Jupiter resonance

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Mechanism of resonance

Basic relations

Period of resonance 1/S - 1/U + 1/N = 1/35.587 years corresponds to 3 Jupiter's periods (3*J).
The three outer planets Saturn, Uranus and Neptune synchronize motion with regards to perihelion Ljp resp. aphelion Lja of Jupiter:

L_S – L_U + L_N +90° ~ L_J – L_Jp = L_J – L_Ja + 180°

Jupiter's resonance - table

Instants, when Ls-Lu+Ln+90º = 0 (~perihelion) resp. Ls-Lu+Ln-90º = 0 (~aphelion) are in the column Resonance:

Resonance	Perihelion	*	Resonance	Perihelion	Resonance	Aphelion	*	Resonance	Aphelion
1311,6	1311,31	*	1738,7	1738,34	1329,9	1329.08	*	1756,4	1756,16
1347,1	1346,85	*	1773,4	1773,90	1364,0	1364,64	*	1790,7	1791,70
1382,0	1382,47	*	1809,2	1809,55	1400,7	1400,24	*	1827,9	1827,29
1418,6	1418,03	*	1845,4	1845,09	1435,6	1438,83	*	1862,3	1862,91
1452,8	1453,62	*	1879,8	1880,74	1471,2	1471,39	*	1898,3	1898,48
1489,9	1489,22	*	1916,7	1916,28	1507,6	1507,01	*	1933,8	1934,13
1524,4	1524,78		1951,0	1951,87	1541,9	1542,55	*	1968,9	1969,67
1560,4	1560,40	*	1987,6	1987,52	1578,8	1578,20	*	2005,7	2005,26
1596,0	1595,94	*	2022,6	2023,05	1613,0	1613,76	*	2039,8	2040,88
1630,9	1631,59	*	2058,0	2058.63	1649,7	1649,33	*	2076,5	2076.44
1667,8	1667,13	*	2094,4	2094.21	1685,0	1684,98	*	…	…
1701,9	1702,75	*	…	…	1720,0	1720,52	*	…	…

Angles Ls-Lu+Ln+90° in time of Jupiter in perihelion P and aphelion A.

1809,56	2,1	1845,09	359,7	1880,74	359,3	1916,31	3,5	1951,90	16,1	1987,52	0,5
1815,50	53,9	1851,03	60,1	1886,65	63,8	1922,25	70,5	1957,81	69,8	1993,46	54,7
1821,41	111,5	1856,98	128,5	1892,57	126,5	1928,22	129,1	1963,75	120,9	1999,40	116,3
1827,32	178,7	1862,94	194,9	1898,48	181,5	1934,13	184,2	1969,67	177,6	2005,28	185,3
1833,24	245,7	1868,89	251,0	1904,42	234,6	1940,07	245,1	1975,61	242,7	2011,23	251,3
1839,18	304,6	1874,83	302,8	1910,37	294,6	1945,96	312,3	1981,58	305,6	2017,14	308,5

See also Bruckner‘s cycle (below).

Differences from precise angles of the hexagon:
c_hexadiffs

Graph of differences

We can observe the values even outside the selected points (hexagon vertices).. Let us mark:

α = (Lj - LPj) - (Ls - Lu + Ln + 90) * 3,

where Li are longitudes of planets, LPj longitude of Jupiter perihelion. The progress of f(α) in time - the function f translates the given angle into the interval (-180 dg, +180 dg) - is shown in the following graph.

In the chart, we see the minimum around y.1820 (Dalton's minimum) and the maxima in the years 1870, 1950. After developing the chart into history - Norman, Wolf and Sporer minimum is similarly observable, partly even Maunder's minimum and also some significant known maxima (1190, 1270, 1370, 1600, 1780).

Main points

In the following charts, the Jupiter passages are marked with a perihel (blue little circles) and aphel (red little circles) every third pass (Bruckner period):

Note the exceptions to the standard course at points 1774 and 1952 (perihel) and 1863 (aphel). These exceptions (extremes) progress approximately with period of 89 years. See Gleissberg's cycle

Symmetry

The 89 year (178 years/2) cycle can not last for centuries (it is inconsistent with the 171 year cycle of Uranus-Neptune conjunctions, ...)
In the vicinity of 1569, however, we observe an axis of symmetry ...!?

                    1454      1489      1525      1561 *       1596      1632      1667     
                         1472      1507      1543      *  1579      1614      1650      1685

According to this axis - also 89-year intervals of extremes develop:

                    1009 1098 1187 1276 1365 1454 1543 * 1596 1685 1774 1863 1952 2041 2130

The years around 1560 are connected with so called Suess minimum...

This incredible period of dryness, as they describe it, persisted “from the 1540s to 1580s in Mexico, from the 1550s to 1590s over the [U.S.] Southwest, and from the 1570s to 1600s over Wyoming and Montana.” In addition, it “extended across most of the continental United States during the 1560s,” and it recurred with greater intensity over the Southeast during the 1580s to 1590s. So horrendous were its myriad impacts, Stahle et al. unequivocally state that “the ‘megadrought’ of the sixteenth century far exceeded any drought of the 20th century.” (Climate Change Reconsidered, Observations: Extreme Weather)
Other graphs

Similar symmetry axes are (of course) on the timeline more. It seems to be determined (primarily) by the opposition of planets Uranus and Neptune, and also (secondarily) by the position of the planet Saturn.

Distances of extremes

Let's look at the last 5 extremes (maximum):

12.05.1890 (1890.37)

15.11.1924 (1924.88)

15.11.1949 (1949.88)

30.3.1983 (1983.25)

2.9.2009 (2009.68)

The spacing of this data is:

(1924.88-1890.37 =) 34.51 let (= 4 * 8.62 let)
(1949.88-1924.88 =) 25.00 let (= 3 * 8.33 let)
(1983.25-1949.88 =) 33.37 let (= 4 * 8.34 let)
(2009.68-1983.25 =) 26.43 let (= 3 * 8.81 let)

The average period of extremes appears to be the average period of motion of the (non-oriented) axis of planets Jupiter and Saturn: P = [J,S] / 2 = 8.45662 years.
Let's check what data for extremes we get from the "beginning" in the year 1569 (1569.40, 14.5.1569):

1577.86, 1586.31, 1594.77
1603.23, 1611.68, 1620.14, 1628.60, 1637.05, 1645.51, 1653.97, 1662.42, 1670.88, 1679.34, 1687.79, 1696.25
1704.71, 1713.16, 1721.62, 1730.08, 1738.53, 1746.99, 1755.45, 1763.90, 1772.36, 1780.82, 1789.27, 1797.73
1806.19, 1814.64, 1832.10, 1831.56, 1840.01, 1848.47, 1856.93, 1865.38, 1873.84, 1882.29, 1890.75, 1899.21
1907.66, 1916.12, 1924.58, 1933.03, 1941.49, 1949.95, 1958.40, 1966.86, 1975.32, 1983.77, 1992.23,
2000.69, 2009.14, 2017.60, 2026.06, 2034.51, 2042.97, 2051.43, 2059.88, 2068.34, 2076.80,2085.25, 2093.71

Resulting dates 1890.75 (+0.38), 1924.58 (-0.30), 1949.95 (+0.07), 1983.77 (+0.52), 2009.14 (-0.54) differ from the five extremes observed here for at most half a year (0.52-0.54 year).

Periods

The first triple of extremes 1949.88 - 1890.37 = 59.51 years = 7*8.50 years.
The second triple of extremes 2009.14 - 1949.88 = 59.26 years = 7*8.47 years.
Five Jupiter periods are 59.31 years = 7*8.47 let, two Saturn periods 58.91 years = 7*8.42 years, three conjunctions J-S 59.58 let = 7*8.51 years (three Mayan periods Katun 59.13 years = 7* 8.45 years).

Some theories have reached a period of 8.45 years or its multiple of 16.9 years. But as the source of this period is often considered to be the Moon.

In the book Climate Development and History of the North Atlantic Realm is written: The draconic month has a length 27.21222 days, the sidereal month of 27.321661 days, and the anomalistic month of 27.554551 days. The difference beats between these three latter periods are 18.6 years, 8.85 years, and 6 years. These three periods together produce one more additional beat 16.9 years.
T.C.Royer has detected (in article “High‐latitude oceanic variability associated with the 18.6‐year nodal tide") the 16.9 year period in air temperatures.
...

Modulation of the axial period [J, S] / 2 by the Bruckner 3J period leads to the period:

W = ([J,S]/2, 3J) = (8.45662, 3*11.8620) = 11.09267 years !?

See Solar activity

Note:
The value consensus of stable resonance period: 1/W - 1/J + 1/N - 1/U = 0 (11.09439 let) and the period W = ([J,S]/2, 3*J) considered here is not accidental. By substitution, we get 1/J - 3/S + 3/U - 3/N, which is the relationship from which we came out above.

The second pole of these 2 periods is:

Q = [[J,S]/2, 3J] = 13.66573 years !?

See Earthquakes

Bruckner’s cycle

Bruckner 35 years (33 years-36 years) climatic cycle.

The first known record of the cycle comes from y.1625 from observation of Francise Bacon. The cycle was rediscovered and described in greater detail by Eduard Bruckner in 1890.

Bruckner‘s period

34.5 years: wood of ancient Greece c.(-600,-400)
34.7538 years: EVMeRes (Fairbridge,1997),
35 years: frequency of cold winters, precipitation
35.519 years: ((U,N),S)
35.570 years 3*J sidereal,
35.5884 years anomalistic, (S, 170.8 years)
35.71 years: [P1,P2]= [(J,S/2),(U/2,N/2)]= 1/J-2/S+2/U-2/N
35.862 years (S,N) sidereal, 35.8699 years (S,N) tropical
36 years: cycle of solar motion (T.Landscheidt – “hand”)

Timing

Dr.Bruckner pointed to

1/ cold wet periods: 1700, 1740, 1780, 1815, 1850, 1880

2/ warm dry periods: 1720, 1760, 1795, 1830, 1860.
see Clough, H. W.
Google:Synchronous Variations in Solar and Terrestrial Phenomena (1905)

Action of Jupiter

Resonance:

L_S – L_U + L_N +90° ~ L_J – L_Jp

From the relation we get these extremes of Jovian actions:

1/ cold wet periods:

1702.76,

1738.52, 1772.55, 1809.32, 1845.13, 1880.81

2/ warm dry period:

1720.64, 1755.54, 1790.94, 1827.23, 1862.97 (centers of the dates above)

Extrapolation (prediction)

The extremes of Jovian actions continue:

1/ cold wet periods:

1916.02, 1950.29, 1987.45, 2022.66, 2058.80, 2093.35

2/ warm dry period:

1933.16, 1968.87, 2005.06, 2040.73, 2076.08 (centers of the dates above)

Climatic manifestations

Bruckner data	J-action minimum	Note	Advances of icebergs in the Alps	Wet in Russia	Cold in NW Europe	J-action maximum	Theodor Landscheidt big fingers (BFS) & hands (BHS)	Note
	1594.91		1600-1610			1612.86
	1630.81		1632-1644			1649.17		S-max
	1667.52		1664-1685			1685.14		S-max
1700	1702.76		1712-1716			1720.64
1740	1738.52	S-max	1734-1743	1736-1755	1731-1745	1755.54	1756 - BHS	S-min
1780	1772.55		1767-1770 1787-1790	1771-1780	1756-1790	1790.94
1815	1809.32	S-min	1814-1825	1806-1825	1806-1820	1827.23
1850	1845.13		1845-1856	1841-1855	1836-1850	1862.97	1867 - BFS
1880	1880.81		1880-1894	1871-1885	1871-1885	1898.42	1901- BFS
	1916.02		1914-1924			1933.16	1933 - BHS	S-min
	1950.29					1968.87	1968- BFS	S-max
	1987.45	S-min				2005.06	2007-BFS
	2022.66					2040.73
	2058,80					2076.08
	2093,35					2111.66	2111 - BHS	S-min?

* NW Europe = northwestern Europe (Data according to Vilém Bölsche, Rhodes W. Fairbridge, ...)

Follow-up considerations

Jovian perihelions

Resonance L_S – L_U + L_N +90° ~ L_J – L_Jp )

Jupiter near perihelion - data y.0-800 AD

           30,66      (11,88)    30,01 (11,91)    41,92 (11,86)    53,77
(35,54)    66,20      (11,83)    65,60 (11,86)    77,46 (11,88)    89,34 
(35,07)   101,28      (11,91)   101,25 (11,86)   113,10 (11,80)   124,90
(37,45)   138,73      (11,86)   136,76 (11,88)   148,64 (11,91)   160,55
(34,50)   173,23      (11,86)   172,41 (11,83)   184,23 (11,86)   196,09
(35,37)   208,60      (11,88)   207,97 (11,91)   219,88 (11,86)   231,74
(34,99)   243,59      (11,83)   243,56 (11,83)   255,39 (11,88)   267,27
(35,84)   279,43      (11,91)   279,18 (11,86)   291,04 (11,83)   302,87
(36,99)   316,42      (11,86)   314,72 (11,86)   326,58 (11,91)   338,49
(34,36)   350,78      (11,86)   350,34 (11,83)   362,17 (11,86)   374,03
(35,65)   386,43      (11,86)   385,88 (11,91)   397,79 (11,88)   409,67
(34,58)   421,01      (11,83)   421,50 (11,83)   433,33 (11,88)   445,21
(36,88)   457,89      (11,88)   457,09 (11,88)   468,98 (11,83)   480,80
(36,11)   494,00      (11,83)   492,63 (11,88)   504,51 (11,88)   516,40
(34,69)   528,69      (11,88)   528,28 (11,86)   540,13 (11,83)   551,96
(35,51)   564,20      (11,86)   563,82 (11,88)   575,70 (11,88)   587,58
(34,52)   598,73      (11,86)   599,44 (11,83)   611,27 (11,86)   623,12
(37,59)   636,32      (11,88)   635,00 (11,88)   646,89 (11,86)   658,74
(35,26)   671,58      (11,86)   670,60 (11,86)   682,45 (11,86)   694,31
(35,18)   706,76      (11,88)   706,19 (11,88)   718,07 (11,83)   729,90
(35,02)   741,78      (11,86)   741,75 (11,86)   753,61 (11,88)   765,49
(34,99)   776,77      (11,91)   777,40 (11,83)   789,23

y.800-1600 AD

                                                                  (11,86)   801,08
          (37,62)   814,39      (11,86)   812,94 (11,88)   824,82 (11,88)   836,71
          (34,77)   849,16      (11,86)   848,56 (11,83)   860,39 (11,86)   872,24
          (35,59)   884,76      (11,88)   884,13 (11,91)   896,04 (11,86)   907,89
          (34,50)   919,25      (11,83)   919,72 (11,86)   931,57 (11,88)   943,46
          (35,87)   955,12      (11,91)   955,37 (11,86)   967,22 (11,83)   979,05
          (36,93)   992,05      (11,86)   990,90 (11,88)  1002,79 (11,88)  1014,67
          (34,77)  1026,83      (11,88)  1026,55 (11,80)  1038,35 (11,86)  1050,21
          (35,65)  1062,47      (11,88)  1062,09 (11,91)  1074,00 (11,86)  1085,85
          (34,17)  1096,64      (11,83)  1097,68 (11,86)  1109,54 (11,88)  1121,42
          (36,88)  1133,52      (11,88)  1133,30 (11,88)  1145,19 (11,83)  1157,01
          (36,03)  1169,55      (11,83)  1168,84 (11,88)  1180,72 (11,91)  1192,63
          (35,13)  1204,68      (11,86)  1204,49 (11,83)  1216,32 (11,86)  1228,17
          (35,26)  1239,94      (11,86)  1240,03 (11,91)  1251,94 (11,86)  1263,79
          (34,33)  1274,28      (11,86)  1275,65 (11,83)  1287,47 (11,86)  1299,33
          (37,48)  1311,76      (11,91)  1311,24 (11,88)  1323,12 (11,83)  1334,95
          (35,32)  1347,08      (11,83)  1346,78 (11,88)  1358,66 (11,88)  1370,54
          (35,62)  1382,70      (11,88)  1382,43 (11,83)  1394,25 (11,86)  1406,11
          (34,69)  1417,39      (11,86)  1417,96 (11,88)  1429,85 (11,88)  1441,73
          (34,94)  1452,32      (11,86)  1453,58 (11,83)  1465,41 (11,86)  1477,27
          (37,43)  1489,75      (11,88)  1489,15 (11,88)  1501,03 (11,86)  1512,89
          (35,04)  1524,80      (11,86)  1524,74 (11,83)  1536,57 (11,88)  1548,45
          (35,92)  1560,72      (11,88)  1560,33 (11,88)  1572,22 (11,83)  1584,04
          (34,20)  1594,91      (11,86)  1595,90

After y.1600 AD

                                                 (11,86)  1607,76 (11,88)  1619,64
          (35,89)  1630,81      (11,88)  1631,52 (11,86)  1643,38 (11,83)  1655,20
          (36,72)  1667,52      (11,88)  1667,09 (11,88)  1678,97 (11,88)  1690,85
          (35,24)  1702,76      (11,83)  1702,68 (11,86)  1714,53 (11,86)  1726,39
          (35,76)  1738,52      (11,88)  1738,27 (11,91)  1750,18 (11,83)  1762,01
          (34,03)  1772,55      (11,83)  1773,84 (11,88)  1785,72 (11,86)  1797,57
          (36,77)  1809,32      (11,91)  1809,48 (11,86)  1821,34 (11,83)  1833,17
          (35,81)  1845,13      (11,86)  1845,02 (11,88)  1856,90 (11,91)  1868,81
          (35,67)  1880,81      (11,86)  1880,67 (11,83)  1892,50 (11,86)  1904,35
          (35,21)  1916,02      (11,88)  1916,24 (11,91)  1928,15 (11,86)  1940,00
          (34,28)  1950,29      (11,83)  1951,83 (11,83)  1963,66 (11,88)  1975,54
          (37,15)  1987,45      (11,91)  1987,45 (11,86)  1999,30 (11,83)  2011,13
          (35,21)  2022,66      (11,86)  2022,99 (11,88)  2034,87 (11,91)  2046,78
          (36,14)  2058,80      (11,86)  2058,63 (11,83)  2070,46 (11,83)  2082,29
          (34,55)  2093,35      (11,88)  2094,17

(Computed using simplified VSOP87.)

Axial periods

Let Lj,Ls,Lu,Ln are lengths (longitudes) of outer planets. If angles (Ls-Lj) and (Lu-Ln) are equal, axes of S,N coincide with axes of J,U.

Such configurations repeats with mean period: ([J,U],[S,N]) = 35.5948 years, i.e. period of c. 3 orbital periods of Jupiter (3∙11.8620=35.5860 years).

So:

([J,U],[S,N]) = 3J

In period 1500-2050 coincidence of axes (0°, 180°) happens always after Jupiter passing of perihelion or aphelion (usually within 1 year).

Coincidence of axes

    J perihelion | (interval) Ls-Lj=Lu-Ln | J aphelion 
----------------------------------------------------------------
    1500.95 | (17.51) 1501.71 (18.22) 1519.93 | 1518.74
    1536.54 | (17.91) 1537.84 (17.12) 1554.95 | 1554.33
    1572.13 | (18.06) 1573.02 (18.19) 1591.21 | 1589.91
    1607.72 | (17.54) 1608.75 (18.38) 1627.13 | 1625.50
    1643.31 | (16.63) 1643.75 (18.43) 1662.19 | 1661.09
    1678.89 | (17.75) 1679.93 (17.96) 1697.89 | 1696.67
    1714.49 | (17.78) 1715.67 (17.19) 1732.86 | 1732.26
    1750.08 | (18.20) 1751.06 (18.42) 1769.48 | 1767.84
    1785.66 | (17.14) 1786.62 (18.24) 1804.86 | 1803.43
    1821.25 | (16.84) 1821.70 (18.57) 1840.27 | 1839.02
    1856.85 | (17.83) 1858.10 (17.62) 1875.72 | 1874.60
    1892.43 | (17.79) 1893.50 (17.45) 1910.95 | 1910.19
    1928.02 | (18.18) 1929.13 (18.46) 1947.59 | 1945.77
    1963.61 | (16.81) 1964.40 (18.26) 1982.66 | 1981.36
    1999.20 | (17.14) 1999.79 (18.58) 2018.37 | 2016.95
    2034.79 | (17.78) 2036.15 (17.32) 2053.47 | 2052.53

(Computed using simplified VSOP82.)

(Compare with: 2/S-1/U -> 17.869 years = 3J/2)