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
I prefer 171.39 x 27 = 4627.53, but its just a numbers parlor game. The orbits are what they are and the modern ephemeris will show us when it comes to the repetition of the outer 4 the 4627.25 cycle is by far the closest to a real cycle.
ReplyDeletehttp://www.landscheidt.info/images/Jose_cycle.png
Very interesting indeed. By analysing the perihelia of Jupiter and Saturn I found that they have a 973 year cycle that matches the Roman Warm Period (RWP), the Medieval Warm Period (MWP), and the present, let's call it the the Industrial Warm Period (IWP). This millennial cycle is cause by the precession of their perihelia and having coincided in the same year at that frequency, e.g. 765 CE and 1738 CE.
ReplyDeleteMultiplying the 973 year cycle by 6 takes us to the Holocene Optimum https://www.ncdc.noaa.gov/global-warming/mid-holocene-warm-period. Times 12 gives the start of the Holocene; times 18 gives the start of warming toward the Holocene; and 24 times the cycles gives the about 23,000 year 'precession' cycle seen in southern ocean sediments by Hays, Imbrie, and Shackleton (1976). The other precession was about 19,000 years and matches the 'actual repetition cycle of 18,512' years as referred to by Ninderthana.
The Jose cycle is about 3 times the roughly 60-year 5:2 orbital ratio cycle of Jupiter and Saturn phasing with the NH solstices.