Solar activity - Resonance

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Wood's resonance

Wood
Wood[],

Wood model

One of suggested models of solar activity is Wood's model of influences of planet Jupiter, Earth and Venus on Sun. Configuration E-V-Sun-J or Sun-V-E-J repeats with period approximately 22 years.

E.g. configurations:
1727.87, 1748.63, 1793.40, (20.76+44.77+44.77 y)
1838.17, 1882.94, 1903.70, (44.77+20.76+44.77 y)
1948.47, 1993.25, 2038.01, (44.78+44.76+20.77 y)

Conjunctions and oppositions V-E-J launch near maxima of solar activity, see e.g. Jean-Pierre Desmoulins .


Resonance

The following relationships result from Wood's model. Let ((E,J)/5 ,(V,J)/3) = 2∙W. Then 1/(2W) = 3/V-5/E+2/J. Hence 2W = 22.13505 years and W = 11.06753 years
Maximum of solar activity appears approximately, when it holds (for longitudes of Venus, Earth and Jupiter):

3LV - 5LE + 2LJ = kπ



Resonance according to quadratures

The existence of a certain relationship between quadratures of planets and solar activity is known for a longer time, but an exact theory has not yet been established. The advantage of such a theory would be, among other things, that the contributions of individual pairs of planets could be expressed as a vector products (that become extreme just under the action of two perpendicular forces ...).


Mörth-Schlamminger theory

H.T.Mörth (United Kingdom) and L.Schlamminger (Germany) published in 1979 (in collection Solar-Terrestrial Influences on Weather an Climate) article PLANETARY MOTION, SUNSPOT AND CLIMATE.

It is written here: „The long period peak amplitude variation appears to be associated with the angular separation of Uranus and Neptune, greatest amplitudes at angular separation 90°, smallest amplitudes near conjunction and opposition“.

They provide graph of function |Ln-Lu| + |Ls-Lj| for period 1750-2000, that cover progress of solar activity – e.g. estimated maxima from the graph are around years 1780,1840,1870,1960. Based on these assumptions they derive cycle ((J,S),(U,N)) = 22.46 years.

Coincidence of geometrical axes

Mutual motion of two synodical periods is difficult to visualize. Let us rewrite ((J,S),(U,N))=1/(1/J-1/S-1/U+1/N) to ([J,N],[S,U])/2 i.e. to mutual motion of geometrical axes of bodies J-N and S-U:

Axis of angle Jupiter-Sun-Neptune move with period: [J,N] = [11.8620,164.770132] = 22.1307494 years ( 8083.256 days)

Axis of angle Saturn- Sun -Uranus with period: [S,U] = [29.457159, 84.020473] = 43.6210092 years (15932.574 days)

These axes align with mean period: ([J,N],[S,U])/2 = (22.1307494, 43.6210092)/2 = 44.92108 years/2 = 22.46054 years = 2∙11.23027 years.

 1541.0 (+1.9) min  1546.9 ( 1.1) MAX
 1551.6 (+2.1) min  1558.1 (-0.1) MAX
 1563.6             1570.0 (+2.0) MAX
 1574.7             1580.4 (+0.6) MAX
 1585.3 (-1.5) min  1591.6 (-0.6) MAX
 1597.1 (-0.8) min  1602.7 (+1.3) MAX
 1607.8 (+1.0) min  1613.0 (+2.5) MAX
 1619.2 (+1.0) min  1625.3 (+0.7) MAX
 1631.2 (+1.7) min  1636.2 
 1642.2             1647.4 (+1.6) MAX
 1654.1 (+0.7) min  1659.2 (+0.8) MAX
 1665.0 (+0.8) min  1669.5
 1675.7             1681.0 
 1687.4 (+1.9) min  1692.1 (+0.9) MAX
 1697.7 ( 0.0) min  1703.0 (+2.5) MAX
 1709.4 (+2.2) min  1715.2 (+3.0) MAX
 1721.1 (+2.2) min  1726.2 (+1.3) MAX
 1731.6 (+2.1) min  1737.7 (+1.0) MAX
 1743.5 (+1.2) min  1749.2 (+1.1) MAX
 1753.9 (+1.1) min  1759.6 (+1.9) MAX
 1764.7 (+1.6) min  1771.4 (-1.7) MAX
 1776.4        MAX? 1782.3        min?
 1787.1        MAX? 1793.3        min? 
 1799.2 (-1.0) min  1805.6 (-0.4) MAX
 1810.6 (-0.2) min  1816.2 (-0.2) MAX
 1821.6 (+1.4) min  1827.7 (+2.2) MAX
 1833.5 (+0.2) min  1838.7 (-1.5) MAX
 1844.1 (-0.8) min  1848.9 (-0.8) MAX
 1855.3 (+0.5) min  1860.7 (-0.6) MAX
 1866.9 (+0.1) min  1871.6 (-1.0) MAX
 1877.7 (+1.0) min  1882.9 (+1.0) MAX
 1889.9 (-0.5) min  1894.9 (-0.8) MAX
 1900.8 (+0.6) min  1905.6 (+1.4) MAX
 1911.7 (+1.6) min  1917.2 (+0.4) MAX
 1923.3 (+0.1) min  1928.3 (+0.1) MAX
 1933.3 (+0.2) min  1939.1 (-1.7) MAX
 1944.7 (-0.7) min  1951.1        ???  

Rezonance

Consider rezonance: (LJ + LN)/2 - (LS + LU)/2 = π/4 + kπ/2

(LJ - LS) + (LN - LU) = kπ/2

with period (according to previous praragraph) W = 11.23027 years.

But period 11.23 years seems to be too long! On long-term scale it does not fit Schove’s extremes. Quadratures of outer planets disagree with course of solar activity!? Regularity cease (resp. it goes to the opposite polarity) after some centuries (eg. before y.1540 and after y. 1950). Some similar variation also appears in the vicinity of the 1780th.

...
1518.1 (-0.9) MAX  1523.7 (+0.2) min
1528.9 (-0.9) MAX
                
1776.4        MAX? 1782.3        min?
1787.1        MAX? 1793.3        min? 
1956.2 (+1.7) MAX  1962.1 (+2.3) min
1967.0 (+1.9) MAX  1973.8
1979.3 (+0.6) MAX  1985.5 (+0.9) min
1990.2 (-0.6) MAX  1996.1 (+0.3) min
...

Note that squaring of Uranus-Neptune occurred in the years 1519-1530, 1778-1787 and 1946-1957 along with squaring of Jupiter-Saturn. These configurations appear more precisely e.g. in years: 585.9, 754.4, 843.9, 1013.3, 1102.3, 1271.7, 1528.7, 1786.9, 1956.2, 2214.5, 2372.7, ... that may be preceded or followed (with a period (J,S)/2 i.e. approx. 9-10 years) by other quadrature with less precision ...



Balancing of Jupiter

Influence of Neptune

Line of conjunctions V-E-J move (backward) with period: P= (W,J) = (11.06753, 11.861983) = 165.25 years, i.e. approximatelly with orbital period of Neptune.
Axial period Jupiter-Neptun [J,N] = 22.13075 y = 2*11.06538 years coincides with period of Solar activity.
Some authors (Ray Tomes,…) connect solar period with these two bodies ( Jupiter, Neptune).
(In combination with resonance of inner planet it leads to 6/V-10/E+3/J-1/N = 0, i.e. unstable resonance).

Importance of Jupiter (with a view to the weight) is clear. Neptune might acquire its influence by the distance from the sun, see, for example value (M * R2 (moment of inertia):

M [1024 kg] a [10&sup9; m] M*a2 [1039kg*m²]
Jupiter 1899,0 778,6 1151,2
Saturn 568,0 1433,5 1167,2
Uran 86,8 2872,5 716,2
Neptun 102,0 4495,1 2061,0.

Resonance

Also period of resonance 1/W = 1/J + 1/U – 1/N correlates by value W = 11.094 years with the mean period of the Solar cycle. Let us write it to form of stable resonance: 1/W - 1/J + 1/N - 1/U = 0.

Resonance maxima occur, when it holds (for longitudes of Jupiter, Jupiter perihelion, Uranus and Neptune):

Lj – Ljp + Lu - Ln = π+2kπ

Resonance minima occur, when it holds (for longitudes of Jupiter, Jupiter perihelion, Uranus and Neptune):

Lj – Ljp + Lu - Ln = 2kπ

This resonance binds the period of solar activity W with orbital periods of planets Jupiter, Neptune, Uranus. Saturn's here seemingly outside game - however it is bound by resonance of outer planets to Jupiter perihelion (viz Influence of Jupiter)!?



Depiction of the relationship

The resonance arise as a sum of the two delta angles ∆J + ∆UN where:

n Mo ∆J ∆UN n Mo ∆J ∆UN n Mo ∆J ∆UN n Mo ∆J ∆UN
-30 1416,7 316 224 -14 1594,4 306 234 2 1772,0 296 244 18 1949,5 283 257
-29 1428,0 296 244 -13 1605,6 286 254 3 1783,1 273 267 19 1960,5 257 283
-28 1439,2 275 265 -12 1616,6 262 278 4 1794,1 246 294 20 1971,4 229 311
-27 1450,2 251 289 -11 1627,6 235 305 5 1805,0 218 322 21 1982,4 203 337
-26 1461,2 224 316 -10 1638,5 207 333 6 1815,9 192 348 22 1993,4 180 0
-25 1472,0 197 343 -9 1649,4 182 358 7 1826,9 168 312 23 2004,5 159 21
-24 1483,0 172 8 -8 1660,5 160 20 8 1838,1 149 31 24 2015,7 140 40
-23 1494,1 150 30 -7 1671,6 140 40 9 1849,3 130 50 25 2026,8 120 60
-22 1505,3 130 50 -6 1682,8 120 60 10 1860,4 109 71 26 2037,9 96 84
-21 1516,4 110 70 -5 1694,0 99 81 11 1871,5 85 95 27 2049,0 70 110
-20 1527,5 88 92 -4 1705,0 74 106 12 1882,5 58 122 28 2060,0 42 137
-19 1538,6 63 117 -3 1716,0 47 133 13 1893,5 31 149 29 2071,1 18 162
-18 1549,6 36 144 -2 1727,1 21 159 14 1904,6 7 173 30 2082,3 356 184
-17 1560,7 10 170 -1 1738,2 357 183 15 1915,9 346 194 31 2093,6 336 204
-16 1571,9 346 194 0 1749,5 336 204 16 1927,2 326 213 32 2104,8 316 224
-15 1583,7 326 214 1 1760,8 316 224 17 1938,4 306 234 33 2116 294 246
Simplified diagram of solar activity power follows.
Observed maximum so (according to axes direction) can be of 4 distinct types,
see e.g. I.1727.5 (140.0), II.1870.6 (140.5), III. 1989.6 (150.1), IV. 1957.9 (201.3) :

Solar activity circle diagram

Maxima of Solar activity

Comparison of extremes

In the following overview these maxima are compared:
1500-1650
N WS WI WO WA WI-WS Wo-WS Wo-WI
-23 1492 1494,6 1494,1 1490,4 2,6 2,1 -0,5
-22 1505 1505,8 1505,2 1501,6 0,8 0,2 -0,6
-21 1519,0 1517,3 1516,4 1513,1 -1,7 -2,6 -0,9
-20 1528,0 1527,5 1527,5 1523,7 -0,5 -0,5 0,0
-19 1539,0 1539,1 1538,6 1535,6 0,1 -0,4 -0,5
-18 1548,0 1549,6 1549,6 1546,9 1,6 1,6 0,0 P-maximum
-17 1558,0 1560,8 1560,7 1558,1 2,8 2,7 -0,1
-16 1572,0 1572,5 1571,9 1570,1 0,5 -0,1 -0,6
-15 1581,0 1583,6 1583,7 1580,4 2,6 2,7 0,1
-14 1591,0 1594,6 1594,4 1591,7 3,6 3,4 -0,2
-13 1604,0 1606,2 1605,6 1602,8 2,2 1,6 -0,6 1607 - Kepler's spot
-12 1615,5 1616,8 1613,1  1613,0 1,3 1,1 -0,2 1618 - Simon Mair's (Marius) spots
-11 1626,0 1627,8 1627,6 1625,3 1,8 1,6 -0,2
-10 1639,5 1638,8 1638,5  1636,3 -0,7 -1,0 -0,3
1650-1800
n WS WI WO WA WI-WS WO-WS WO-WI
-9 1649,0 1649,9 1649,4 1647,5 0,9 0,4 -0,5
-8 1660,0 1660,8 1660,5 1659,2 0,8 0,5 -0,3 1660 - Hevelius spots, 1661 - Boyle and Picard sunspot group
-7 1675,0 1672,2 1671,6 1669,5 -2,8 -3,4 -0,6 1671 (August) - Pickard spot, Hevelius spot, 1676 - Pickard extreme, Maunder
-6 1685,0 1682,5 1682,8 1681,0 -2,5 -2,2 0,3 1684 - Pickard extreme, Cassini, Kirch
-5 1693,0 1693,5 1694,0 1692,2 0,5 1,0 0,5
-4 1705,5 1705,2 1705,0 1703,1 -0,3 -0,5 -0,2
-3 1718,2 1716,0 1716,0 1715,2 -2,2 -2,2 0,0 1716 - visible aurora, 1714-15 - P-maximum, end of Maunder period
-2 1727,5 1727,4 1727,1 1726,3 -0,1 -0,4 -0,3
-1 1738,7 1738,5 1738,2 1737,8 -0,2 -0,5 -0,3
0 1750,3 1750,1 1749,5 1749,2 -0,2 -0,8 -0,6 1752 - second maximum
1 1761,5 1761,3 1760,8 1759,7 -0,2 -0,7 -0,5
2 1769,7 1771,8 1772,0 1771,4 2,1 2,3 0,2 1774 - second maximum
3 1778,4 1782,8 1783,1 1782,3 4,4 4,7 0,3
4 1788,1 1794,5 1794,1 1793,4 6,4 6,0 -0,4
1800-1950
n WS WI WO WA WI-WS WO-WS Wo-WI
5 1805,2 1805,5 1805,0 1805,7 0,3 -0,2 -0,5
6 1816,4 1815,6 1815,9 1816,3 -0,8 -0,5 0,3
7 1829,9 1827,2 1826,9 1827,7 -2,7 -3,0 -0,3
8 1837,2 1838,3 1838,1 1838,7 1,1 0,9 -0,2
9 1848,1 1849,2 1849,3 1848,9 1,1 1,2 0,1 1847-48 - Giant sunspots
10 1860,1 1860,2 1860,4 1860,7 0,1 0,3 0,2 1859 - proton event (Carrington), 1864 - second maximum, 1859-60 - Giant sunspots
11 1870,6 1871,3 1871,5 1871,6 0,7 0,9 0,2 1870-71 - Giant sunspots, 1870 - proton event (Young)
12 1883,9 1881,7 1882,5 1882,9 -2,2 -1,6 -0,8 1882 - P-maximum, 1882 - Giant sunspot, 1882 - proton events (Maunder)
13 1894,1 1893,5 1893,5 1894,9 -0,6 -0,6 0,0 1892-93 - Giant sunspots,  1892 -  proton events (Rudeaux)
14 1907,0 1904,5 1904,7 1905,7 -2,5 -2,3 -0,2 1905,07,08 - Giant sunspots, 1908 - proton event
15 1917,6 1916,1 1915,9 1917,3 -1,5 -1,7 -0,2 1917 - Giant sunspot, 1917 - proton event
16 1928,4 1926,7 1927,2 1928,4 -1,7 -1,2 -0,5 1926,29 - Giant sunspots, 1926 - proton event
17 1937,4 1937,9 1938,4 1939,1 0,5 1,0 0,5 1935,37-42 - Giant sunspots, 1938 - proton event
18 1947,5 1949,5 1949,6 1951,1 2,0 2,1 0,1 1946 - proton event, 1949 - proton event
1950-2100
n WS WI WO WA WI-WS WO-WS WO-WI
19 1957,9 1960,5 1960,5 1962,1 2,6 2,6 0,0 1958 - the highest level since Galileo's observations (1610), 1956,59-61 - proton events
20 1968,9 1972,2 1971,4 1973,8 3,3 2,5 -0,8 1969 - proton event, 1972 - extreme flare, 1972 - second maximum
21 1979,9 1983,2 1982,4 1985,5 3,3 2,5 -0,8 1981 - extreme flare
22 1989,6 1993,2 1993,4 1996,1 3,6 3,8 0,2 1990 - the second highest level since Galileo's observations (1610)
23 2000,5 2004,3 2004,6 2007,8 3,8 4,1 0,3
24 ? 2015,3 2015,7 2018,3 ? ? 0,4
25 ? 2026,1 2026,8 2028,9 ? ? 0,7
26 ? 2036,6 2037,9 2040,9 ? ? 1,3
27 ? 2048,1 2049,0 2051,5 ? ? 0,9 2050-51 - P-maximum
28 ? 2059,5 2060,0 2063,4 ? ? 0,5
29 ? 2070,6 2071,1 2074,7 ? ? 0,5

Subsequent considerations

Regularities

Theoretical extremes (maxima as well as minima) of solar activity take place about with the same period as the actual extremes. The biggest differences in maximum are observed in years 1583-1606, 1675-1685, 1778- 1788, 1829, 1958-2000. The biggest differences in minimum are observed in years 1553,1619, 1784, 1902-1924,1996.

Justin Flynn has noticed certain regularities of these deviations (personal communication).

Consider the following chart:

graph_resonant

Rule of alternating deviations

Let us divide the Uranus-Neptune conjuction cycle to following time-periods, and to write departures taken from the column Mo-MS of the tables above:

    Time-      Departures
    period     sign  maxima   minima
    ------------------------------------
    1543-1586  -
    1586-1628  +
    1628-1671  -
    1671-1714  +
    1714-1757  -  1718-1761  1745-1765
    1757-1800  +  1769-1788  1777-1799
    1800-1842  -  1805-1830  1810-1832
    1842-1885  +  1838-1871  1844
    1885-1928  -  1884-1928  1856-1943
    1928-1971  +  1938-2004  1954-2008
    1971-2014  -  ?????????
    2014-2057  +

For the period 1714 -1971 all seems to work quite well. But this rule (like the rule from the paragraph Coincidence of geometrical axes) fails - and again roughly after year 1960!?)

Correction of extremes WO

Let dUN = Neptune.Longitude - Uranus.Longitude, dJJa = Jupiter.Longitude - Jupiter.LongPerihelion - 180 and we look for extremes where dUN + correction = dJJa (with a given precission, e.g. 5 dg).

The following function was derived from the previous paragraph: f = Cos(2*dUN) * abs(Cos(2*dUN)) = sign(Cos(2*dUN)) * Cos2(2*dUN) with a correction angle equal to k * f. For value of the constant k = 120 we get the following table:

Table of corrected extremes
    Diff    Theory     Jp    J    S    U    N  f(dUN)  Corrected   Observation
 ------------------------------------------------------------------------------
    11,28   1749,39 -  15  346  231  322  118  +0.38   1750,73     1750.3  *
1757
    11,25   1760,65 -  14  326  358    6  143   0.00   1760,72     1761.5  *
    11,20   1771,84 +  14  305  146   51  167  -0.30   1770,79     1769.7  *
    11,09   1782,93 +  13  281  276   98  191  -0.87   1779,56     1778.4  *
    11,01   1793,94 +  14  256   46  148  215  -0.70   1791,19     1788.1  ?
1800
    10,92   1804,86 -  15  229  191  200  238  +0.06   1805,13     1805.2  *
    10,92   1815,79 -  15  203  314  249  262  +0.98   1819,56     1816.4  ?
    11,01   1826,79 -  14  179   92  296  286  +0.73   1829.80     1829.9  *
    11,14   1837,94 +  14  159  233  340  310  +0.21   1838,80 	   1837.2  . 
1842
    11,17   1849,11 +  14  140  359   24  334  -0.02   1849,04     1848.1  *
    11,17   1860,28 +  14  119  147   69  359  -0.48   1858,55     1860,1  *
    11,12   1871,39 +  15   97  277  118   24  -0.99   1868,05     1870,6  ?
    10,98   1882,37 -  15   69   48  169   48  -0.29   1881,41     1883,9  ?
1885
    11,01   1893,38 -  14   41  193  220   72  +0.25   1894,28     1894,1  *
    11,14   1904,52 -  14   17  318  270   97  +1.00   1908,13     1907,0  *
    11,23   1915,75 -  14  356  101  315  122  +0.66   1918,04 	   1917,6  *
    11,34   1927,08 -  16  338  242  360  147  +0.14   1927,54     1928,4  *
1928
    11,23   1938,31 +  16  317   10   44  171  -0.08   1938,11     1937,4  *
    11,12   1949,42 +  14  294  157   91  195  -0.63   1947,03 	   1947,5  *
    10,98   1960,40 +  14  267  284  141  218  -0.99   1956,54     1957,9  *
    10,90   1971,30 +  14  239   55  192  242  -0.03   1971,21     1968,9  ?
1971
    10,95   1982,25 +  15  214  199  242  265  +0.68   1984,90     1979,9  ??
    11,03   1993,29 +  16  191  323  289  289  +0.94   1997,03     1989,6  ??
    11,12   2004,40 +  15  170  105  334  313  +0.47   2006,28 	   2000,5  ??
    11,14   2015,55    14  150  243   17  338  +0.78   2015,70             ?
2014

Rows with "acceptable" results are marked by asterisks.

Other resonances

Listing

Resonances observed above are not only resonances producing cycles with period close to the period of solar activity. For example (J/1,-S/2,+U/4,-N/3) = 21.8 years while (J/1,-S/3,+U/4,-N/2) = 55.8 years. Also (S/1,+U/3,-N/4) = 22.0 years, therefore e.g. cos(Ls+3*Lu-4*Ln) oscillates with 11-years period etc.

    J  S  U  N        k*W          M 
    ------------------------------------
    0  3  1 -4        11,2       -971,5
    1  0  2 -3        11,1      -1671,2
    2 -3  3 -2        11,1      -5971,4
    0  1  3 -4        22,0       7807,8
    1 -1 -1  1        22,5      -1376,5
    0  1 -1  0        45,4      -1724,2
    1 -2  0  1        44,5      -6717,5
    0  0  2 -2        85,7       2829,8
    0  1 -3  2        96,3      -1072,9
    1 -3  3 -1        82,7       1275,0

Resonance with inclusion of Saturn

Now let us consider resonance with period 44.5 years according to row:

 J  S  U  N        k*W          M 
 ------------------------------------
 1 -2  0  1        44,5      -6717,5

After rewriting to the form:

LJ - 2* LS + LN = LJP + k*π/2

we get new values WN (we will compare them to extremes WO):

Spacing     WN     WO
   0,00   1605,503	1605,6
   9,09   1614,593	1613,1
  14,84   1629,433	1627,6
   8,27   1637,701	1638,5
  10,82   1648,516	1649,4
  13,03   1661,548	1660,5
   8,10   1669,652	1671,6
  14,26   1683,917	1682,8
   9,67   1693,582	1694,0
   9,75   1703,329	1705,0
  13,61   1716,936	1716,0
   9,42   1726,355	1727,1
  11,80   1738,155	1738,2
  12,21   1750,366	1749,5
   9,34   1759,702	1760,8
  13,53   1773,228	1772,0
   9,91   1783,139	1783,1
Spacing   WN     WO
   9,75   1792,886	1794,1
  14,35   1807,232	1805,0
   8,19   1815,419	1815,9
  12,70   1828,123	1826,9
  11,14   1839,266	1838,1
   8,27   1847,534	1849,3
  14,59   1862,127	1860,4
   9,25   1871,382	1871,5
    
  10,16   1881,539	1882,5
  13,28   1894,818	1893,5
   9,34   1904,154	1904,7
  12,54   1916,694	1915,9
  11,47   1928,166	1927,2
   9,75   1937,913	1938,4
  13,61   1951,520	1949,6
   9,58   1961,103	1960,5
   
Spacing   WN     WO
  10,98   1972,082	1971,4
  13,11   1985,196	1982,4
   8,27   1993,465	1993,4
  14,10   2007,565	2004,6
  
   9,58   2017,148	2015,7
   8,52   2025,663	2026,8
  14,76   2040,420	2037,9
   8,76   2049,181	2049,0

Other observations

Significant deviation

Interval of years 1761 - 1805 (with a centre around y. 1783) may be important. There would be solar-activity extremes expected on years marked by # (odd rows), but real activity was observed rather on years marked by asterisks:

  Theory      Jp    J    S    U    N    Observation
-------------------------------------------------------
# 1760,65 ***  14  326  358    6  143    1761.5 
  1765,96      14  136   66   27  154    
# 1771,85 ***  14  305  146   51  167    1769.7
  1777,08 ***  13  115  211   73  179    1778.4
# 1782,94      13  281  276   98  191   
  1788,14 ***  13   90  334  122  202    1788.1
# 1793,94      14  256   46  148  215  
  1799,14      14   63  117  173  226  
# 1804,87 ***  15  229  191  200  238    1805.2

There is certain symmetry or perpendicularity, alignment of outer planets on the year. 1783 (see image of planetary position - Jupiter perihelion is on the right side of the image...!?)

syst17830101 Usoskin, Ilya
Usoskin, Ilya, physicist working in Finland. Author of a long series of scientific publications in the field of solar physics and physics of cosmic radiation.

Missing maximum y.1796

It seems like maximum of the year 1796 in data of solar activity „drops out“?!

Planets Jupiter, Saturn and Uranus were near their perihelia in the year 1797. Consider the position of the planets in the year 1796, for example 19.August 1796 (when also Mars was near its perihelion):

syst17960819

There were only 2 such years on interval 0-2100 (with precision 10 dg) about 1090 years apart...(Program skips 100 day after an event found - this is why we see here 2 rows for each of these years ...)

           J      Jp      S      Sp      U       Up      N        Np  
706,05    4,41 ( 11,53)  75,01 ( 84,93) 169,74 (170,33) 356,59 ( 30,47)  706 Jan 14 AD
706,38   15,35 ( 11,51)  79,55 ( 85,03) 171,27 (169,98) 357,32 ( 32,41)  706 May 14 AD
1797,41   5,38 ( 13,85)  93,33 ( 91,95) 164,69 (169,11) 222,35 ( 40,70) 1797 May 27 AD
1797,74  16,37 ( 13,85)  97,83 ( 92,04) 166,24 (168,74) 223,05 ( 42,48) 1797 Sep 24 AD

And the cycle 699-714 (i.e. distance of extremes, similarly to 1788-1805) was also (in the series of extremes according to J.Schove) relatively long!