# Action of Jupiter

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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

Ratio of orbital periods of Uranus and Jupiter makes approximately U/J ~ 7,  where value  7/U-1/J ~ 12*U.
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

Ratio of Jupiter period to synodic period of Earth-Mars makes approximately 11.8620/2.1353487= 5.555057.
Let 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
During period of inequality Earth-Mars (1:2), i.e. during (E,R/2) = 15.7712 years, Jupiter makes 4/3 of orbit (4/3 J= 15.8087 years).
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
```
We observe that: Values J/(M,R), J/(M,V) and J/(V,R)  are nearly integers.

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

It holds in the mentioned model:

#### 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 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).