Updated 13/04/2012

There is some dispute about how long it takes for the four Jovian

planets to re-align. Some people claim that there is a ~ 178 year

re-alignment period (Jose, P.D., ApJ (1965)), while others say

that the long-term re-alignment period (as measured by

asymmetries in the Sun's angular momentum about the

Barycentre) is 171.4 years and the ~ 178 year Jose cycle does

not exist.

The argument presented below investigates if there really is a

~ 178 year Jose Cycle for the re-alignment of the Jovian planets.

Using the following orbital periods of the Jovian planets:

Ju = 11.862 yrs Sa = 29.457 yrs

Ur = 84.01 yrs Ne = 164.79 yrs

we get the following synodic periods between the Jovian planets:

A___B__Synodic Period______Orbits A_____Orbits B___dir_

Ju - Sa___19.858 yrs________1.6741_______0.6741__retro

Ju - Ur___13.812 yrs________1.1644_______0.1644__prog

Ju - Ne___12.782 yrs________1.0776_______0.0776__prog

Sa - Ur___45.363 yrs________1.53997______0.53997_retro

Sa - Ne___35.869 yrs________1.2177_______0.2177_prog

Ur- Ne___171.379 yrs_______2.03998______1.03998_prog

where columns 1 and 2 give the two planets (A and B) that are

being considered; column 3 gives the synodic period in years;

columns 4 and 5 the number of orbits completed by planets A

and B,respectively over one synodic period; and column 6 the

direction of movement of the alignments i.e. prog = prograde

and retro = retrograde.

This means that there are three possible alignments of the Jovian

planets:

1. Ju - Sa re-alignments will align with Ur - Ne re-alignments after

a whole multiple of the following number of years:

i.e. (19.858 x 171.379) / (171.379 + 19.858) = 17.7959 yrs

2. Ju - Ur re-alignments will align with Sa - Ne re-alignments after

a whole multiple of the following number of years:

i.e. (13.812 x 35.869) / (35.869 - 13.812) = 22.461 yrs

3. Ju - Ne re-alignments will align with Sa - Ur re-alignments after

a whole multiple of the following number of years:

i.e. (12.782 x 45.363) / (45.363 + 12.782) = 9.9721 yrs

Hence, these re-alignments of the four Jovian planets take place:

After one Gleissberg cycle of ~ 89 years:

Ju - Ne / Sa - Ur___9 x 9.9721 yrs___= 89.75 yrs

Ju - Sa / Ur - Ne___5 x 17.7959 yrs__= 88.98 yrs

Ju - Ur / Sa - Ne___4 x 22.461 yrs___= 89.84 yrs

and then again after one Jose cycle ~ 179 years:

Ju - Ne / Sa - Ur__18 x 9.9721 yrs___= 179.50 yrs

Ju - Sa / Ur - Ne__10 x 17.7959 yrs__= 177.96 yrs

Ju - Ur / Sa - Ne__8 x 22.461 yrs____= 179.69 yrs

Since the actual orbital periods of the four Jovian planets

slowly drift over the centuries you would expect these two

cycles to slowly drift in and out depending on the actual

orbital periods of the planets, however, the whole

re-alignment pattern seems to reset itself once every

4628 yrs.

The actual dates upon which the re-alignments of Uranus and

Neptune are re-synchronized with the re-alignments of Jupiter

and Saturn are:

_________= 7949 B.C.

5725 B.C. = 7949 B.C. + 2224 yrs

3322 B.C. = 5725 B.C. + 2403 yrs

1098 B.C. = 3322 B.C. + 2224 yrs

1306 A.D. = 1098 B.C. + 2405 yrs

3530 A.D. = 1306 A.D. + 2224 yrs

5933 A.D. = 3530 A.D. + 2403 yrs

As you can see, there is an oscillation between a period of 2224

years and 2403.7 yrs, giving a full repetition period (where all the

Jovian planets are lined up on the same side of the Sun) of ~4628

yrs. This means that the Jovian planets reset their alignments

roughly once every 26 Jose cycles = 26 x 178 yrs = 4628 yrs.

The actual repetition cycle is 18,512 (= 4 x 4628) yrs long,

as after each 4628 yrs, the four Jovian planets come back

into alignment along an axis that rotates through a quarter of

a full revolution around the Sun.

The ~ 18500 year repetition cycle for the gravitational influence

of the Jovian planets is responsible for the slow precession of the

line-of-Apsides of the Earth's orbit, causing perihelion (and

aphelion) to advance by roughly 1 day every 58 years.

Thanks Ian for continuing this interesting topic. The maths over the longer term do seem to work out but when looking at the actual planet alignments for practical purposes the 179 Jose period is just not observed. In my line of research the actual planet positions when the sun goes on its altered path around the SSB are crucial. This happens when Jupiter/Uranus and Neptune are together with Saturn opposing, the Saturn position being the ultimate key with its exact position determining the shape of the altered path and the precise timing of the angular momentum disturbance felt at the Sun (strength of grand minima). This precise position does not repeat every Jose cycle and in fact is very different each cycle. It also does not follow a 172 year cycle but averages out at 172 over 5000 years or so. The 172 year average cycle usually also has at least 2 extra partial alignments of J/U/N with S opposing that further complicates the issue and also shows why FFT analysis is unable to show a regular pinpoint cycle in grand minima.

ReplyDeleteI stumbled on the 4628 year cycle while playing around with a solar system viewer, but did notice that even that cycle is not precise. Jupiter in particular precesses every 4628 years and I wonder if over many thousands of years this cycle would also disappear. I personally think when it comes to the Jovians there is no long term precise returning cycle. This is inherent in the solar system and explains how we get different grand minima every time and why the Holocene record has so much modulation in solar output.

http://www.landscheidt.info/?q=node/226

www.math-ed.com/Resources/GIS/Geometry_In_Space/java1/Temp/TLVisPOrbit.html

Geoff says: "It also does not follow a 172 year cycle but averages out at 172 over 5000 years or so."

ReplyDeleteI believe this because what you are seeing is a rough long term average of the orbital period of Neptune and the 178 year Jose cycle:

(164.79 + 178)/2 = 171.395 years

In addition, I believe you need be very careful what you are taking taking the FFT of if you are looking for the 179 year cycle.

If you take a FFT of the magnitude of the momentum of the Sun about the Barycentre you will not get a 59.6 year period. This is because the magnitude of momentum is a scalar quantity. However, if you take the FFT of the vector quantity angular-momentum of the Sun about the Barycentre, the 59.6 year period will dominate.

The same is true when you are looking at the FFT of the relative orientation of the Jovian planets. The 178 Jose cycle will only be evident if you take the FFT of a quantity that includes both magnitude and direction.

The 4628 year cycle is 233 Jupiter-Saturn synods = about 4627.5 years, so it's one conjunction short of 26 Jose cycles (26x9 = 234)

ReplyDeleteThe Uranus-Neptune synodic period occurs 27 times in this period (4627.5/27 = 171.39 years)

~ Oldbrew

An excellent piece of investigation Anon!

ReplyDeleteJS synodic = 19.859 yrs

Jose Cycle = 178.72 yrs

233x19.859 = 4627.15 yrs

26x178.72 = 4646.72 yrs = 4626.86 + 19.859 yrs

27x171.39 = 4627.53 yrs

Thanks!

By extension there are 233 Jose cycles in 9 Grand Synods i.e. 9 x 4627.15 yrs. (Jose = 178.731)

ReplyDeleteThe question might then be: are there 233 Grand Synods too?

~ Oldbrew