﻿ Hallstatt cycle

# Hallstatt cycle

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By the term "Hallstatt" is called the cycle of about 2300 years. For the first time, I read about the existence of the 2300-year cycle in texts published on the Internet by Ray Tomes. There was probably also written the relationship 1/J-3/S+1/U+1/N (= 1/H).

The ratios of the synodic periods of the outer planets p1 = (U,N)/(J,S) and p2 = (U,N)/(S,U) are approximately p1 = 171/20 = 8.5 and p2 = 171/45 = 3.8. It offers to balance these to the ratio: (U,N):(S,U):(J,S) = 1: 1/4: 1/9. And here a series of relationships - dominated by the period (H) - follows. I thought it might be related to some unknown (hypothetical) planet and began to call it H (Hypos). Until recently (in 2018) I have read that it is customary to use the name "Hallstatt" for the period (so there is no need to change the abbreviation "H" ...).

## Resonance of inverse motion

### Period H

Difference (LS-LU) a -(LS-LN) je d = LS-LU+LS-LN = 2∙LS-LU-LN = 2∙(J,S)/S -(J,S)/U-(J,S)/N = (J,S)∙(2/S-1/U-1/N).
Deviation from full angle during (J,S): (1-d) = 1 - (J,S)∙(2/S-1/U-1/N).

During 1 year: h = (1-d)/(J,S) = 1/(J,S) - (2/S-1/U-1/N) = 1/J-1/S-2/S+1/U+1/N  = 1/J-3/S+1/U+1/N.

So

#### 1/H = 1/J-3/S+1/U+1/N

In degrees:

```  d∙360° = 19.859∙(2/29.457-1/84.020-1/164.770)∙360° = 0.991433 ∙ 360° = 356.916°
(1-d)∙360° = -3.084° (= 157.601° - 160.685°)
h∙360° = -3.084° /19.859 years  =  0.1553°/year.
h = 0.1553/360 = 0.00043139 full angles / year.
Period H:
H = 1/h = 1/0.00043139 = 2318.1 years.
```

## World of synodical periods

### Conjunction

Let us assume fictive space, where only synodical periods can be perceived (motion of bodies is hidden).

E.g. we can hear a crack (AB) during conjunction of two bodies (A and B); during conjunction of three bodies (A,B,C) three cracks (AB, AC, and BC).

(Similarly was world observed by ancient astronomers...)

### Simple ratios

Motion of an observer in the fictive space of synodical periods does not modulate orbital periods, but synodical periods.

Let H is period of stable resonance, 1/H=1/J-3/S+1/U+1/N (c. 2320 years). Observer moving with this period (in the world of combined synodical periods) will get the following values of ((J,S),(S,N)), ((J,S),(U,N)) and ((J,U),(U,N)):

```  1/((J,S),(S,N))-1/H = 1/J-2/S+1/N-1/H      = 1/S-1/U = 1/(S,U)
1/((J,S),(U,N))-1/H = 1/J-1/S-1/U+1/N-1/H  = 2/S-2/U = 2/(S,U)
1/((J,U),(U,N))-1/H = 1/J-2/U+1/N-1/H      = 3/S-3/U = 3/(S,U)
```

Therefore for this observer it holds:

### Coordination

Resonant ratio of orbital periods of Uranus and Neptune is 1:2 (N/U =1.961); period of inequality I = (U, N/2), approximately 4200 years.
Observer moving with period I gets periods of outer planets J',S',U',N':

``` 1/J' = 1/J-2/N+1/U = 11.8953 years
1/S' = 1/S-2/N+1/U = 29.6636 years
1/U' = 1/U-2/N+1/U = 2/U-2/N = 85.722 years
1/N' = 1/N-2/N+1/U = 1/U-1/N = 171.444 years
```

For this observer N':U' is exactly 2/1. Ratio S'/J' is approximately 5:2 and U'/S' approximately 3:1.
Period of inequality J-S: (S'/5,J'/2) = 2362 y and period of inequality S-U: (U'/3,S'/1) = 778 y.
Value of period H (1/H = 1/J-3/S+1/U+1/N) remain the same: H = 2320 y.

Sidereal periods of outer planets fulfill equation:

#### 3/J-8/S-2/U+7/N = 0

``` For synodic periods:
1/H = 1/(J,S)-2/(S,U)-1/(U,N)
3/H = 4/(U,N)-1/(S,U)
5/H = 9/(U,N)-1/(J,S)
7/H = 4/(J,S)-9/(S,U)
Generally m2/P-n2/Q = k/H, so P∙Q/(Q∙m2-P∙n2) = H/k.
For comparison Bohr's quantization of atoms:
1/T = c∙R∙(1/m2-1/n2)
```

Our observer therefore realizes:
5/S'-2/J'=1/H (=5/S-2/J+3/U-6/N=1/J-3/S+1/U+1/N)
3/U'-1/S'=3/H (=5/U-4/N-1/S =3/J-9/S+3/U+3/N)
It holds: 1/H = 1/J- 3/S+1/U+1/N 3/H = -1/S+5/U-4/N 5/H = -1/J+1/S+9/U-9/N 7/H = 4/J-13/S+9/U

### Course of resonance

Values L=(3LJ-8LS)-(2LU-7LN), where  LJ,LS,LU,LN  are longitudes of planets in selected moments oscillates approximately around 120˚:

#### LH = 3LJ -8LS+2LU-7LN  ~ 120˚

In conjunctions J-S is (3LJ-8LS)/5 = LJ = LS, in conjunctions U-N is (2LU-7LN)/5 = LU = LN.

 Year 3 LJ[˚] 8 LS [˚] 2 LU [˚] 7 LN [˚] (3LJ-8LS)-(2LU-7LN)  [˚] 1810,46 124 230 83 309 254 – 134 = 120 1824,28 322 139 215 157 183 -  58 = 125 1838,09 141 51 334 7 90 – 327 = 123 1851,90 300 320 80 219 340 – 221 = 119 1865,70 98 229 185 73 229 – 113 = 116 1879,52 272 142 302 287 131 -  15 = 116 1893,33 108 49 72 142 58 – 290 = 128 1907,15 306 325 204 356 341 – 208 = 133 1920,97 127 230 325 208 257 – 116 = 141 1934,77 287 146 72 59 142 -  13 = 129 1948,58 84 49 176 268 35 – 269 = 127 1962,39 257 326 291 115 291 – 176 = 115 1976,21 91 230 61 323 221 -  97 = 123 1990,02 290 148 193 172 142 -  21 = 121 2003,84 113 52 315 22 61 – 293 = 128 2017,65 275 328 63 234 307 – 189 = 118 2031,45 71 233 167 88 198 -  80 = 118 2045,26 242 146 281 302 95 – 339 = 116 2059,08 74 55 50 157 19 – 253 = 126 2072,90 274 326 183 11 307 – 172 = 136 2086,71 98 238 306 223 220 -  83 = 138

## Wilson's model

### Synchronization V-E-J

Ian R.G. Wilson published a tidal model of Venus, Earth and Jupiter with a period of 11.07 years. He notices that the derived period of synchronization of these planets 575.52 years can be exactly a quarter of the Hallstatt cycle. At the same time he pointed out the possible connection with the moon's tidal tides, which show a significant period of 574.6 years.

While observing the alignment of planets V-E-J, it is actually possible to find the period H/4 - planetary configurations even show some kind of symmetry in time here. Symmetry centers appears in years:

The following intervals appear between these data: (derived from observed Jupiter-Earth-Venus conjunctions with accuracy up to 2 degrees).

```------      111.5 AD
44.8, 65.6, 44.8, 44.8, 65.6,  89.5, 65.6, 155.1 years
155.1, 65.5, 89.5, 65.5, 89.5, 65.5, 44.8 years
44.8, 65.5, 89.6, 65.5, 89.5, 65.6, 155.1 years
155.0, 65.6 years
```

All intervals are multiples of approximately 11 years:

``` 44.8 years = 4 * 11.20 years
65.6 years = 6 * 10.93 years
44.8 years = 4 * 11.20 years
44.8 years = 4 * 11.20 years
65.6 years = 6 * 10.93 years
89.5 years = 8 * 11.19 years
65.6 years = 6 * 10.93 years
155.1 years = 14 * 11.08 years
```

Here two periods take turns: one when "wins" average interval of the V-E conjunctions, from which come the periods 11.19-11.20 years and second with periods of the average interval of J-E conjunctions, fitting to 10.92-10.93 years. (Which one have to win is decided by speeds on elliptical orbits ...!?)

The average period from the observed H/4 = 575.55 years results to be 575.55 = 52 * 11.068 years.

### Incorporating Mars

At the breaks, Mars is emerging (in combination with V, E and J). With the period of 1151.1 years, Mars comes in line with the tides of Jupiter-Earth-Venus.

6.8.1262             9.3.1838

### Counts of orbits

In 1151.1 years Venus will make 1871 orbits (+ about 15 degrees extra) The Earth make 1151 orbits (+ approx. 15 degrees extra) and Mars approximately 612 orbits ... - Difference 1871- 1151 = 720 = 4 * 180, difference 1151-612 = 539 = 3 * 180 - 1 !?

## Inner planets

### Period h

Let us try to look for some period h that can have for inner planets meaning similar to period H of outer planets.

Let h is period of stable resonance, 1/h = 1/M-4/V+2/E+1/R (c. 5.504 years). Observer moving with this period (in the world of combined synodical periods) will get the following values of ((M,V),(V,R)),((M,V),(E,R)) and ((M,E),(E,R)):

```1/((M,V),(V,R))-1/h = 1/M-2/V+1/R-1/h     = 2/V-2/E = 2/(V,E)
1/((M,V),(E,R))-1/h = 1/M-1/V-1/E+1/R-1/h = 3/V-3/E = 3/(V,E)
1/((M,E),(E,R))-1/h = 1/M-2/E+1/R-1/h     = 4/V-4/E = 4/(V,E)
```

Therefore for this observer it holds: