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The last maxima of Wolf's cycle were in years 1979, 1989 and 2000 (List_of_solar_cycles).

Schwabe, Heinrich Samuel 1789-1875, amateur astronomer and botanist. Since 1826, he started (in an effort to find intra-merkurial planet Vulcan) the detailed observations of the Sun. After years of observation in y.1843 he noticed a significant ten-year period of the occurrence of sunspots. |

Period of ten-years

- 9.823563 years: S/3 (anomalistic)
- 9.85 years: temperature cycle (New Haven)
- 9.885526 years: Ja/P (Fairbridge,1997) , 9.9 years: cycle in various phenomena
- 9.93-9.94 years: cycle of solar flares, length of solar cycle (Charvátová)
- 10 years: Schwabe’s approximation of solar cycle, atmosphere, rotation E (also variation of field)
- 10.1466 years:9*1.1274 years, E-Moon
- 10.2 years: winter temperature cycle (Hudson Valley)
- 10.2-11.0 years: geomagnetic activity, 10.2-11.2 years: flare activity
- 10.0-10.3 years: one of period of triad (Charvátová)
- 10.24 years = 4*2.56 years, bimodal solar cycles 10 and 12 years
- 10.4 years: strong annual temperature cycle (Hudson Valley), cycle in tree rings (giant sequoia)
- 10.40 years: 52 years/5, 10.4163 years: B/41, 10.47 years: cycle of solar flares
- 10.54 years: ((J,S)/2,(U,N)), 10.566 years: ((J,S)/2,N)
- 10.8 years: volcanic activity, 10.80774 years: 3/J-2/S=5.40387 years, 10.81254 years: Jakubowski
- 10.00 years: Wilson 1. mode (116-124 months)

Wolf, Rudolf

Wolf, Rudolf, 1816-1893, Swiss astronomer, organizer of the first international project for tracking sunspots. Reconstructed solar activity back to y.1730 and adjusted mean sunspot period to about 11 years. |

- 10.7-11.5: changes in high of zone of flares (Gleissberg)
- 10.914 years: tritos = inex-saros (solar eclipses); 135 lunation (3987 days)
- 10.97 years: 32.9 years/3, 11 years: inversion of solar mg.field, 10 oscillation years
- 11.01: 2*5.504 years (M-V interactions)
- 11.03-11.14 years (Schove 1955, for period c. 500 years)
- 11.0324 years: 31/2 tzolkin = 15.5*0.71177 years, 11.03295 years: (J,S) * 5/9; 11.03942 years: 9/J-25/S
- 11.04 years: Barnes,1980(±2.02 years)
- 11.05-11.09 – mean cycle solar activity (Jakubowski), 11.0515 years: S*3/8; [18.62,27.19]
- 11.065 years: [J,5*32.9 years] = [J,164.5], 11.0657 years: [J,N] sidereal, maxima (Schove, through 2000 years)
- 11.08 years: acceleration and impulses of planets (R.Wolf), 11.0857 years: minima (Schove 1955, derived from 1932-155.2*n)
- 11.095080 years: [3J,2S] = 9*1.2328 years =177.52/16, 11.09551 years: [J,(U,N)] anomalistic
- 11.1 years: generally (Schwabe-Wolf’s, Astronomy 1947), between maxima (Ellison 1958)
- 11.1188 years = 3/S-1/U = 1/(S,U)+2/S = 1/(S,U)+2/U, 1/11.1188-1/11.0657 => H (2318 years)
- 11.121217 years: SSC, Sun-Spot-Cycle (Fairbridge,1997), 11.13: mean length (Mirošničenko)
- 11.1426 years: (V/2, E'/3) = (0.61518/2, 0.94899/3)
- 11.1719 years: nodal cycle of moon Dione, 11.17 years: 178.73/16 = 279.3/25
- 11.19 years: solar activity minima, 11.20 years: Mirošničenko 1986; 7*(V,E)
- 11.2 years: solar activity (4.2 vzestup+7 sestup), <11.2 years: (A.Rima 1961)
- 11.214 years: 4096 days =64*64 days (Chinnese cycle, see 384 days), 11.22788 years: 3/4*14.9705 years
- 11.233 years: ((J,S)/2, 170.8 years/2), 11.23845 years: (J,B/2) (anomalistic)
- 11.261 years: ((J,S)/2,U), 11.274 years:10*1.1274 years, E-Moon, 11.30 years: Dvořák, 1989
- 11.34 years: (2071 days) libration of Galilean moons (Meeus)
- 11.3480 years: 16*Tzolkin = 8*1.4185 years, 11.3883 years: [J,24 J] = 16 tzolkin = 12*346.6314 d
- 11.4 years: cycle solar flares (Winkless, Browning), sediments (R.J.Hugget), alignment Moon-Saturn; [18.61 years,29.46 years]
- 11.42 years: (M/3,(Moon,E))= (87.969/3, 29.530588)= 4171.4 d
- 11.5 years: analysis of wood from Ancient Greek c.(-600,-400)
- 11.67 years: Wilson 2. mode (135-145 months)

Also referred to as a 5-6 year Hellmann's period.

- 5.125 years: temperature cycle (New Haven)
- 5.2 years: cycles in history (N.S.Nesterov) (R.Tomes) , 5.25 years: climatic cycle (de Boer, 1938)
- 5.504 years: 1/M-4/V+2/E+1/R (synchron. period h of inner planets)
- 5.5 years: atmosphere, rotation E (also variation of poles)
- 5.560608 years: JEV (Fairbridge,1997)
- 5.6 years: climatic cycle (Polli, 1950) , 5.6370 years:5*1.1274 years, E-Moon
- 5.7 years: cycle in Cotton Acreage

Hale, George Ellery

Hale, George Ellery, 1868-1938, American astronomer. He derived - based on observations of magnetic fields on the Sun - 22-year cycle. |

- 22 years: solar flares, reversing of solar magnetismus, tree rings
- 22.065 years: 31 tzolkin = 31*0.71177 years,
- 22.18 years: ((J,S),189.8 years) (tropically)
- 22.40 years (67.2 years) 14 * (E,V) = Ts = 14*1.6 years
- 22.422 years: Dicke,1979 (±0.036 years),
- 22.4558 years: 3/2*14.9705 years
- 22.462 years: ((U,N),(J,S)), axes [S,U][J,N] right-angle (90˚) axes [J,S][U,N] angle 120˚
- 22.5 years: cycle of flood levels
- 22.56 years: N with regard to (J,S),
- 22.58 years: ((J,S),N), 22.6002 years
- 22.75 years: solar cycle (Winkless, Browning)
- 22.7766 years: 32 tzolkin = 32*0.71177 years
- 23.0 years: Hale’s solar cycle, cycle in tree rings (Abbot)
- 23.2 years: seismicity (+-6.4), 23.4 years: volcanism (+-6.0), 23.6 years: temperature

- 44.45 years: [61.01,N]
- 44.77 years: V-E-J simulation, 4*11.19 years
- 45 years: double Hale's solar magnetic cycle
- 45 years: solar cycle (Precambrium)
- 45.2 years: cycle of flood levels
- 45.5532 years: 64 tzolkin = 64*0.71177 years
- 46 years: climatic cycle, cycle of growth rings of trees (Abbot, 1937)
- 46 years: transit of Mercury through Solar disc, 46=(6+7)+33=13+33 years
- 46 years: occultations of stars by the eclipsed Moon (65-19 years)

discovered by Wolfgang Gleißberg during research of the solar activity.

Gleissberg observed 17 cycles from the year 290 AD (with mean duration c. 78 years), see below.

Length of the cycle is not constant - it varies quite considerably (approximately 85 ± 15 years).

Chandler's period

- 40.0 years: changes Chandler (S-Moon-E)
- 40 years: [60, 120]
- 40 years: intensity of geomg. field, archeomg. intensity
- 40.50 years: beats 779.94/365.256 = 15/7 (1.004);
- 40.66 years: conjunction M-V-E patterns
- 40.67 years: 2*B/21 (anomalitic)
- 40.7 years: spectrum of solar activity (Vztahy S-Zeme III)
- 40.79 years: beats 686.96/365.256 = 15/8 (1.003)
- 40.82 years: beats ((M,V),(V,E)) (1:4)
- 40.84 years: beats [E,V]/[E,M]=583.921/115.877=5.0391
- 40.85 years: beat(4/E-5/V+1/M) = 5*8.169 years
- 40.88 years: (E/8,R/15) tropical
- 42.12 years: beats from J/V = 19.282

- 77 years: floods on Nile (Hameed, 1984)
- 78 years: isotopes of oxygen (Grónsko) (Dansgaard, 1973)
- 78.5 years: cycle of growth rings of trees (a giant sequoia)
- 78.8 years: solar activity (Gleissberg)
- 79 years: solar cycle (Precambrium)
- 80 years: growth rings of trees v Californii (Maksimov, 1952)
- 80 years: level of Kaspic sea (Maksimov, 1952)
- 80 years: surovost zim (Evropa) (Maksimov, 1952)
- 80 years: Island - concentration of ice (Maksimov, 1952)
- 80 years: interdiurnal thermal (Berkes, 1955)
- 80 years: cycle of growth rings of trees (14C)
- 80.427 years: (J/2,6.4 years)
- 83 years: solar activity (Wolf, 1853)
- 83 years: growth rings of trees (sequoia growth per decade, Clough, 1933)
- 83 years: low levels of Nile (Clough, 1933)
- 83 years: crudeness of winters (Europe) (Clough, 1933)
- 83.034 years: 7*J
- 83.4 years: Gleisberg cycle (Fairbridge,1997)
- 84 years: Beijing rainfall (Burroughs, 1992)
- 86.124 years: 121 tzolkin = 121*0.71177 years
- 88 years: cycle of growth rings of trees (Japanese cedar tree)
- 88 years: aurora, 89 years: climatic cycle
- 83 years: E-J synodic multiple, 76*(E,J)
- 83.0397 years: 7*J
- 84.0 years: solar activity (Maximov)
- 88 years: aurora (north lights, polar flares)
- 89 years: Budapešť, Prague - klima (Thraen, 1949)
- 90 years: growth rings of trees (Moseley, 1940; Lamb, 1972)
- 90 years: drought (Moseley, 1944; Burroughs, 1992)
- 90.4 years: cycle of flood levels
- 92 years: cycle of growth rings of trees (Abbot)

1710-1720, 1760-1770, 1840-1850 and 1950-1960..

The last minima of Gleissberg cycle then fit approximately to years:

1740, 1810, 1900.

Configurations S-UN and SUN follows each other with period c.
18-21 years. So the interval of two
configurations SUN is 2 times longer, i.e. approximately 40
years (e.g.1672 minus 1630 or 1851 minus 1810).

Now, years us consider configurations (not necessarily exactly
aligned), in which the planets S,U and N “pull against” Jupiter
(like three men with ropes) from the opposite site of
the Sun.

Allowing wider angles (max c.60 dg from the exact oppositions on
both sides) the set of configurations J-SUN extends to
(years): 1630-1670-(1711),(1770)-1810-1850, 1950-1990-2030.

The first 2 triads (1630-1711, 1770-1850) corresponds to Gleissberg extremes:

But it is sometimes considered to be minimum.

So, probably, it is passing point - see the graph from the work of Prof.Silvia Duhau:

In some cases are "the ropes" of planets Uranus and Neptune nearly perpendicular to "ropes" of Jupiter and Saturn. E.g around the minimum 1890-1910:

Here are written some 100-year intervals, where no configuration J-SUN or only some weak configrations can be found: 660-760, 840-940, 1020-1120, 1160-1270, 1350-1450, 1530-1630, 1670-1770, 1850-1950.
Special alignment of the year 1990
reminds the year 1810, i.e. Gleissberg minimum.

But was the activity of the 1990 really longterm minimum? Do we have
to expect maximum around the year 2030?

These intervals follows from the previous schemes:

580-620-660, 760-800-840, 940-980-1020, 1120-1160,
1270-1310-1350, 1450-1490-1530,
(look on the Gleissberg cycles and some 180-year cycles...)

Gleissberg's extremes

Gleissberg (1965)

Gleissberg | U#N | J - SUN |

? | 64 | 84 |

? | 150 | 124 |

? | 236 | 263 |

360 | 322 | 303 |

440 | 409 | 443 |

510 | 495 | 483 |

575 | 581 | 583 |

665 | 667 | 662 |

755 | 754 | 762 |

840 | 839 | 801 |

920 | 926 | 941 |

990 | 1011 | 980 |

1115 | 1098 | 1120 |

1185 | 1183 | 1174 |

1250 | 1270 | 1299 |

1305 | 1270 | 1299 |

1375 | 1355 | 1353 |

1455 | 1441 | 1453 |

1545 | 1527 | 1491 |

1605 | 1613 | 1632 |

1715 | 1698 | 1671 |

1765 | 1784 | 1771 |

1840 | 1869 | 1851 |

1955 | 1955 | 1950 |

? | 2041 | 2029 |

It maybe linked with the 55-year cycle of solar activity.

The last extremes of the Kondratiev cycle were approximately in the years:

1810,1865,1920,1975 (maximum), 1835,1890,1945,2000 (minimum).

Cycle 55 years

The period was observed in the following phenomena:

Martin Roy on Solar Activity
- 53.0 +- 0.6 years - dominant periods of sunspots of years 1700-2010 (J.-E.Solheim)
- 53.2 years: cycle from tree-rings (a giant sequoia)
- 53.3 years: 5*10.66 years (J.-E.Solheim)
- 53.38 years: 9*J/2; B/8; 75 tzolkin
- 53.5558 years: 8/S-3/J, beats (J/3,S/8) - approximately 268 years/5 = 53.6 years
- 53.9 years: from spectrum of solar activity (textbook)
- 54 years: Contradieff economic cycle
- 54.093 years: Exeligmos=3*Saros, cycle of solar eclipses =669 lunations =19756 days
- 54.91 years: from spectrum of solar activity
- 55 years: cycle from tree-rings (Japanese cedar tree)
- 55.24 years: conjunction Jupiter-Uran, 4*(J,U)
- 55.33 years: M-V 224.701/87.969 = 2.5543 23/9 beats
- 55.408 years: [U,N] (tropical periods), 55.6449 years: [U,N] (sidereal periods)
- 56.1 years: cycle of solar spots
- 56.64 years: 1/J-3/S+3/U-3/N

Mean period of 4 conjunctions J-U is 4*(J,U)=4*13.81=55.24 years:

Minima
29.4.1893
27.7.1948
31.10.2003

Maxima

16.12.1920
14.3.1976
12.6.2031

(http://dollarcollapse.com/wp-content/uploads/2010/05/Kondratieff.jpg)

- 110.31: V-E-J simulation 2*44.77+20.77 years, 10 * 11.031 years
- 110.500 years: 8*(J,U) = 8*13.8125 (317.77/3 = 105.923 years)
- 111.050 years: Moon tides cycle (Wood)
- 112 years: 4*28 years, "calendars of weather", "centennial calendars"

Year |
∆L |
L |

643.85 |
3 |
9 |

753.59 |
-4 |
10 |

863.92 |
-1 |
9 |

974.97 |
-5 |
-7 |

1085.42 |
-9 |
2 |

1195.35 |
-9 |
-2 |

1306.56 |
0 |
-8 |

1416.79 |
-5 |
-9 |

1527.02 |
4 |
-9 |

1637.71 |
-5 |
-9 |

Year |
∆L |
L |

1278.11 |
-4 |
-2 |

1389.38 |
-1 |
-10 |

1499.69 |
-5 |
-8 |

Synodic period (R,S) = 2.009131627 fits (by 55 multiple) into 110.5 years period.
16.12.1920

Oppositions R-S coincide with oppositions J-U in years:

594.9, 705.47, 815.99, 926.48, 1036.96, 1147.48, 1257.98, 1368.46, 1478.97, 1589.47, 1699.95, 1810.46, 1920.96, 2031.45, 2141.95.

Some of the data (e.g.1699.95, 1810.46, 1920.96) point to periods with locally lower Solar activity. The last know decrease of solar activity is from the beginning of 20-th century.

Conjunctions J-X
Oppositions R-S coincide with oppositions J-U in years:

594.9, 705.47, 815.99, 926.48, 1036.96, 1147.48, 1257.98, 1368.46, 1478.97, 1589.47, 1699.95, 1810.46, 1920.96, 2031.45, 2141.95.

Some of the data (e.g.1699.95, 1810.46, 1920.96) point to periods with locally lower Solar activity. The last know decrease of solar activity is from the beginning of 20-th century.

Period 110.5 years coincide approximately with 9
conjunctions J-X (see Planet X)
#### 9 * (J,X) = 9*12.2368 years = 110.13 years

E.g. 1686,12 ( 12,27) 1698,38 ( 12,27) 1710,65 ( 12,24)

1722,89 ( 12,27) 1735,15 ( 12,24) 1747,39 ( 12,24)

1759,63 ( 12,21) 1771,84 ( 12,21) 1784,05 ( 12,21)

1796,26

31.1.1686 13.6.1796

- 220 years in the spectrum of solar activity.
- 220.55 years: 9*(U,N)/7 (anomalistic)
- 222.019 years: Wood’s moon tidal cycle (Fairbridge,1997).
- 222.6 years: ((J,S/2),U) = (60.85,83.75) (anomalistic)

Rainy periods

Opposition J-U Rainy period

-------------------------------------------------

27.10.1782 31.10.2003 26.10.2224

-------------------------------------------------

898.86 898 Nov 5 ?

1119.83 1119 Oct 23 1078-1118 (I.)

1340.85 1340 Oct 27 1310-1350 (II.)

1561.84 1561 Oct 22 1560-1600 (III.)

1782.83 1782 Oct 27 1763-1804 (IV.)

2003.84 2003 Oct 31 1995-2035 (V.)

2224.83 2224 Oct 26 ?

23.10.1119 27.10.1340 22.10.156127.10.1782 31.10.2003 26.10.2224

- 165.25 years: (W,J) = (11.06753, 11.861983), see Wood’s resonance
- 165.5 years ± 0.5 years: deviation of centers of mass Sun-JSUN and Sun-JS
- 165.75 years: 12 * (J,U) = 12*13.812; 166.17 years: 13 * (J,N) = 13*12.782
- 332.27 years: beats 4/(J,S) – 9/(S,U) = 4/J – 13/S + 9/U = 1/332.27 years
- 334 years: climatic cycle (Auric, 1936)

Period 884.1 years is multiple of period 5*S,
884.1=6*147.35 years, 30*S=30*29.457=883.715 years, 64*(J,U) =
64*13.812 = 883.965 years, 139* I = 139*6.3611 years =
884.193 years.
Ratio S/J corresponds to 149/60, so 30*S = 44.5 (J,S) = 74.5 J = 884.1 years.

Oppositions V-ER and at the same time opposition J-U occurs
approximately in years: 17.7.235, 31.7.1119, 31.7.2003, 16.9.2887,…

23.10.1119 22.10.2887

Cycle 1216 years

According to analysis in project (Charvatova,Strestik) is significant climatic period equal to 1214 years. Let us note, that 1215.5 years = 11 * 110.5 years. Exact conjunctions V-E-R do not appear always after c. 300 years, period changes in span c. 298.9-318.2 years (298.9 years ~ 47*6.4-1.88 years, 318.2 years ~ 50*6.4-1.88 years). E.g. we find E-V-R in one line in years 1044.05,1343.00,1661.19,1960.13,2259.09; difference 2259.09-1044.05=1215.04 years.

According to 1767.4 years: 2*883.7 years=3*589.1
years = 17* 103.96 years = 89 * 19.859 years
.
(If in conjunctions V-E-R one period of Mars drop out after c.
300 years, it is like one Wolf’s period during 1768 years…)

In connection to cycles of ice ages (stadial cycles) mainly triad of periods 550 years–1100 years–1650 years was alluded. Reflection of multiples of c. 280 years period in climatic oscillations (Stacey, Karlstrom,..)

- 278.0304 years: 14SJ/EV (Fairbridge,1997)
- 280 years: biologic cycle (tree rings)
- 280.054 years: 2*140.027 years
- 283.0 years: glacier-iceberg changes
- 284.7075: Mayan cycle, part of Babylonian cycle, 24*J= 2*B/3 = 400 tzolkin (151 R)
- 285.0 years: (32.87, S)
- 286.1 years: E-R cycle, 7* 40.876 years
- 286.96 years: 8*(S,N) = 8*35.87 years
- 290 years: solar cycle (old Chinese observations)

For sidereal periods of outer planets the following equation
holds (see Stable resonance ):
#### 3/J-8/S-2/U+7/N = 0

Two analogous relations 8/S-3/J=5/G and 7/N-2/U=5/G compose equation (8/S-3/J) - (7/N-2/U) = 0,
that holds precisely, at least for average periods.
Hence G=267.67-267.78.
Is it possible that motion of Sun-J-S makes pentagon instead of trigon
(with regard to notional period G…) according to resonance S:J not 5:2, but 8:3 ?
With regard to period G=270-285 years synodical periods
(S,G):(J,G) makes ratio 8:3;
(J,G)=12.4 years (see P.Kalenda,J.Málek: theory of solar dynamo)
(S,G)=33.0 years (3 Wolf’s cycles).

Indicia for five-fold motion
c. 2003.7 (18.8.2003-31.8.2003)
when planets aligned to line according to minimal interaction,
spacing of Jupiter and Saturn was c. 54˚, i.e. (360˚+180˚) /10.
Landscheidt’s five-fold property
observation of c. 270-ti years period in tidal
theory (see P.Kalenda,J.Málek: theory of solar dynamo)
observation of shifts of 180 years cycles with
synchronization each 2*270 years (P.Kalenda)

Stacey‘s cycle

- 536.2 years: 3*178.73 years
- 536.2 years: mutual motion J-S-Hidalgo, 7* 76.6 = 7*(J,Hidalgo) = 20*26.81 = 20*(S,Hidalgo),
- 537.0 years: beats 3/J-2/V+3/E
- 540-580 years: Pearson’s-Stacey’s cycle
- 550.0 years: Feirbridge’s cycle 550,1100,1650 (3600) years
- 556 years: Stacey’s - Zero-check cycle/3, (539.8-556.0, mean 548 years)
- 556 years: multiple of conjunctions J-S (28*19.86=3*185.3)
- 556.027 years: advance of moon perigee (Fairbridge, Sanders)
- 556.0609 years: SQ-1 (Fairbridge,1997)
- 558 years: moon tidal cycle (Wood)
- 560 years: S-U perturbations (Schlyter)
- 566.58 years: (S,U/3) (anomalistic)
- 567 years: Pearson’s geologic cycle
- 570 years: temperature cycle, geologic cycle (sandstone formations)

- 1000 years climatic cycle
- 1112 years: Stacey’s cycle, (anomalistic)
- 1118.23 years: Jakubowski - model of solar activity
- 1133.0 years: Karlstrom’s stadial cycle

- 1665.7 years: 9/25 *4627 years = 9* 185.08 years
- 1668.1825 years: SQ-3 (Fairbridge,1997)
- 1668 years Stacey’s Zero-check cycle 3*556 years, Earth-Moon, 84*(J,S)
- 1700.0 years: geophysical cycle of iceberg changes; motion of icebergs (Pleistocene)
- 1703.5 years: inequalities (544.79,800.94) (tropical periods)
- 1708 years: 5125 years/3 (cycle derived from Mayan), 4*B = 144*J=1708.245 years
- 1708 years: eruptions of volcanoes (-3341 Avelino,-1633 Thera,+75 Vesuv,+1783 Laki)

- 3336.365 years: SQ-6 (Fairbridge,1997)
- 3400.0 years: Karlstrom’s cycle of ice ages