935,29.4235181382615)
11.8565239747501 = harmean(11.85652502,11.8565229295003)
0.999978358596783 = harmean(0.99997862,0.999978097193703)
0.615181976306751 = harmean(0.61518257,0.615181382614647)
explore what others might have in mind:
0.615181976285804 — tuned to “4670 years” (remember Bond pub. with 1800 & 4670 graph)
0.999978614647502 — Meeus & Savoie (1992) rounded-off value used by so many
1791.85469669027 = 1/(-8/11.8565239747501+16/29.4235187441307+13/0.615181976285804-21/0.999978614647502)
1799.99949076613 = 221/220/(-8/11.8565239747501+16/29.4235187441307+13/0.615181976285804-21/0.999978614647502)
1791.85469669027 = axial(395999.88796855,1799.99949076613)
1791.85469669027 = axial( 220 * 1799.99949076613 , 1799.99949076613 )
gives:
1.59868553691508 = beat(0.999978614647502,0.615181976285804)
0.799342768457541 = 1.59868553691508 / 2
0.399671384228771 = 1.59868553691508 / 4
0.761743227089166 = harmean(0.999978614647502,0.615181976285804)
0.380871613544583 = axial(0.999978614647502,0.615181976285804)
0.190435806772291 = 0.380871613544583 / 2
0.0952179033861457 = 0.380871613544583 / 4
0.771361261986248 = beat(61.0913999839243,0.761743227089166)
0.385680630993124 = 0.771361261986248 / 2
0.192840315496562 = 0.771361261986248 / 4
1.50472418232299 = harmean(61.0913999839243,0.761743227089166)
0.752362091161495 = axial(61.0913999839243,0.761743227089166)
0.376181045580747 = 0.752362091161495 / 2
0.188090522790374 = 0.752362091161495 / 4
22.0353413519587 = slip(1.59868553691508,0.771361261986248)
11.0176706759793 = slip(1.59868553691508,0.385680630993124)
12.8009052113462 = slip(1.59868553691508,0.752362091161495)
304.013638441169 = slip(22.0353413519587,0.761743227089166)
152.006819220584 = slip(22.0353413519587,0.380871613544583)
76.0034096102922 = slip(22.0353413519587,0.190435806772291)
76 = 163 mod 24 + 67 mod 24 + 43 mod 24 + 19 mod 24 = 19 + 19 + 19 + 19
1791.85469667879 = slip(12.8009052113462,1.59868553691508)
1799.99949075461 = 221 / 220 * 1791.85469667879
164.876143595902 = slip(22.0353413519587,0.399671384228771) ———– z
4670.79912511218 = slip(164.876143595902,11.0176706759793)
perfect: s(496) = 496 = s(652) = s(s(608))
608.027276881365 = 2/(-29/11.8565239747501+58/29.4235187441307-44/0.615181976285804+72/0.999978614647502)
1216.05455376273 = 4/(-29/11.8565239747501+58/29.4235187441307-44/0.615181976285804+72/0.999978614647502)
2432.10910752546 = 8/(-29/11.8565239747501+58/29.4235187441307-44/0.615181976285804+72/0.999978614647502)
1800 & 4670 years:
weather myth or math?
lunisolar precession with tropical “Consenzus”
11.8619917685154 = beat(25721.8900031954,11.8565239747501) — LLR
11.8619917394734 = beat(25722.0265616918,11.8565239747501) — harmean(LLR,W94)
11.8619917104315 = beat(25722.1631216381,11.8565239747501) — W94
with anomalistic heavyweight Jupiter
198078.497253751 = beat(11.8627021700857,11.8619917685154) ; * 2 = 396156.994507502
198070.399443988 = beat(11.8627021700857,11.8619917394734) ; * 2 = 396140.798887976
198062.302295769 = beat(11.8627021700857,11.8619917104315) ; * 2 = 396124.604591539
1799.99857738802 = beat(396156.994507502,1791.85700697991)
1799.9989117563 = beat(396140.798887976,1791.85700697991)
1799.99924612472 = beat(396124.604591539,1791.85700697991)
gives 4672.37005613987 (using 0.615181976306751 = harmean(0.61518257,0.615181382614647))
1799.9962460564 = beat(396156.994507502,1791.85469669027)
1799.99658042381 = beat(396140.798887976,1791.85469669027)
1799.99691479137 = beat(396124.604591539,1791.85469669027)
gives 4670.7991 (using 0.615181976285804)
a reverse view bringz estimate ll’un ‘uz ole lore PR’ cz!sun from tropical!Jupiter “consensus”
with 0.615181976306751 = harmean(0.61518257,0.615181382614647) & 4672.37005613987 :
396088.097411778 = beat(1800,1791.85700697991) ; / 2 = 198044.048705889
11.8619916449528 = axial(198044.048705889,11.8627021700857)
25722.4710182008 = beat(11.8619916449528,11.8565239747501)
with 0.615181976285804 & 4670.7991 :
395975.242590358 = beat(1800,1791.85469669027) ; / 2 = 197987.621295179
11.8619914424619 = axial(197987.621295179,11.8627021700857)
25723.4232260154 = beat(11.8619914424619,11.8565239747501)
also note
Standish sidereal with Standish anomalistic
197810.936263778 = beat(11.8627021700857,11.861990807677) ; / 2 = 395621.872527555
Standish sidereal with NASA ‘factsheet’ tropical
25721.4885660692 = beat(11.861990807677,11.8565229295003)
25721.8900031954 = LLR lunisolar precession
11.8565229295003 = NASA ‘factsheet’ tropical Jupiter
11.8565230147972 = axial(25721.8900031954,11.861990807677)
4 those who (anomalistically) are averse (“Can˚T get from the Cab to the C[I]RB” — The ‘PR 10’ drs)
2 amicable bonds
Enough $aid Sir Pentagon
terre$ketchof whether
loony so lure
buy USamicably
COMBINE Sidorenkov (2017) short-duration sidereal
WITH Standish long-duration anomalistic
883.352600477237 = harmean(936.955612197409,835.550927105136)
984.598022541318 = beat( 25771.4533429313 / 3 , 883.352600477237 )
˚T?hird harmonic of General precession arises from opposing trigon COefficients (5 – 2 = 3) in sidereal-tropical conversion (use to detect bias inside pub.lists)
979.992217251443 = beat(984.598022541318,491.144860474028) ; * 75 / 2 =
36749.7081469291 ; compare:
36749.7014379182 — La2011 Table 6 La2010a
lunisolar bias estimate using Seidelmann (1992) short-duration sidereal JSU
491.144860474028 = 1/(-3187.5/11.8626151546089+10462.5/29.4474984673838-7275/84.016845922161-37.5/30031-3/25771.4533429313+1/883.339228237648)
noteworthy: 50482100 (rounded-off version of 50482096)
systematically links NA!SA ‘factsheet’ & Seidelmann (1992) tropical (no. mystery in such hindsite)
0.999978614647502 widely-cited rounded-off Meeus & Savoie (1992) tropical
0.99997861640616 = 31/(-3187.5/11.8626151546089+10462.5/29.4474984673838-7275/84.016845922161-37.5/30031+21/0.0745030006844627+10/0.0754402464065708-31/0.0808503463381246-3/25770.7446092762+1/883.339228237648)
off by 1 minute (time no. T˚angle) per century
0.999978616353183 unrounded Meeus & Savoie (1992)
supplementary
0 = -42.5 + 139.5 – 97
33052.6240611784 = 1/(-42.5/11.8626151546089+139.5/29.4474984673838-97/84.016845922161)
36750.3253473747 = 1/(-85/11.8626151546089+279/29.4474984673838-194/84.016845922161-1/30031)
36135.2499680199 = 1/(-85/11.8626151546089+279/29.4474984673838-194/84.016845922161-1/30031+0.5/83.7474058863792-0.5/163.723203285421-0.5/84.0331316671926+0.5/164.793624044745)
15009.1624932282 = 1/(-85/11.8626151546089+279/29.4474984673838-194/84.016845922161-1/30031+0.5/83.7474058863792-0.5/163.723203285421-0.5/84.0331316671926+0.5/164.793624044745+2/25721.8900031954-1/25771.4533429313)
5482096.60065159 = 365.25/(-85/11.8626151546089+279/29.4474984673838-194/84.016845922161-1/30031+0.5/83.7474058863792-0.5/163.723203285421-0.5/84.0331316671926+0.5/164.793624044745+2/25721.8900031954-1/25771.4533429313)
0 = 31 – 21 – 10
491.132481368366 = 1/(31*(1/0.999978614647502+1/0.0808503463381246)-21/0.0745030006844627-10/0.0754402464065708)
491.145236548486 = 1/(31*(1/0.999978616353183+1/0.0808503463381246)-21/0.0745030006844627-10/0.0754402464065708)
derive
0.0748024157879311 = axial(0.999978616353183,0.0808503463381246)
5.99685290323073 = beat(0.0754402464065708,0.0745030006844627)
18.6129703214384 = beat(0.0748024157879311,0.0745030006844627)
8.84735306511776 = beat(0.0754402464065708,0.0748024157879311)
16.8627866218841 = beat(18.6129703214384,8.84735306511776)
179.333487684639 = slip(18.6129703214384,8.84735306511776)
ace shown
491.145236537217 = slip(179.333487684639,16.8627866218841)
984.581409347557 = beat( 25771.4533429313 / 3 , 883.339228237648 )
984.584512785494 = beat( 25770.7446092762 / 3 , 883.339228237648 )
984.587616242996 = beat( 25770.0359146014 / 3 , 883.339228237648 )
980.01017321043 = beat(984.581409347557,491.145236537217)
980.007098542353 = beat(984.584512785494,491.145236537217)
980.004023893569 = beat(984.587616242996,491.145236537217)
36750.3814953911 = 75 / 2 * 980.01017321043
36750.2661953382 = 75 / 2 * 980.007098542353
36750.1508960089 = 75 / 2 * 980.004023893569
36135.3042523091 = axial(2159056.00745389,36750.3814953911)
15009.1718585901 = axial(36135.3042523091,25672.5169367299)
5482100.02135004
review
Berger 1988 Table 4 (based on Berger 1978)
2166101.14285714 = beat(75259,72732)
36748.2810485504 = beat(2166101.14285714,36135.2404360745)
note$ trees in llUNe^don foresst matrix calllculaceyen
2159056.00745301 = 2 * beat(171.471519050756,171.444286952825)
SSTand!sh anomalistic with ‘factsheet’ tropical
PC in
fact ch.UK IT
luke dawn sank$yuan tyrant$
R out of ˚T ou ch! within UKquality
36750.3190131859 = 1/(g_3+g_4) — La2021 Table 2 with explore a tory add “just” (weather mint or) mean˚T
36135.2438440821 = axial(2159056.00745389,36750.3190131859)
15009.1614366987 = axial(36135.2438440821,25672.5169367299)
5482096.21475421 —- pub.list.cz!is note$baseofllreflect$yen=peace$ together quickly
120,000 “noteworthy” Typo Solutions
won over UN √8
1800 ~= 1 / √8 * 5090
4670 = s(4370) + (378-178)*2
owe bowl’n’Valley
323 = 196883-196560
“bye don!” Jail˚Talk
25746 = Σs(5090) – ΣΦ(323)
25746 = Σs(5090) – ΣΦ(936)
0 LA˚Table
25722 = Σs(5090) – (378-178)*2 – 71
25746 = Σs(5090) – (378-178)*2 – 47
25770 = Σs(5090) – (378-178)/2 – 196883 + 196560
too Sell a con
25808 = Σs(5090) – 11#/3#
25808 = Σs(5090) – 7*(28^2-27^2)
25808 = Σs(5090) – 7*(1^2+2^2+3^2+4^2+5^2)
——————–
s(5090) = 4090
s(4090) = 3290
s(3290) = 3622
s(3622) = 1814
s(1814) = 910
s(910) = 1106
s(1106) = 814
s(814) = 554
s(554) = 280
s(280) = 440
s(440) = 640
s(640) = 890
s(890) = 730
s(730) = 602
s(602) = 454
s(454) = 230
s(230) = 202
s(202) = 104
s(104) = 106
s(106) = 56
s(56) = 64
s(64) = 63
s(63) = 41
s(41) = 1
s(1) = 0
th borg herd sum??un
26193 = Σs(5090)
ABout what nos.˚TemperUN
317 years
anomalistic JSU
the very top-level cycle is a familiar one
16.9161211952138 = harmean(29.4701958106261,11.8627021700857)
19.8549641949401 = beat(29.4701958106261,11.8627021700857)
21.1796477480038 = beat(84.0331316671926,16.9161211952138)
317.450267066043 = slip(21.1796477480038,19.8549641949401)
ok
2545 = ΣΣδ(220)
5090 = ΣΣδ(220) * 2
unI˚Que.T˚A CO$metallica
400 = s(2401) = 2*(378-178) = s(836-42) = s(496+28) = 744-104-240
400 = ΣΦ(323) – Σφ(323) ; 447 = ΣΦ(323) ; 47 = Σφ(323)
400 = Σs(242) ; 242 = ΣΣΔ(178)-ΣΣφ(178) = average(ΣΔ(220),Σδ(220)) = ΣΦ(163)-Σφ(163)
993 = (σ^2)(400) ; Σδ(Σδ(993)) = Σδ(Σδ(Σδ(378))) = 902 = Σδ(894) ; Σδ(902) = 894
σ(894) = σ(1691) = 1800 ; ΣΦ(1800) = 735 ; 600 = σ(216)
216 = 378 – (163+67+43+19+28) + (10+13+18+22+37+58)
J[amai$SUNami]11buy
100 = average(-ΣΦ(220),Σφ(220)) = average(-178,378) = 71-Σδ(42)
100 = average(-Σφ(323),ΣΦ(323))/2 = 4370-s(4370) = s(194)
100 = 2+3+5+7+11+13+17+19+23 = Σ(primes up to 23)
100 = 2+3+5+7+11+13+17+19+23 = 41+59 = 29+71 = 31+47+(378 mod 178)
178 = 2+3+5+7+11+13+17+19+23 + 31+47
200 = 2+3+5+7+11+13+17+19+23 + 41+59
300 = 2+3+5+7+11+13+17+19+23 + 41+59 + 29+71
378 = 2+3+5+7+11+13+17+19+23 + 41+59 + 29+71 + 31+47
done “ch.op.eur.bri˚k
25722 = Σs(5090) – 400 – 71
25746 = Σs(5090) – 400 – 47
25770 = Σs(5090) – 100 – 196883 + 196560
f(sst) 0˚NA(!w)ru|ur”
σ(Φ(47))^5 – Φ(47)^5 – 47^5 = 19^5 + 43^5 + 67^5
25722 = Σs(5090) – s(2401) – 71
25746 = Σs(5090) – ΣΦ(196883-196560) + Σφ(196883-196560)) – 47
25770 = Σs(5090) – 4370 + s(4370) – 323 ; 4370 – s(4370) = s(194)
Standish (1992) anomalitic:
317.450267066044 = 1/(1/2/11.8627021700857-3/2/29.4701958106261+1/84.0331316671926)
˚Too *$ the conCOIIUSh’n’writeSAMicAB11y
25674 = Σs(5090)-Σs(242)-47-average(59*59,-47*71)
242 = 71 + 171
714463914.954807 = beat(29.42351935,29.4235181382615) —– (Seidelmann1992,NASA’factsheet’)
1714009140.222 = beat(29.447498973306,29.4474984673838) — (Seidelmann1992,Sidorenkov2017)
IT$UNknown ‘weather friendly’ giants are in2cn moonSST!R UShine
1225154850 = beat(1714009140.222,714463914.954807)
2450309700, 4900619400, 9801238800, …
3675464550, 7350929100, 14701858201, …
(m)essturn wise sh!owe D-IT B(!w)(un)k(umou)
242 = ΣΣΔ(178)-ΣΣφ(178) = average(ΣΔ(220),Σδ(220)) = ΣΦ(163)-Σφ(163)
29.4474987203449 = harmean(29.447498973306,29.4474984673838) — (Seidelmann1992,Sidorenkov2017)
29.4235187441307 = harmean(29.42351935,29.4235181382615) —– (Seidelmann1992,NASA’factsheet’)
36132.1889074394 = beat(29.4474987203449,29.4235187441307)
25674 = beat(36132.1889074394,15009.1608487337) ; 15009.1608487337 = 5482096/365.25
142 = ΣΔ(220) = 2*71
242 = average(142,342) = 2*11^2 = 71+171
342 = Σδ(220) = 2*171
4724 to 5256
25761.5669315114 = beat(1.00001743371442,0.999978616353183) —- Seidelmann1992
25768.5314808954 = harmean(25775.4997969807,25761.5669315114) —————————-
25775.4997969807 = beat(1.00001741273101,0.999978616353183) —- Sidorenkov2017
25773.8517155112 = beat(1.0000174152119,0.999978616353183) — Standish1992 (mediates)
5256.6393995685 J
5254.8227273181 S
5258.32377697949 U
5255.227007452 N
5256.25286945517 = JSUN harmean
5256.24218758401
= beat( beat( 25808.2447032344, 25773.8517155112 / 2 ) / 6 , 2362.08778401782 )
anomalistic-nodal 2320 years
16.9161211952138 = harmean(29.4701958106261,11.8627021700857) — anomalistic
61.0124738503575 = slip(29.4511026866654,11.862499899747) —– nodal
851.495746676794 = slip(61.0124738503575,19.8630730877524) — nodal
derivation (via generalized Bollinger method)
16.5866057119762 = axial(851.49574667679,16.9161211952138)
100.762038265834 = slip(19.8549641949401,16.5866057119762)
2320.03347068461 = slip(100.762038265834,16.9161211952138)
2320.03347068424 = 1/(-7/2/11.8627021700857+17/2/29.4701958106261-12/11.862499899747+30/29.4511026866654)
purely anomalistic 2362 years derived above
2362.08778401334 = 1/(31/11.8627021700857-77/29.4701958106261)
combine
130310.598028785 = beat(2362.08778401334,2320.03347068424)
130310.598021243 = 1/(-69/2/11.8627021700857+171/2/29.4701958106261-12/11.862499899747+30/29.4511026866654)
compare
130192.356944535 = beat(2362.05130068208,2319.96076275948) — NASA ‘factsheet’ tropical
orbital invariant with harmonic means of Seidelmann & NASA ‘factsheet’ tropical:
130476.603432851 = 1/(3/11.8565239747501-8/29.4235187441307-2/83.7474063531896+7/163.72320389271)
130762.093817962 = beat(2361.92512664087,2320.01916295313) — Seidelmann tropical
130704.452624679 = beat(173901.37537739,74619.9907876555) — La(2004a,2010a)average
nodal-anomalistic 836 years
9.93153654387618 = 19.8630730877524 / 2
19.8630730877524 = beat(29.4511026866654,11.862499899747) —————– nodal
16.912768715208 = harmean(29.4511026866654,11.862499899747) ————- nodal
6.57189983390616 = axial( 29.4701958106261 / 2 , 11.8627021700857 ) —- anomalistic
10.7485186386365 = beat(16.912768715208,6.57189983390616)
130.662968425853 = slip(19.8630730877524,10.7485186386365)
835.601801700049 = slip(130.662968425853,9.93153654387618)
836 = 11 * ( mod(163,24) + mod(67,24) + mod(43,24) + mod(19,24) )
“836 is the smallest weird number that is also an untouchable number”
JS Heart
4.96576827193809 = 19.8630730877524 / 4
9.93153654387618 = 19.8630730877524 / 2
19.8630730877524 = beat(29.4511026866654,11.862499899747) —————– nodal
2.114096089401 = 8.456384357604 / 4
4.228192178802 = 8.456384357604 / 2
8.456384357604 = axial(29.4511026866654,11.862499899747)
16.912768715208 = harmean(29.4511026866654,11.862499899747) ————- nodal
6.57189983390616 = axial( 29.4701958106261 / 2 , 11.8627021700857 ) —- anomalistic
set up generalized Bollinger method
10.7485186386365 = beat(16.912768715208,6.57189983390616)
5.37425931931824 = 10.7485186386365 / 2
2.68712965965912 = 10.7485186386365 / 4
4.73283332391597 = axial(16.912768715208,6.57189983390616)
2.36641666195799 = 4.73283332391597 / 2
1.18320833097899 = 4.73283332391597 / 4
130.662968425853 = slip(19.8630730877524,10.7485186386365)
65.3314842129265 = slip(19.8630730877524,5.37425931931824)
50.6802153502585 = slip(19.8630730877524,2.68712965965912)
100.895781229192 = slip(19.8630730877524,4.73283332391597)
50.4478906145961 = slip(19.8630730877524,2.36641666195799)
93.4596178908348 = slip(19.8630730877524,1.18320833097899)
derive 317, 836, 1470, 1800, 4670, 100ka, & more (some omitted for now)
2937.90591403587 = slip(100.895781229192,16.912768715208)
1468.95295701793 = slip(100.895781229192,8.456384357604)
734.476478508967 = slip(100.895781229192,4.228192178802)
734.476478508967 = slip(50.4478906145961,4.228192178802)
1798.69939643745 = slip(93.4596178908348,8.456384357604)
899.349698218727 = slip(93.4596178908348,4.228192178802)
317.021047394046 = slip(100.895781229192,4.96576827193809)
317.021047394066 = slip(93.4596178908348,19.8630730877524)
835.601801700049 = slip(130.662968425853,9.93153654387618)
835.601801700049 = slip(309.763646655713,130.662968425853)
835.601801700042 = slip(225.988187105058,130.662968425853)
835.60180170002 = slip(130.662968425853,112.994093552529)
where
309.763646655713 = slip(130.662968425853,19.8630730877524)
225.988187105058 = slip(65.3314842129265,19.8630730877524)
112.994093552529 = slip(50.6802153502585,19.8630730877524)
4670.02054486764 = slip(1344.24031754827,130.662968425853)
where
1344.24031754827 = slip(130.662968425853,4.228192178802)
1344.24031754825 = slip(144.731137488337,130.662968425853)
144.731137488337 = slip(65.3314842129265,4.228192178802)
198956.792259811 = slip(14755.2250793229,130.662968425853)
99478.3961299054 = slip(14755.2250793229,65.3314842129265)
where
14755.2250793229 = slip(50.6802153502585,16.912768715208)
compare sidereal vs. anomalistic
16.9132450828034 = harmean(29.4571309198874,11.861990807677)
16.9161211952138 = harmean(29.4701958106261,11.8627021700857)
99476.8155050052 = beat(16.9161211952138,16.9132450828034)
99477 review
Seidelmann (1992) sidereal earth
1.00001743390371 = (1-(1/240)^1)^(0/1)/(1-(1/240)^2)^(2/2)/(1-(1/240)^3)^(3/3)/(1-(1/240)^4)^(2/4)/(1-(1/240)^5)^(5/5)/(1-(1/240)^6)^(1/6)
1.00001743390371 = (1-(1/σ(σ(σ(73))))^1)^(0/1)/(1-(1/σ(σ(σ(73))))^2)^(2/2)/(1-(1/σ(σ(σ(73))))^3)^(3/3)/(1-(1/σ(σ(σ(73))))^4)^(2/4)/(1-(1/σ(σ(σ(73))))^5)^(5/5)/(1-(1/σ(σ(σ(73))))^6)^(1/6)
1.00001743390371 = (1-(1/σ(209))^1)^(0/1)/(1-(1/σ(209))^2)^(2/2)/(1-(1/σ(209))^3)^(3/3)/(1-(1/σ(209))^4)^(2/4)/(1-(1/σ(209))^5)^(5/5)/(1-(1/σ(209))^6)^(1/6)
1.00001743390371 = (1-(1/σ(47+59+71))^1)^(0/1)/(1-(1/σ(47+59+71))^2)^(2/2)/(1-(1/σ(47+59+71))^3)^(3/3)/(1-(1/σ(47+59+71))^4)^(2/4)/(1-(1/σ(47+59+71))^5)^(5/5)/(1-(1/σ(47+59+71))^6)^(1/6)
1.00001743390371 = (1-(1/σ(average(320,158)))^1)^(0/1)/(1-(1/σ(average(320,158)))^2)^(2/2)/(1-(1/σ(average(320,158)))^3)^(3/3)/(1-(1/σ(average(320,158)))^4)^(2/4)/(1-(1/σ(average(320,158)))^5)^(5/5)/(1-(1/σ(average(320,158)))^6)^(1/6)
1.00001743390371 = (1-(1/σ(average(28+163+67+43+19,10+13+18+22+37+58)))^1)^(0/1)/(1-(1/σ(average(28+163+67+43+19,10+13+18+22+37+58)))^2)^(2/2)/(1-(1/σ(average(28+163+67+43+19,10+13+18+22+37+58)))^3)^(3/3)/(1-(1/σ(average(28+163+67+43+19,10+13+18+22+37+58)))^4)^(2/4)/(1-(1/σ(average(28+163+67+43+19,10+13+18+22+37+58)))^5)^(5/5)/(1-(1/σ(average(28+163+67+43+19,10+13+18+22+37+58)))^6)^(1/6)
keywords: Schneider, E8, monster, Ramanujan
73: lowest prime congruent to 1 mod 24
another 317 year note
744 = σ(743)
743.744122286576 = slip(317.021047394066,130.662968425853)
744 = σ(240)
240 = σ(σ(σ(73))) = σ(average(320,158)) = σ(average(28+163+67+43+19,10+13+18+22+37+58))
examples:
104 = d(2,1/2,58) = R(2,1/2,58) – R(1,1/2,58)
104 = d(4,1/2,58) = R(4,1/2,58) – R(1,1/2,58)
R(4,1/2,58) = 104.000034332275 = ⌊(e^√58π)^(1/4)⌉^4 – e^√58π
R(2,1/2,58) = 104.000034332275 = ⌊(e^√58π)^(1/2)⌉^2 – e^√58π
R(1,1/2,58) = 0.000034332275390625 = ⌊(e^√58π)^(1/1)⌉^1 – e^√58π
744 = d(3,1/2,28) = R(3,1/2,28) – R(1,1/2,28)
R(3,1/2,28) = 744.01187441498 = ⌊(e^√28π)^(1/3)⌉^3 – e^√28π
R(1,1/2,28) = 0.0118744149804115 = ⌊(e^√28π)^(1/1)⌉^1 – e^√28π
The middle argument “1/2” corresponds to “√” — i.e. raise to power 1/2; e.g. 28^(1/2) = √28
744 = σ(240)
240 =σ(209) = σ(47+59+71) = σ(average(ΣΦ(216),Σφ(216)))
216 = 378-ΣΔ(378) = Φ(ΣΦ(323)+Σφ(323))
1.00001743390371 = (1-(1/σ(average(ΣΦ(216),Σφ(216))))^1)^(0/1)/(1-(1/σ(average(ΣΦ(216),Σφ(216))))^2)^(2/2)/(1-(1/σ(average(ΣΦ(216),Σφ(216))))^3)^(3/3)/(1-(1/σ(average(ΣΦ(216),Σφ(216))))^4)^(2/4)/(1-(1/σ(average(ΣΦ(216),Σφ(216))))^5)^(5/5)/(1-(1/σ(average(ΣΦ(216),Σφ(216))))^6)^(1/6)
Seidelmann (consciously? or not?) simply substituted 240 for Schneider‘s phi.
Seidelmann (1992) synodic helps clarify bias structure.
11.8619992845449 = 1/(-1/1.0920848733744+1/1.00001743301243) — note sidereal earth period
29.4571720000365 = 1/(-1/1.03515920602327+1/1.00001743301243)
936.955612647599 = 1/(178/11.8619992845449-442/29.4571720000365)
1800.77215359294 = 1/(29/11.8619992845449-72/29.4571720000365)
11.8619992845449 = beat(1.0920848733744,1.00001743301243)
29.4571720000365 = beat(1.03515920602327,1.00001743301243)
set up generalized Bollinger method
19.8589101021728 = beat(29.4571720000365,11.8619992845449)
9.92945505108639 = 19.8589101021728 / 2
4.9647275255432 = 19.8589101021728 / 4
16.9132604709107 = harmean(29.4571720000365,11.8619992845449)
8.45663023545537 = axial(29.4571720000365,11.8619992845449)
4.22831511772768 = 8.45663023545537 / 2
2.11415755886384 = 8.45663023545537 / 4
10.7442781148351 = beat(16.9132604709107,6.57038853131229)
5.37213905741754 = 10.7442781148351 / 2
2.68606952870877 = 10.7442781148351 / 4
9.46417591360268 = harmean(16.9132604709107,6.57038853131229)
4.73208795680134 = axial(16.9132604709107,6.57038853131229)
2.36604397840067 = 4.73208795680134 / 2
1.18302198920033 = 4.73208795680134 / 4
derive 936 & 1800
130.930052601617 = slip(19.8589101021728,10.7442781148351)
65.4650263008087 = slip(19.8589101021728,5.37213905741754)
506.04166179034 = slip(130.930052601617,16.9132604709107)
703.826579261491 = slip(130.930052601617,9.92945505108639)
1800.77215358773 = beat(703.826579261491,506.04166179034)
351.913289630745 = slip(130.930052601617,4.9647275255432)
936.955612639497 = slip(351.913289630745,65.4650263008087)
3747.82245055826 = slip(130.930052601617,4.22831511772768) ; / 4 = 936.955612639565
Introducing Moonshine Bias
1.0000262476142 —- Standish (1992) anomalistic earth period
1.00002624761586 = 30/(15/0.0745030006844627+16/0.0754402464065708-31/0.0808503463381246-1/2364963.50364963+8/7201)
2364963.50364963 = beat(74619.9907876555,72337.575351641) — La(2004a,2010a)average
7201: 1, 19, 379, 7201; harmean = 3.79
7201 = 19 + ( 19 * 378 )
7200.99967683779 = 8/(30/1.0000262476142-15/0.0745030006844627-16/0.0754402464065708+31/0.0808503463381246+1/2364963.50364963)
7201.000000 = 8/(30/1.00002624761586-15/0.0745030006844627-16/0.0754402464065708+31/0.0808503463381246+1/2364963.50364963)
_____________________________________________________________________________________________
monstrous error:
-0.000023823837 seconds ( temporal (not angular) ) per century
supplementary art dove wiser
118239.762151809 = beat(1814.75583949423,1787.32381267774)
1800.249870433 = harmean(2364795.24303618,900.467685151888)
1800.2498895435 = harmean(2364861.19623035,900.467685151888)
1800.24991918585 = harmean(2364963.50364963,900.467685151888)
scale(un)80/4
84.021214079097 = beat(1.0120629705681,1.00001743390371)
164.770564556546 = beat(1.00612375085558,1.00001743390371)
111.291642790288 = harmean(164.770564556546,84.021214079097)
111.307357343015 = harmean(164.793624044745,84.0331316671926)
788287.065410296 = beat(111.307357343015,111.291642790288)
2364861.19623089 = 3 * 788287.065410296
Swiss bunkers watch M11
0 = ⌊(70^2-55)/2^x-2^(2^2^2-x)*27/365.25⌉, x=0,1,2,…
317.44 = s(s(608))*(2/(Φ+φ))^4
317.44 = 496*(4/5)^2 = 496*16/25
What Fairbridge said was:
‘[…] 317.749 years […]. A storminess record in geomorphic (that is, physical) form is preserved in a “staircase” of 184 isostatically uplifted beach lines on Hudson Bay (Fairbridge and Hillaire-Marcel” 1977, Nature. Vol. 268), which date back to more than 8,000 years. Their extraordinary regularity is duplicated in other parts of the Arctic, which denies any theory of randomness in storminess cycles. […]’
25684 = Σs(5090) – 509 ; 509 * 59 = 30031; 30031 lowest primorial+1 not prime
25808 = beat(beat(25746,25684),25746) = 1/(2/25746-1/25684)
Phi(un)ally Perfect
sidereal JS estimates
x = average(Φ,φ)√√(y/496); search “why?” = 317.45026706604
106975.540995836 = beat(1.00001743390371,1.00000808573393)
19.8549641949401 = beat(29.4701958106261,11.8627021700857) — anomalistic
16.9161211952138 = harmean(29.4701958106261,11.8627021700857)
with sense(un)a dove mercury:
231842.576028623 = 1 / g_1
σ(25808) = 50034; * 2 = 100068
198928.033687742 = beat(231428.571428571,106975.540995836)
16.9132447127788 = axial(99464.016843871,16.9161211952138)
19.8589044939136 = beat(100068,19.8549641949401)
14.7285651846795 = beat(19.8589044939136,8.45662235638942)
5.93099526646578 = axial(19.8589044939136,8.45662235638942)
19.8589044939136 = beat(29.4571303693591,11.8619905329316) — compare Standish sidereal
4.73208318183218 = axial(16.9132447127788,6.57038170393041)
2.36604159091609 = 4.73208318183218 / 2
1.18302079545805 = 4.73208318183218 / 4
100.985212897808 = slip(19.8589044939136,4.73208318183218)
50.4926064489041 = slip(19.8589044939136,2.36604159091609)
93.0623385488049 = slip(19.8589044939136,1.18302079545805) ~= 744/8
⌊744.498708390439⌉ = 744
3455.67836213557 = slip(50.492606448904,16.9132447127788)
enlightenin’12sense: aro(un)d‘ve 3456 sing un
1727.83918106778 = slip(50.492606448904,8.45662235638942)
1186.17557935921 = slip(100.985212897808,19.8589044939136)
3455.67836213692 = slip(100.985212897808,16.9132447127788)
3455.67836213692 = slip(50.4926064489041,16.9132447127788)
1727.83918106846 = slip(100.985212897808,8.45662235638942)
1727.83918106846 = slip(50.4926064489041,8.45662235638942)
⌊1727.83918106846⌉ = 1728
no. won nos. weather myth or math
at the Heart of Fleur Dehli nos.
317.021047394046 = “why?”
2876.43697242977 = beat(1.00001743390371,0.999669890283597)
2876.43340223995 = (5+Φ)*2^9
100, 496, 836, 73500
19.8589044939136 = beat(28.8814946499969,11.7675450749242)
9.92945224695679 = 19.8589044939136 / 2
4.9647261234784 = 19.8589044939136 / 4
16.7218853102037 = harmean(28.8814946499969,11.7675450749242)
8.36094265510182 = axial(28.8814946499969,11.7675450749242)
4.18047132755091 = 8.36094265510182 / 2
2.09023566377546 = 8.36094265510182 / 4
10.5902904904416 = beat(16.7218853102037,6.48390755374098)
5.29514524522082 = 10.5902904904416 / 2
2.64757262261041 = 10.5902904904416 / 4
159.124845970951 = slip(19.8589044939136,10.5902904904416)
1246.02534363448 = slip(159.124845970951,2.09023566377546); coefficient 76
7350.70156103038 = slip(1246.02534363448,159.124845970951)
2492.05068726896 = slip(159.124845970951,4.18047132755091)
7350.70156103038 = slip(2492.05068726896,159.124845970951)
79.5624229854757 = slip(19.8589044939136,5.29514524522082)
3675.35078051519 = slip(1246.02534363448,79.5624229854757)
3115.06335908839 = slip(79.3092165212675,4.9647261234784)
7350.70156127398 = slip(3115.06335908839,159.124845970951)
12460.2534363458 = slip(159.124845970951,19.8589044939136)
30082.0055397318 = slip(12460.2534363571,4.18047132755091)
323010.783812806 = slip(30082.0055397318,79.5624229854757); coefficient 378
simple enough
plate 000˚k (Alive in 1728 over herd “he’s just taco˚k shun”)
quote:
12 = 71-59 = 59-47
3^3 = 27
4^3 = 64
5^3 = 125; 125+64+27 = 216; 216000 = 125*64*27
6^3 = 216
supplement:
Φ(25771) = 25770
σ(σ(25770)) = 216216
σ(σ(25770)) = (3^3*4^3*5^3)+(6^3)
σ(σ(25770)) = (3^3*4^3*5^3)+(3^3+4^3+5^3)
1 / g_3 =
74619.9907876555 — La2011 Table 6 La2004a
74619.9907876555 — La2011 Table 6 La2010a
74621: σ(σ(74621)) = σ(σ(Φ(25771))) = σ(σ(25770)) = 216216
74626.0277273697 — La2011 Table 5
with NASA ‘factsheet’ synodic
1.00001743356471 = 1/(1/100/(φφ/(1/11.8629550321199+1/29.4600280504908)+1/(1/11.8629550321199-1/29.4600280504908))+1/√5/√√(1/(1/11.8629550321199-1/29.4600280504908)/496))
blaring Soundgarden’s “black hole sun”
speedboat cruised at sunset
past an island up the inlet between the mountains
starboard featured nice blue pentagon design
understand how whoever came with that for the ‘factsheet’?
above used right side of illustration
x = average(Φ,φ)√√(y/496)
left side:
z = 2*average(Φ,φ)√√(u/496) = (√5)*(√√(u/496))
‘factsheet’ synodic: substitute u =
19.8602908360448 = beat(29.4600280504908,11.8629550321199)
4200.19506151223 = beat(1.00025558289712,1.00001743371442)
underscore this: try same calculation on EVERY other parameter list ever featured at the talkshop — you won’t find ANYTHING even remotely close — TUNING is the obvious interpretation
compare:
8.45735138020641 = axial(29.4600280504908,11.8629550321199)
22.1416333681812 = φφ * 8.45735138020641
42.001924204226 = 22.1416333681812 + 19.8602908360448 —- review
4200.1924204226 = 100 * 42.001924204226
a little algebra, arrive (it isn’t really curious) at a very precise estimate of their (lunisolar-biased) sidereal earth year-length
recommendation: stop the sanctions now (PLEASE: don’t delay)
Mayan Sun
review — notes shared a few years ago now connected with k & s_3
25684.9315068493 = 360*60*60/50.4576
68756.6342763388 = beat(41001.6165713381,25684.9315068493)
68756.6342763387 = 1/(1/360/60/60*50.4576-1/2^9/5^3/13/(5256.63940169013)*(44.2784629967671)*(73.0002008969005)*11*3)
41001.6165713381 = 2^9*5^3*13*(5256.63940169013)/( 44.2784629967671)/(73.0002008969005)/11/3
5125.20207141727 = 41001.6165713381 / 8
394.246313185944 = 5125.20207141727 / 13
143998.465891166 = 394.246313185944 * 365.25
NASA ‘factsheet’ synodic
carefully scrutinize 365.256 days in concert with scaling featured in last few comments
11.8631499061245 = beat(1.09207392197125,1.00001642710472)
29.4605119934568 = beat(1.03515400410678,1.00001642710472)
83.9387085475763 = beat(1.01207392197125,1.00001642710472)
164.501359353944 = beat(1.00613278576318,1.00001642710472)
68753.7838334262 = 1/(-2067/11.8631499061245+6233/29.4605119934568-2075/83.9387085475763-2075/164.501359353944)
41002.6302294426 = beat(68753.78398,25684.9315068493)
5125.32877868033 = 41002.6302294426 / 8
394.256059898487 = 5125.32877868033 / 13
144002.025877922 = 394.256059898487 * 365.25
baktun balance with Standish (1992) long-duration sidreal earth year-length
11.8632889636452 = beat(1.09207392197125,1.0000174152119)
29.4613695891215 = beat(1.03515400410678,1.0000174152119)
83.9456708028269 = beat(1.01207392197125,1.0000174152119)
164.528101664775 = beat(1.00613278576318,1.0000174152119)
5125.26068671143 = 1/(32.5/11.8632889636452-81.5/29.4613695891215+1.5/83.9456708028269+1.5/164.528101664775)
5125.26068671143 = 2/(65/11.8632889636452-163/29.4613695891215+3/83.9456708028269+3/164.528101664775)
68755.3156707909 = beat(41002.0854936914,25684.9315068493)
41002.0854936914 = 5125.26068671143 * 8
5125.26068671143 = 41002.0854936914 / 8
394.250822054725 = 5125.26068671143 / 13
144000.112755488 = 394.250822054725 * 365.25
generalized Bollinger (1952) method used to derive all of the preceding
typo near end of lunisolar 1800 comment
supplementary
68952.9911154182 = slip(1800.93537030388,0.999978616353183) — M&S unrounded
68961.1021023274 = slip(1800.93537030388,0.999978614647502) —— M&S rounded
The Real Thing
generalized Bollinger setup
NASA ‘factsheet’ “Perihelion (10^6 km)”
18.5132744565067 = beat(27.1859355652811,11.0133345026533)
9.25663722825335 = 18.5132744565067 / 2
4.62831861412668 = 18.5132744565067 / 4
15.6761007011677 = harmean(27.1859355652811,11.0133345026533)
7.83805035058385 = axial(27.1859355652811,11.0133345026533)
3.91902517529192 = 7.83805035058385 / 2
1.95951258764596 = 7.83805035058385 / 4
crossed with Standish (1992) anomalistic
11.3158491444058 = beat(15.6761007011677,6.57189983390616)
5.65792457220292 = 11.3158491444058 / 2
2.82896228610146 = 11.3158491444058 / 4
9.26121549052347 = harmean(15.6761007011677,6.57189983390616)
4.63060774526174 = axial(15.6761007011677,6.57189983390616)
2.31530387263087 = 4.63060774526174 / 2
1.15765193631543 = 4.63060774526174 / 4
hierarchy top levels
50.8673777758235 = slip(18.5132744565067,11.3158491444058)
68.039402479501 = slip(18.5132744565067,5.65792457220292)
40.616453731329 = slip(18.5132744565067,2.82896228610146)
9362.47281505814 = slip(18.5132744565067,4.63060774526174)
4681.23640752907 = slip(18.5132744565067,2.31530387263087)
2340.61820376454 = slip(18.5132744565067,1.15765193631543)
33052.6407001566 = slip(9362.47281505814,18.5132744565067)
Standish anomalistic JS
16.9161211952138 = harmean(29.4701958106261,11.8627021700857)
19.8549641949401 = beat(29.4701958106261,11.8627021700857)
crossed with nasa ‘factsheet’ synodic (using Standish long-duration earth sidereal)
10.7452986346853 = beat(16.9161211952138,6.57120187976141)
130.437274099443 = slip(19.8549641949401,10.7452986346853)
451.069113778482 = slip(130.437274099443,16.9161211952138)
984.586552944021 = slip(451.069113778482,130.437274099443)
980.005077317815 = beat(984.586552944021,491.145236537217)
73500.3807988361 = 980.005077317815 * 75
36750.1903994181 = 73500.3807988361 / 2
33052.6407001566 ; / 8 / √φ = 5255.45105486596 ; / 8 / √φ = 835.629626106117
36133.4834429326 = beat(29.4474984673838,29.42351935)
36133.4519209772 = axial( 500 * 835.629626106117 , Φ * 64000 )
36133.2446397442 = axial( 500 * 835.546575435627 , Φ * 64000.2003306117 )
11.8619906635942 = axial( 250 * 835.629626106117 , 11.8627021700857 )
11.861990807677 — compare Standish sidereal
JS Seidelmann short-duration
19.8650360864628 = beat(29.4474984673838,11.8626151546089)
9.93251804323141 = 19.8650360864628 / 2
4.9662590216157 = 19.8650360864628 / 4
16.9122914926352 = harmean(29.4474984673838,11.8626151546089)
8.4561457463176 = axial(29.4474984673838,11.8626151546089)
4.2280728731588 = 8.4561457463176 / 2
2.1140364365794 = 8.4561457463176 / 4
crossed with Standish anomalistic
10.7487113950462 = beat(16.9122914926352,6.57189983390616)
5.37435569752312 = 10.7487113950462 / 2
2.68717784876156 = 10.7487113950462 / 4
9.46559190444059 = harmean(16.9122914926352,6.57189983390616)
4.73279595222029 = axial(16.9122914926352,6.57189983390616)
2.36639797611015 = 4.73279595222029 / 2
1.18319898805507 = 4.73279595222029 / 4
generalized Bollinger top-level
130.804508068333 = slip(19.8650360864628,10.7487113950462)
65.4022540341667 = slip(19.8650360864628,5.37435569752312)
50.6080139018586 = slip(19.8650360864628,2.68717784876156)
100.676696558682 = slip(19.8650360864628,4.73279595222029)
50.3383482793411 = slip(19.8650360864628,2.36639797611015)
94.2634877779342 = slip(19.8650360864628,1.18319898805507)
~ 2 * 1470 :
2940.22366441706 = slip(639.79104597475,65.4022540341667)
639.79104597475 = slip(94.2634877779342,8.4561457463176)
astronomical delight
23098.5346098618 = slip(2081.08715717028,130.804508068333) ~= 23.1 ka
2081.08715717028 = slip(130.804508068333,4.2280728731588)
concise lunisolar review
29976.553895592 = beat(179.333323110834,178.266850068779) — M&S rounded tropical
29971.9562539596 = beat(179.333487684639,178.266850068779) — M&S unrounded tropical
contains
29972.4308734593 = slip(6642.042967895,130.804508068333)
6642.042967895 = slip(50.6080139018586,16.9122914926352)
50.6080139018586 = slip(19.8650360864628,2.68717784876156)
Your foray into orbital resonance is fascinating. To even understand orbital resonance I found this video https://youtu.be/Qyn64b4LNJ0 very explanatory to me. You all may enjoy it, not for what you already know, but for the last third or so, where the video gets into converting orbital resonance into sound. Very interesting and cool.
David A – in reality there are no *exact* orbital resonances that we know of. The true resonances are synodic, i.e. based on periods when two bodies are in line with the body they’re orbiting.
However the Galilean moons of Jupiter are very close to an exact orbital resonance, but see here:
David A: reference framing & sampling/aggregation biases (not resonance) have been the more memorable exploration spices. (Look for “anomalistic periods” on the net, find little, wonder why.)
no. fancy policy
132942.038841156 = slip(2493.45557752384,50.8673777758235)
2493.45557752384 = slip(50.8673777758235,3.91902517529192)
anomalistic purpose?
132942.038841155 = beat(2361.4060221632,2320.1931882465)
2340.61820376454 = harmean(2361.4060221632,2320.1931882465)
Dow

non-Mayan
pleas
28.8 & 29.8 ka note
background
28861.8479491577 = slip(521.471474393677,65.3314842129265)
521.471474393677 = slip(93.4596178908348,4.96576827193809)
1268.08418957619 = slip(100.895781229192,19.8630730877524)
59572.1478647727 = slip(1268.08418957619,50.6802153502585) ; / 2 =
29786.0739323864
image disappeared from here
Vert
anomalistic
19.8549641949401 = beat(29.4701958106261,11.8627021700857)
9.92748209747005 = 19.8549641949401 / 2
4.96374104873503 = 19.8549641949401 / 4
16.9161211952138 = harmean(29.4701958106261,11.8627021700857)
8.45806059760692 = axial(29.4701958106261,11.8627021700857)
4.22903029880346 = 8.45806059760692 / 2
2.11451514940173 = 8.45806059760692 / 4
cross with nodal
10.7419198566295 = beat(16.9161211952138,6.56993811757712)
5.37095992831474 = 10.7419198566295 / 2
2.68547996415737 = 10.7419198566295 / 4
9.46415641396783 = harmean(16.9161211952138,6.56993811757712)
4.73207820698391 = axial(16.9161211952138,6.56993811757712)
2.36603910349196 = 4.73207820698391 / 2
1.18301955174598 = 4.73207820698391 / 4
top level
130.937221254586 = slip(19.8549641949401,10.7419198566295)
65.4686106272931 = slip(19.8549641949401,5.37095992831474)
50.4636420418041 = slip(19.8549641949401,2.68547996415737)
–
101.392224425295 = slip(19.8549641949401,4.73207820698391)
50.6961122126475 = slip(19.8549641949401,2.36603910349196)
91.6213954766362 = slip(19.8549641949401,1.18301955174598)
so what?
323.049985568367 = slip(130.937221254586,19.8549641949401)
220.179370109776 = slip(65.4686106272931,19.8549641949401)
110.089685054889 = slip(50.4636420418041,19.8549641949401)
504.343543575558 = slip(130.937221254586,16.9161211952138)
no. doubt:
2998.18929479554 = slip(50.4636420418041,16.9161211952138)
1499.09464739777 = slip(50.4636420418041,8.45806059760692)
86900.0492950508 = slip(504.343543575558,50.4636420418041)
86900 = 11 * 25 * 316
con$hiver˚T review:

JEV nodal-anomalistic (casual intro)
nodal
320.347986973937 = slip(44.2875117414503,0.761762061330659)
320.347986973937 = slip(22.1437558707251,0.761762061330659)
23.7880850683634 = slip(11.0718779353626,0.761762061330659) ———-
160.173993486969 = slip(44.2875117414503,0.38088103066533)
160.173993486969 = slip(22.1437558707251,0.38088103066533)
160.173993486969 = slip(11.0718779353626,0.38088103066533)
99.0755539755134 = slip(44.2875117414503,0.190440515332665) ———-
80.0869967434843 = slip(22.1437558707251,0.190440515332665)
80.0869967434843 = slip(11.0718779353626,0.190440515332665)
anomalistic
575.799247511725 = slip(44.2411450188424,0.761769224080824)
575.799247511725 = slip(22.1205725094212,0.761769224080824)
23.0043337056467 = slip(11.0602862547106,0.761769224080824) ———–
287.899623755862 = slip(44.2411450188424,0.380884612040412)
287.899623755862 = slip(22.1205725094212,0.380884612040412)
287.899623755862 = slip(11.0602862547106,0.380884612040412)
143.949811877931 = slip(44.2411450188424,0.190442306020206)
143.949811877931 = slip(22.1205725094212,0.190442306020206)
143.949811877931 = slip(11.0602862547106,0.190442306020206)
reorganizing
320 = 28+163+67+43+19 (the 744 levels)
320.347986973937 = slip(44.2875117414503,0.761762061330659) — n
575.799247511725 = slip(44.2411450188424,0.761769224080824) — a
576 = 320+256 = 28+163+67+43+19 + 2^8 = 4 * 12^2
320.347986973937 = slip(22.1437558707251,0.761762061330659) — n
575.799247511725 = slip(22.1205725094212,0.761769224080824) — a
23.7880850683634 = slip(11.0718779353626,0.761762061330659) — n
23.0043337056467 = slip(11.0602862547106,0.761769224080824) — a
160.173993486969 = slip(44.2875117414503,0.38088103066533) — n
287.899623755862 = slip(44.2411450188424,0.380884612040412) — a
288 = 160+128 = 2 * 12^2
160.173993486969 = slip(22.1437558707251,0.38088103066533) — n
287.899623755862 = slip(22.1205725094212,0.380884612040412) — a
160.173993486969 = slip(11.0718779353626,0.38088103066533) — n
287.899623755862 = slip(11.0602862547106,0.380884612040412) — a
99 = 163-64 —————————————————————————————— note well
99.0755539755134 = slip(44.2875117414503,0.190440515332665) — n
143.949811877931 = slip(44.2411450188424,0.190442306020206) — a
80 = 144-64
80.0869967434843 = slip(22.1437558707251,0.190440515332665) — n
143.949811877931 = slip(22.1205725094212,0.190442306020206) — a
144 = 80+64
80.0869967434843 = slip(11.0718779353626,0.190440515332665) — n
143.949811877931 = slip(11.0602862547106,0.190442306020206) — a
144 = 59*59 – 47*71 = 12^2
Tortoise
576 = 24^2
23 = 99 – 76
“Experts” misled us severely last decade.
76 = 163 mod 24 + 67 mod 24 + 43 mod 24 + 19 mod 24 = 19 + 19 + 19 + 19
JEV nodal
417.865531943236 = slip(160.173993486969,44.2875117414503)
417.865531943179 = slip(99.0755539755134,44.2875117414503) ————
417.865531943236 = slip(80.0869967434843,44.2875117414503)
208.93276597159 = slip(99.0755539755134,22.1437558707251) ————-
208.932765971618 = slip(80.0869967434843,22.1437558707251)
compare with
JEV anomalistic
417.781912370365 = slip(49.480945018333,44.2411450188424)
208.890956185182 = slip(49.480945018333,22.1205725094212)
104.445478092591 = slip(49.480945018333,11.0602862547106)
46 = 209 – 163 = 2 * 23
σ(Φ(47))^5 – Φ(47)^5 – 47^5 = 19^5 + 43^5 + 67^5
835.563824740778 = slip(6.84967828238651,0.761769224080824)
417.781912370389 = slip(6.84967828238651,0.380884612040412)
208.890956185194 = slip(6.84967828238651,0.190442306020206)
104.445478092597 = slip(6.84967828238651,0.095221153010103)
Study carefully:
2096.44010053095 = slip(135.584676517528,44.2411450188424)
135.584676517528 = slip(44.2411450188424,1.59867106414771)
supplementary
49.480945018333 = slip(6.84967828238651,0.399667766036927)
anomalistic
835.56382473927 = 1/(-14/0.615197860179071+22/1.0000262476142+9/11.8627021700857)
nodal
835.731063859634 = 4/(-1387/0.615194395759546+2333/1.00001071395229-930/11.862499899747)
derive from:
anomalistic
1.59867106414771 = beat(1.0000262476142,0.615197860179071)
0.799335532073854 = 1.59867106414771 / 2
0.399667766036927 = 1.59867106414771 / 4
0.761769224080824 = harmean(1.0000262476142,0.615197860179071)
0.380884612040412 = axial(1.0000262476142,0.615197860179071)
0.190442306020206 = 0.380884612040412 / 2
0.095221153010103 = 0.380884612040412 / 4
0.814043420635227 = beat(11.8627021700857,0.761769224080824)
0.407021710317613 = 0.814043420635227 / 2
0.203510855158807 = 0.814043420635227 / 4
1.43160709790728 = harmean(11.8627021700857,0.761769224080824)
0.715803548953639 = axial(11.8627021700857,0.761769224080824)
0.35790177447682 = 0.715803548953639 / 2
0.17895088723841 = 0.715803548953639 / 4
44.2411450188424 = slip(1.59867106414771,0.814043420635227)
22.1205725094212 = slip(1.59867106414771,0.407021710317613)
11.0602862547106 = slip(1.59867106414771,0.203510855158807)
6.84967828238651 = slip(1.59867106414771,0.715803548953639)
3.42483914119326 = slip(1.59867106414771,0.35790177447682)
24.0670906604157 = slip(1.59867106414771,0.17895088723841)
nodal
1.59868736807262 = beat(1.00001071395229,0.615194395759546)
0.799343684036311 = 1.59868736807262 / 2
0.399671842018155 = 1.59868736807262 / 4
0.761762061330659 = harmean(1.00001071395229,0.615194395759546)
0.38088103066533 = axial(1.00001071395229,0.615194395759546)
0.190440515332665 = 0.38088103066533 / 2
0.0952202576663324 = 0.38088103066533 / 4
0.81403619360271 = beat(11.862499899747,0.761762061330659)
0.407018096801355 = 0.81403619360271 / 2
0.203509048400678 = 0.81403619360271 / 4
1.43159297613223 = harmean(11.862499899747,0.761762061330659)
0.715796488066113 = axial(11.862499899747,0.761762061330659)
0.357898244033057 = 0.715796488066113 / 2
0.178949122016528 = 0.715796488066113 / 4
44.2875117414503 = slip(1.59868736807262,0.81403619360271)
22.1437558707251 = slip(1.59868736807262,0.407018096801355)
11.0718779353626 = slip(1.59868736807262,0.203509048400678)
6.84843333335951 = slip(1.59868736807262,0.715796488066113)
3.42421666667975 = slip(1.59868736807262,0.357898244033057)
24.1324516929722 = slip(1.59868736807262,0.178949122016528)
sh: most replayed time index? 209
99476.8446931352 = beat(130901699.437495,99401.3061146969)
“…wwwo˚k T˚he lline like Can. edge? yep…”
Call off ice$UNhhowe???0vertThe
Horizon$1929.72222222222 (in sidereal hindsight NA!SA)
99401.3061147312 = 2/(1/11.8619848807702+1/29.4571542179636-1/11.8627021700857-1/29.4701958106261)
Sidellmann (1992) tropical wwwithconvert$yen
25761.5669315114 = beat(1.00001743371442,0.999978616353183) give$ :
99438.5571830642 = 2/(1/11.8619843895747+1/29.4571637875065-1/11.8627021700857-1/29.4701958106261)
11.8619855226385 = beat(25746.362539063,11.8565229295003)
29.4571824642891 = beat(25746.362539063,29.4235181382615)
223486.379079769 = beat(11.8626151546089,11.8619855226385)
89574.6192358693 = beat(29.4571824642891,29.4474984673838)
63945.0695493213 = axial(223486.379079769,89574.6192358693)
99438.3330129135 = harmean(111743.189539885,89574.6192358693)
llunisolr biasXbias
11.8619844613515 = 1/(-1/0.999978616353183+1/1.00001741273101-1/27500000+1/11.8565229295003)
29.4571759194281 = 1/(-1/0.999978616353183+1/1.00001741273101-1/27500000+1/29.4235181382615)
223110.291681529 = beat(11.8626151546089,11.8619844613515)
89635.1786377776 = beat(29.457175919428,29.4474984673838)
63945.0695493126 = axial(223110.291681529,89635.1786377776)
99401.0566990933 = harmean(111555.145840765,89635.1786377776)
catchSSTand!sh(1992)fi$[hh]calefidereal
99476.8155050703 = 2/(1/11.861990807677+1/29.4571309198874-1/11.8627021700857-1/29.4701958106261)
1.00001743390371 = (1-(1/σ(209))^1)^(0/1)/(1-(1/σ(209))^2)^(2/2)/(1-(1/σ(209))^3)^(3/3)/(1-(1/σ(209))^4)^(2/4)/(1-(1/σ(209))^5)^(5/5)/(1-(1/σ(209))^6)^(1/6)
25761.4413131157 = beat(1.00001743390371,0.999978616353183)
11.8619833699953 = beat(25761.4413131157,11.8565239747501)
29.4571633444961 = beat(25761.4413131157,29.4235187441307)
16.9132428669975 = harmean(29.4571633444961,11.8619833699953)
16.9161211952138 = harmean(29.4701958106261,11.8627021700857)
99400.2228512541 = beat(16.9161211952138,16.9132428669975)
$0 few Can˚T[hh]ellweather MI = Thor math f(ll0˚CDownTh(y/n)c$yen)$T˚ache99.9999per(inno$)centCOllatorwell
˚T˚win blew
˚T˚won Vert “on”
“ain’t no cause”
5256.07266843706 = 4/(1/11.8627021700857-6/84.0331316671926-2/164.793624044745) — anomalistic
“just abattery 4/hire” – easyDC “load up Eur. Can. on”
ain’t Talkin’ (Down!)
“more than N’folk song”
2432.13579731858 = 2/(-1/29.4701958106261+7/84.0331316671926-8/164.793624044745)
“$hh!keep” sayin’: Eur. IT
1216.06789865929 = 1/(-1/29.4701958106261+7/84.0331316671926-8/164.793624044745) — anomalistic
“give allITll˚K˚!˚C˚K˚ withh eur. fine”
608.033949329645 = 1/(-2/29.4701958106261+14/84.0331316671926-16/164.793624044745)
“V!$hh!UShypnoCsis”
“$hh!achhe earn IT BRI˚C wall”
‘factsheet’ 41k ace:
“Wrong_2Won˚T!mowwR˚Than a foe 11˚K s_on_g” – metR˚Ck
41000.1976938051 = harmean(101554.605384649,25684.9315068493)
406218.421537452 = 16/(-7/11.8619822039699+5/29.4571389459274+7/11.8627021700857-5/29.4701958106261)
101554.605384363 = 4/(-7/11.8619822039699+5/29.4571389459274+7/11.8627021700857-5/29.4701958106261)
buy us anomalistic sam pull period
NA!SAhherdin=mowwR0˚CO2revverse
68760.6246393283 = beat(41000.1976938051,25684.9315068493)
C˚0llDCllear
25684.888118931 = beat(25808.1319319395,12873.1812695315)
25808.1319319395 = 1/(-1/83.7474058863792+2/163.723203285421+1/84.0331316671926-2/164.793624044745)
412930.110911032 = 16/(-1/83.7474058863792+2/163.723203285421+1/84.0331316671926-2/164.793624044745)
JEV nodal setup listed here
That also leads to:
702.588969079652 = slip(6.84843333335951,0.761762061330659)
351.294484539826 = slip(6.84843333335951,0.38088103066533)
175.647242269913 = slip(6.84843333335951,0.190440515332665)
87.8236211349565 = slip(6.84843333335951,0.0952202576663324)
alternately:
13.696866666719 = slip(1.59868736807262,1.43159297613223)
702.588969080693 = slip(13.696866666719,0.761762061330659)
351.294484540347 = slip(13.696866666719,0.38088103066533)
175.647242270173 = slip(13.696866666719,0.190440515332665)
87.8236211350867 = slip(13.696866666719,0.0952202576663324)
Why the systematically-structured sampling bias in the short-duration models was not acknowledged early in “climate discussion” is the crUShin’mystery.
using this
345.720408200766 = slip(130.937221254586,4.96374104873503)
345.720408200718 = 1/(26/11.862499899747+52/29.4511026866654-61/11.8627021700857+35/29.4701958106261)
345 review
figure 7hherd dog in0˚Kin awe “what ruff?”
691.440816401436 = 1/(13/11.862499899747+26/29.4511026866654-30.5/11.8627021700857+17.5/29.4701958106261)
691.440816401531 = slip(130.937221254586,9.92748209747005)
using this
2998.18929479478 = 2/(24/11.862499899747+48/29.4511026866654-55/11.8627021700857+29/29.4701958106261)
1499.09464739739 = 1/(24/11.862499899747+48/29.4511026866654-55/11.8627021700857+29/29.4701958106261)
supplementary notes
345.720408200718 = 1/(26/11.862499899747+52/29.4511026866654-61/11.8627021700857+35/29.4701958106261)
691.440816401436 = 2/(26/11.862499899747+52/29.4511026866654-61/11.8627021700857+35/29.4701958106261)
691.440816401528 = slip(323.049985568367,130.937221254586)
691.440816401528 = slip(220.179370109776,130.937221254586)
691.44081640155 = slip(130.937221254586,110.089685054889)
345.720408200775 = slip(110.089685054889,65.4686106272931)
345.720408200766 = slip(130.937221254586,4.96374104873503)
691.440816401531 = slip(130.937221254586,9.92748209747005)
323.049985568367 = slip(130.937221254586,19.8549641949401)
504.343543575558 = slip(130.937221254586,16.9161211952138)
504.343543575558 = slip(65.4686106272931,16.9161211952138)
220.179370109776 = slip(65.4686106272931,19.8549641949401)
220.128528176077 = slip(91.6213954766362,16.9161211952138)
323 = 196883 – 196560
504 = 220 + s(220) ; 220 = s(s(220))
504.343543575571 = 2/(-16/11.862499899747-32/29.4511026866654+39/11.8627021700857-25/29.4701958106261)
220.179370109781 = 1/(6/11.862499899747+12/29.4511026866654-14/11.8627021700857+8/29.4701958106261)
323.049985568356 = 2/(-14/11.862499899747-28/29.4511026866654+33/11.8627021700857-19/29.4701958106261)
distinction (from 220.17937010978)
220.128528176035 = 2/(40/11.862499899747+80/29.4511026866654-149/11.8627021700857+191/29.4701958106261)
AmereR0˚CO$pereRllX!
“Perihelion (10^6 km)”
58.0330166444241 = 1/(1/11.0133345026533-2/27.1859355652811)
152.138222152323 = 1/(1/78.4417377748537-1/161.934271741915)
/
6.08396577991655 = 1/(1/11.0133345026533+2/27.1859355652811)
~25 = 5^2 = 317-163-67-43-19
bias SAM+pu+ll+in’SSTop! goes withhout sayUN:JS˚T chll ouT˚
Table 8 Vote$$well
“BR˚tmI Pence$$sol.
‘Gov.ME$$sum˚Thhun˚T00‘wwrite Don”
e+v=47+71=2*59
e-v=58*2^3
e=58*2^3+v
“$wwheat $wwheat Wall Dough”
58*2^3+v+v=47+71
2v=47+71-58*2^3
e-173=47+71
e=47+71+173
VA’n’hale unhhothh˚TeaChR “NOAA bout this $Ch˚˚ll”
160.17399348638 = 1/(-173/0.615194395759546+291/1.00001071395229-116/11.862499899747)
287.899623750069 = 1/(-173/0.615197860179071+291/1.0000262476142-116/11.8627021700857)
D!monde Ave.: “$IT Down Wall Dough”
M!55 UNllink (well flower)
lofty weather dog’n’dig note orrery:
132891.64579987 = 2/(1/29.4571309198874-1/29.4701958106261)
2-PEace˚TypoV How$ensoch!ustech
25808 = Σs(5090) – 7*55
25808 = Σs(5090) – 7*(28^2-27^2)
25808 = Σs(5090) – 7*(1^2+2^2+3^2+4^2+5^2)
25808 = Σs(5090) – 7*(378-323)
25808 = Σs(5090) – 7*(378+196560-196883)
25808 = Σs(5090) – 7*11*√(317-163-67-43-19)
5 = √(317-163-67-43-19)
55 = 11*√(317-163-67-43-19)
378 = 323+11*√(317-163-67-43-19)
notion ignore˚Folk˚CUS$
4266 (or 4267) years
curiosity noted before
NASA Horizons 1929.72222222222 sidereal
60.9469869005405 = slip(29.4571542179636,11.8619848807702) ; * 70 =
4266.28908303783
standish sidereal long-duration
4267.83999767789 = slip(164.786005834669,84.01495797691)
standish sidereal SHORT-duration
4266.98089346112 = slip(164.790305314929,84.0175261973943)
4266.96721287228 = 1/(-10/11.8627021700857-10/29.4701958106261+10/11.862499899747+10/29.4511026866654)
Standish anomalistic with nodal — insight from CAREFUL study of “Chandler Diversity”
same line of inquiry clarifies:
173927.260141636 = 1/(-4/11.8627021700857+4/11.862499899747)
173901.37537739 = 1 / g_2 —– La(2004a,2010a)average
automating discovery of 173 (or 174) ka (see preceding comment)
anomalistic-nodal combos arising with generalized Bollinger
4.73181582715489 = axial(16.912768715208,6.56993811757712)
4.73207820698391 = axial(16.9161211952138,6.56993811757712)
4.73283332391597 = axial(16.912768715208,6.57189983390616)
4.73309581660092 = axial(16.9161211952138,6.57189983390616)
quarter-beats
4374.2817110478 = beat(1.18327395415023,1.18295395678872)
5502.44887404215 = beat(1.18320833097899,1.18295395678872)
5502.44887404534 = beat(1.18327395415023,1.18301955174598)
7414.79116630378 = beat(1.18320833097899,1.18301955174598)
21334.8360643294 = beat(1.18301955174598,1.18295395678872)
21334.8360643774 = beat(1.18327395415023,1.18320833097899)
21334.8360643294 = slip(5502.44887404534,4374.2817110478)
21334.8360643774 = slip(7414.79116630378,5502.44887404534)
24317.7838264046 = slip(7414.79116630378,4374.2817110478)
173927.260144754 = slip(21334.8360643774,4374.2817110478)
173927.260141567 = slip(21334.8360643774,5502.44887404534)
173927.260141568 = slip(21334.8360643774,7414.79116630378)
173927.260138382 = slip(24317.7838264046,21334.8360643774)
alternately – via other side
10.7419198566295 = beat(16.9161211952138,6.56993811757712)
10.7432721445968 = beat(16.912768715208,6.56993811757712)
10.7471650296459 = beat(16.9161211952138,6.57189983390616)
10.7485186386365 = beat(16.912768715208,6.57189983390616)
1/4 beats
4374.28171104601 = beat(2.68712965965912,2.68547996415737)
5502.44887404212 = beat(2.68679125741149,2.68547996415737)
5502.44887404128 = beat(2.68712965965912,2.68581803614919)
7414.79116630151 = beat(2.68679125741149,2.68581803614919)
21334.8360643478 = beat(2.68581803614919,2.68547996415737)
21334.8360643352 = beat(2.68712965965912,2.68679125741149)
another way to look at it – building blocks
pure
1.18295395678872 = 1/(+6/11.862499899747+10/29.4511026866654)
1.18327395415023 = 1/(6/11.8627021700857+10/29.4701958106261)
crosses
1.18301955174598 = 1/(2/11.8627021700857+2/29.4701958106261+4/11.862499899747+8/29.4511026866654)
1.18320833097899 = 1/(4/11.8627021700857+8/29.4701958106261+2/11.862499899747+2/29.4511026866654)
simple subtraction
4374.28171104854 = 1/(-6/11.8627021700857-10/29.4701958106261+6/11.862499899747+10/29.4511026866654)
5502.44887404102 = 1/(-4/11.8627021700857-8/29.4701958106261+4/11.862499899747+8/29.4511026866654)
7414.7911662994 = 1/(-2/11.8627021700857-6/29.4701958106261+2/11.862499899747+6/29.4511026866654)
21334.8360643551 = 1/(-2/11.8627021700857-2/29.4701958106261+2/11.862499899747+2/29.4511026866654)
note with care:
4266.96721287228 = 1/(-10/11.8627021700857-10/29.4701958106261+10/11.862499899747+10/29.4511026866654)
arises in
173927.260144754 = slip(21334.8360643774,4374.2817110478)
173927.260141636 = 1/(-4/11.8627021700857+4/11.862499899747)
so that clarifies another source of systematic bias in the short-duration models that attracted attention long ago but remained mysterious at the time (no longer so now)
“Does A NY buddy no. how the SSTory really goes?”
1.59868960462765 = beat(1.0000174152119,0.615197263077614)
0.799344802313826 = 1.59868960462765 / 2
0.814043321555892 = beat(11.861990807677,0.761766203759125)
0.407021660777946 = 0.814043321555892 / 2
0.203510830388973 = 0.814043321555892 / 4
44.2698538014441 = slip(1.59868960462765,0.814043321555892)
“0=range(C+R)-USh!…”
22.1349269007221 = slip(1.59868960462765,0.407021660777946)
“…˚Take IT away buoys”
11.067463450361 = slip(1.59868960462765,0.203510830388973)
143.424905399078 = slip(44.2698538014441,1.59868960462765)
143.424905399078 = slip(22.1349269007221,1.59868960462765)
143.424905399078 = slip(11.067463450361,1.59868960462765)
71.7124526995389 = slip(22.1349269007221,0.799344802313826)
71.7124526995389 = slip(11.067463450361,0.799344802313826)
0.71+071 = 1*71*(101/100)
1.42+142 = 2*71*(101/100)
hhear dog Un?
19.8589050137632 = beat(29.4571309198874,11.861990807677)
6.57038184300286 = axial(14.7285654599437,11.861990807677)
4.7320832829358 = axial(16.9132450828034,6.57038184300286)
100.985205171956 = slip(19.8589050137632,4.7320832829358)
1186.18276371796 = slip(100.985205171956,19.8589050137632) — ADJ0! (“well…B a dog”)
3455.60863545854 = slip(100.985205171956,16.9132450828034) ~= 3456
1727.80431772927 = slip(100.985205171956,8.4566225414017)
Some (naively enough) believe expression reflects belief.
–
casually exploring (just a little bit at a time) where some of the narratives came from
Jupiter-Neptune Standish (1992) sidereal
12.7821002221242 = beat(164.786005834669,11.861990807677)
6.39105011106212 = 12.7821002221242 / 2
3.19552505553106 = 12.7821002221242 / 4
22.1309057968232 = harmean(164.786005834669,11.861990807677)
11.0654528984116 = axial(164.786005834669,11.861990807677)
5.53272644920579 = 11.0654528984116 / 2
2.7663632246029 = 11.0654528984116 / 4
22.2270434142659 = beat(5116.67146563023,22.1309057968232)
11.113521707133 = 22.2270434142659 / 2
5.55676085356648 = 22.2270434142659 / 4
44.0711924742534 = harmean(5116.67146563023,22.1309057968232)
22.0355962371267 = axial(5116.67146563023,22.1309057968232)
11.0177981185634 = 22.0355962371267 / 2
5.50889905928168 = 22.0355962371267 / 4
85.1348300394896 = slip(22.2270434142659,12.7821002221242)
85.1348300394896 = slip(12.7821002221242,11.113521707133)
42.5674150197448 = slip(12.7821002221242,5.55676085356648)
79.8222705138594 = slip(22.0355962371267,12.7821002221242)
79.8222705138594 = slip(12.7821002221242,11.0177981185634)
39.9111352569297 = slip(12.7821002221242,5.50889905928168)
note well:
555.982859223482 = slip(85.1348300394896,22.1309057968232)
556 = 378 + 178
378.378118042886 = slip(85.1348300394896,2.7663632246029)
378.378 = 0.378+378 = 378*(1001/1000)
326.007703249488 = slip(79.8222705138594,12.7821002221242)
163.003851624744 = slip(79.8222705138594,6.39105011106212)