Action of Jupiter
Jupiter – due to eccentricity of its orbit (c. 0.05) -
is by half of astronomical unit (75 million kilometers)
nearer to the Sun in perihelion than in aphelion.
Thus Jupiter compresses and releases
space for the bodies inside of its orbit.
Action on outer planets
The main action of Jupiter - the action on outer planets - is described on the separate page:
Jupiter resonance
So longitudes Lj-7*Lu makes stepwisely 12-gon (with interval U between vertexes).
The following table brings values Lx = (Lj-Ljp)-7*(Lu-Lup) in time of Uranus in perihelion (Lu-Lup=0):
During period U Jupiter makes just its 7 periods and c. 30º more:
| Lx | -1310,57 | -301,87 | 706,01 | 1714,16 | |
| 0 | 0 | 1,3 | 14,0 | 357,4 | 352,1 |
| +84,01 | 30 | 30,4 | 39,0 | 28,2 | 18,0 |
| +168,02 | 60 | 57,1 | 65,5 | 56,8 | 50,2 |
| +252,03 | 90 | 88,0 | 94,0 | 84,7 | 85,7 |
| +336,04 | 120 | 125,6 | 121,5 | 115,3 | 119,2 |
| +420,05 | 150 | 164,8 | 155,8 | 146,2 | 153,7 |
| +504,06 | 180 | 197,4 | 195,7 | 176,0 | 188,2 |
| +588,07 | 210 | 230,6 | 227,3 | 214,5 | 215,9 |
| +672,08 | 240 | 258,6 | 258,1 | 246,8 | 250,8 |
| +756,09 | 270 | 285,5 | 283,6 | 277,6 | 282,7 |
| +840,10 | 300 | 314,3 | 308,1 | 303,8 | 315,4 |
| +924,11 | 330 | 343,2 | 331,0 | 328,3 | 343,3 |
In the years 1379,5; 1546,3; 1714,2; 1882,1; 2050,4 (i.e. -120°; -60°; 0°; 60°; 120°)
also Neptune is near to its perihelion (as well as Jupiter and Uranus).
These years corresponds to maxima of solar activity, see P-maxima in Solar activity - resonance .
Action on inner planets
Period Earth-MarsLet us assume, it holds: J/(E,R)= 50/9. During 50 conjunctions E-R, i.e. 106.76 years (quarter of Babylonian period) Jupiter makes 9 orbits.
In the following table, the differences Le-Lr of Earth and Mars longitudes are given.
All the angles are in the time of Jupiter in perihelion. Alignment E-R are in the first row (below header):
| Le-Lr | 1145,27 | 1252,02 | 1358,71 | 1465,49 | 1572,28 | 1679,03 | 1785,78 | 1892,56 | 1999,39 | |
| 0 | 0 | 15,7 | 357,5 | 341,9 | 0,6 | 5,6 | 347,5 | 337,9 | 355,3 | 13,2 |
| +11,86 | 200 | 203,9 | 210,3 | 194,1 | 182,7 | 195,3 | 205,0 | 189,7 | 179,8 | 196,2 |
| +23,72 | 40 | 23,6 | 36,2 | 48,3 | 36,4 | 17,2 | 30,5 | 50,0 | 37,5 | 20,3 |
| +35,58 | 240 | 237,6 | 223,7 | 234,4 | 246,2 | 233,5 | 218,0 | 228,8 | 250,3 | 238,6 |
| +47,44 | 80 | 88,8 | 78,9 | 63,4 | 69,6 | 80,9 | 79,2 | 69,3 | 69,6 | 82,4 |
| +59,30 | 280 | 273,9 | 289,1 | 282,4 | 265,0 | 266,4 | 276,7 | 282,8 | 270,2 | 267,0 |
| +71,16 | 120 | 116,2 | 111,2 | 118,3 | 118,9 | 111,7 | 109,6 | 109,3 | 120,6 | 115,8 |
| +83,02 | 320 | 324,8 | 320,2 | 303,2 | 310,8 | 323,1 | 321,9 | 308,2 | 307,3 | 322,7 |
| +94,88 | 160 | 153,3 | 161,5 | 156,9 | 144,8 | 144,6 | 158,8 | 162,6 | 158,2 | 143,1 |
From unstable resonance (beats c. 1781 years).
3/J-8/R+4/E = 0
In view of the Jupiter's perihelion the resonance (E, (R/2) makes rectangle. This rectangle is rotated 45° to Jovian ellipse
(the principle of minimum interaction).
| Le-2*Lr-45° | 1560,4 | 1607,85 | 1655,29 | 1702,77 | 1750,24 | 1797,67 | 1845,11 | 1892,56 | 1940,06 | 1987,54 | 2034.93 | |
| 0 | 0 | 356,7 | 16,0 | 31,2 | 359,2 | 343,2 | 356,1 | 18,9 | 5,3 | 332,2 | 339,9 | 0,5 |
| +11,86 | 90 | 119,9 | 113,7 | 86,8 | 75,6 | 101,0 | 108,5 | 86,1 | 64,8 | 77,6 | 100,6 | 81,4 |
| +23,72 | 180 | 202,1 | 166,4 | 176,2 | 199,1 | 198,9 | 166,4 | 157,4 | 181,9 | 191,2 | 168,2 | 142,9 |
| +35,58 | 270 | 259,9 | 277,3 | 295,1 | 285,0 | 250,4 | 259,0 | 279,0 | 280,1 | 246,5 | 240,0 | 261,2 |
Beats of synodical periods
Ratios of Jovian period to synodical periods of inner planets:
J/(M,R)= 11.8620/0.2762169= 42.944451 J/(M,E)= 11.8620/0.3172552= 37.389405 J/(M,V)= 11.8620/0.3958007= 29.969586 J/(V,E)= 11.8620/1.5986896= 7.419816 J/(V,R)= 11.8620/0.9142273= 12.974873 J/(E,R)= 11.8620/2.1353487= 5.555057
Beats:
((E,R),J/6) = (2.13535, 1.97700)= 26.660 years ((V,E),J/7) = (1.59869, 1.69457)= 28.255 years ((M,E),J/37)= (0.31726, 0.32059)= 30.462 years ((M,R),J/43)= (0.27622, 0.27586)= 213.563 years ((M,V),J/30)= (0.39580, 0.39540)= 389.986 years ((V,R),J/13)= (0.91423, 0.91246)= 472.085 years
Beats of conjunctions M-V-R are higher then other beats.
Beats ((M,R),J/43) makes nearly exactly half of the Babylonian period (B/2 = 18*J = 213.516 years).
From all combinations of synodical periods the highest value of beats is: (((M,V),(V,R)), J/17)= (0.69798, 0.69776) = 2242.4806 years.
During 1900-2000 conjunctions M-V-R appear after passing of Jupiter through the perihelion:
J in perihelion M-V M-R V-R --------------------------------------- 1904.42 ` 1904.53 1904.52 1904.48 1916.31 1916.39 1916.37 1916.32 1928.19 1928.31 1928.27 1928.20 1940.02 1940.16 1940.15 1940.13 1951.90 1952.01 1952.00 1951.98 1963.78 1963.93 1963.90 1963.85 1975.61 1975.79 1975.79 1975.79 1987.49 1987.64 1987.64 1987.65 1999.38 1999.54 1999.52 1999.50
Model
Let J = 11.8620 years, E = 1.0000174 years. According to
(E,R') = J∙9/50 = 2.1351570 years is R' = 1.8809970 years (687.0342
days).
From (M',R')= J/43= 11.8620/43= 0.2758601, (M',V')= J/30=
11.8620/30= 0.3953994, (V',R')= J/13= 11.8620/13= 0.9124602
it follows:
M'= 0.2405778 years ( 87.8710 days), (M'/M) = 1/1.00112
V'= 0.6144125 years (224.4142 days), (V'/V) = 1/1.00128
R'= 1.8809970 years (687.0342 days), (R'/R) = 1/1.00008
1/M' -5/V'+4/E = 8/B
3/V' -7/E+4/R' = 4/B
where B = 36∙J (c. 427.03 y, see Babylonian period).Oppositions to Jupiter
Conjunctions of inner planets at opposition to Jupiter
(precision 30°):
1243.53, 1288.23, 1332.99; 1529.71, 1574.39,
1619.14; 1815.86, 1860.60, 1905.30.
(Distance of these triads is c. 286.15 years; 24*J= 284.7 years).
Similar configurations (precision 35°) were also in
years: 1905.3, 1950.1, 2005.9, 2050.6.
One of the greatest solar spots was observed (Newcomb
S.) 2.3.1905 (maximum, c. 1/3 of solar hemisphere).
Opposition (precision 20°) happened 22.4.1905.
In years 1905-1906 and about y.1950 seismicity increased.
Gutenberg, Richter, ∑E, interval 1904-1952:
|
Rok |
1905 |
1906 |
1911 |
1917 |
1918 |
1920 |
1923 |
1933 |
1934 |
1938 |
1941 |
1946 |
1950 |
|
∑E>15 |
23.1 |
59.7 |
27.7 |
15.1 |
20.8 |
26.8 |
18.6 |
21.1 |
17.6 |
20.0 |
15.5 |
17.2 |
39.6 |
Date Interval Math.date
137 Mar 17 AD( 0.00) ( 137.21)
282 Jul 14 AD( 145.33) ( 282.54)
468 Feb 18 AD( 185.60) ( 468.14)
754 Apr 12 AD( 286.15) ( 754.29)
1288 Mar 19 AD( 533.94) (1288.24)
1574 May 17 AD( 286.16) (1574.41)
1619 Feb 20 AD( 44.74) (1619.14)
1860 Aug 10 AD( 241.46) (1860.61)
1905 Apr 22 AD( 44.70) (1905.31)
2191 Jun 26 AD( 286.17) (2191.49)
Action on moons and asteroids
Action on own moons
Distant satellites of Jupiter synchronize their periods with the Sun. Their orbital periods are integer fractions of Jupiter period (J/6=722 days, J/17=255 days); period observed in Solar wind (c. 1.3 years) seems to be also such a fraction (J/9=1.317 years).
Gaps in asteroid belt
Orbits and gaps in the Mars-Jupiter belt of asteroids are often determined by ratios:
q = A/J = m/n
where A is orbital period of asteroid.
Ratios r are more intelligible
r= (A,J)/J = ( J-A)/A ≈ m/(n-m)
Ratios for gaps in asteroid belt q= 1/3, 2/5, 3/7, 4/9, 5/11 correspond to r= 1/2, 2/3, 3/4, 4/5, 5/6,...,so
r[GAPS] = k/(k+1)
---------------------------------------- (q=1/4)
Z2 Lucretia, Berolina, Iduberga
-------
Z3 Vesta, Amalasuntha, Leonce, Appenzela, Tinchen
------- q=1/3 à r=1/2
Z4 Eunomia, Adeona, Leto, Lydia, Maria, Dora, Agnia
------- q=2/5 à r=2/3
Z5 Koronis
------- q=3/7 à r=3/4
Z6 Eos (Eds?)
------- q=4/9 à r=4/5
Z7 Themis, Veritas
------- q=5/11 à r=5/6
---------------------------------------- (q=1/2)
Rare occupied zone also: q= 3/5 à r=3/2.
Occupied orbits in asteroid belt
Ratios for asteroid orbits q=2/3 (Hilda), 3/4 (Thule) have r=2/1,3/1,..., i.e.tedy:
r[ORBITS] = k
Computed ratios are simplified (slewing of asteroid orbits is omitted, ratio A/J for Thule is about 0.7386, not exactly 0.75).