Dr Scafetta has a new paper out in 2016

Tom has contacted me with some of his own calculations to support Scafettas findings

He wrote

“Hey Sue,

Scafetta’s new paper is all about validating the 60 year

cycle using highly technical methods.

I use an extremely simple method of sums with

very interesting results.

Here’s a table and a graph I’ve put together:’

————————————————————

l WILL LET TOM EXPLAIN HIS WORK IN THE COMMENTS SECTION BELOW

PLEASE CLICK ON THE TITLE OF THIS POST TO LOAD ALL FURTHER COMMENTS AND DISCUSSION BELOW

PLEASE FEEL FREE TO CONTRIBUTE

STORAGE OF THE ABOVE GRAPHS ARE LOCATED HERE

The above works belongs to TOM MANGO

#### CONTACT TOM MANGO HERE

Readers can contact me at TLMango10@gmail.com

or via this post in the comments section below..

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Thanks so much Sue for posting my graphs.

The table above is based on the 2012 Scafetta paper:

‘Multi-scale harmonic model for solar and climate cyclical variation

throughout the Holocene…..’ Atmos. Sol. Terr. Phys. 80, 296-311.

His paper puts Ogurtsov’s 114 year signal together with the 61

year Jupiter/Saturn beat.

The table is set up like a spreadsheet, each colored section holds

a number of beats between:

60.94838271 /1 and 57.01397771 /1 (first sect.)

60.94838271 / 2 to 57.01397771 / 2 (second sect.)

60.94838271 / 3 to 57.01397771 / 3 (third sect.) . . . / 12 (12th sect.)

………. where: P1 x P2 / ( P1 – P2 ) = P3

………. when: P1 is empty P3 = P2

Each section forms a pattern where S is increased by 5 and J is

increased by 2, producing 90 of Jupiter and Saturn’s stronger beats.

…….57.01397771 = 114.02795542 / 2 (Ogurtsov, 2002)

The graph above is based on the P3 values from this table.

……. Y = the Sum of Cos[2 Pi year / P3]

Each cosine function has a maximum value of 1, so the Y values

can range from -90 to +90. To get the focus just right we had to

limit the view from -6.5 to +10.0. Here, we’re not extracting the 61

and 114 year signals, we’re inserting them to see how they interact.

In order to fully understand what this graph is saying it is

necessary to first read a paper written by Hans Jelbring:

… ‘Celestial commensurabilities: some special cases’

… Pattern Recognition in Physics 1, 143-146, 2013

… page 145 … 4.5 The Jupiter-Saturn commensurability

Jelbring found that there was a very close approximation

regarding the orbital periods of Jupiter and Saturn:

… 11.862242 (149) ~= 29.457784 (60) ~= 19.85931224 (89)

This 149:60 (~2.483) ratio is special because it also happens to be

equivalent to 29.457784:11.862242 (~2.4833). When using the synodic formula:

……………… (J / A) x (S / B) / ( J / A – S / B) = P

if A:B or B:A ~= 2.483 then the period seems to have a special significance.

The earth’s elliptical orbit expands and contracts to a ~99582 year cycle.

……. (2) (J / 60) x (S / 149) / (J / 60 – S / 149) = 99582.6054692 years.

…… 149 : 60 ~= 2.4833

Axial precession:

……. (43 / 3) (S / 72) x (J / 29) / (S / 72 – J / 29) = 25775.93525 years.

……. 72 : 29 ~= 2.4828

Obliquity:

……. (22) (S / 221) x (J / 89) / (S / 221 – J / 89) = 41045.5112124 years.

……. 221 : 89 ~= 2.4831

Earth’s orbital precession of perihelion:

……. (135 / 2) (J / 91) x (S / 226) / (J / 91 – S / 226) = 113209.087559 years.

……. 226 : 91 ~= 2.4835

Notice where the graph is labeled 1766 years. Jelbring found that

11.862242 (149) , 29.457784 (60) and 19.85931224 (89) all ~= 1767.47 years.

There are areas in the graph above that show a confluence of values

(commensurate), such as at {0, 883, 1766, 2649}.

The orbital periods for Jupiter and Saturn have some irregularity about

them, so there is a lot of disagreement about their exact values. Surprisingly

there really isn’t as much room for tweaking these numbers as some would

believe. The exact number of days is pretty solid, it’s the additional hours

that are causing fights to break out. It is important that we address this

issue before we move on.

The best values can be found at: nssdc.gsfc.nasa.gov/planetary/factsheet

by author Dr David R. Williams: using sidereal periods S = 29.457 and

J = 11.862.

Avoid using: the data at ssd.jpl.nasa.gov/?planet_phys_par

This data had a mislabeling problem in which the tropical periods were

listed as sidereal. An attempt to correct the problem resulted in a

period of S = 29.447 years sidereal and S = 29.42351935 tropical.

The Williams data at nssdc.gsfc also had a tropical period of S = 29.424

years, suggesting that the ssd.jpl sidereal period of S = 29.447 is most

likely a typo.

Like I said earlier, there isn’t a lot of room for this much error. The difference

between the sidereal values of 29.447 (ssd.jpl) and 29.457 (nssdc.gsfc)

would be more than 3 and a half days, an obvious typo.

Now we can move on to extol the virtue of Jelbring’s commensurate

orbital periods and why I believe they may be the most accurate of all.

The values that are closest to the actual orbital periods of Jupiter and Saturn

can be found in the factsheets (nssdc.gsfc) authored by Dr David R. Williams.

This would be: S = 29.4571 and J = 11.862 year sidereal periods.

Earlier I stated that I believed that Hans Jelbring’s commensurate orbital periods

( of S = 29.457784 and J = 11.862242 sidereal ) were even more accurate. How

could this possibly be true? Jelbring’s values are quite a bit higher than the actual

orbital periods of Jupiter and Saturn, especially the Saturn value. The reason for

this is simply: the Jelbring periods “are” commensurate with most of the solar

system’s major beats and the Williams periods, at their current values, are not.

But they can be! If we add an “84” on the end of S = 29.4571, we now have

S = 29.457184 and J = 11.862 sidereal periods. These new values “are”

commensurate with all the solar system’s major Jup/Sat beats. In the following

posts I will attempt to prove all these claims.

I hope to persuade others just how important and necessary commensurate

orbital periods really are. Please stick around….

Hans used the 149:60 ratio, in other words 11.862242 (149) ~= 29.457784 (60).

This is a very close approximation but there is an exact ratio that we can use

instead. With a microscopic adjustment to the orbital periods, the ratio

67159:27044 should give us exact values (at least 16 decimal places).

Let’s begin with the ratio 67159:27044 and the sidereal periods

Saturn = 29.457784 and Jupiter = 11.862242.

(11.862242 x 67159 + 29.457784 x 27044) / 2 = 796656.310487 years

the new adjusted S = 796656.310487 / 27044 =

. . . . . . . . . . . . . . . 29.457783999667208992752551398D

the new adjusted J = 796656.310487 / 67159 =

. . . . . . . . . . . . . . . 11.862242000134010333685730877D

S x J / (S – J) = 796656.310487 / 40115 =

. . . . . . . . . . . . . . . 19.859312239486476380406331794D

J x (S / 3) / (J – S / 3) = 796656.310487 / 13973 =

. . . . . . . . . . . . . . . 57.013977706076003721462821158D

(S / 2) x J / (S / 2 – J) = 796656.310487 / 13071 =

. . . . . . . . . . . . . . . 60.948382716471578303113763277D

(2)(J / 60) x (S / 149) / (J / 60 – S / 149) = 796656.310487 / 8 =

. . . . . . . . . . . . . . . 99582.03881087499999999426283D

(S / 72) x (J / 29) / (S / 72 – J / 29) = 796656.310487 / 443 =

. . . . . . . . . . . . . . . 25775.937811091798344620005306D x (3 / 43)

(S / 221) x (J / 89) / (S / 221 – J / 89) = 796656.310487 / 427 =

. . . . . . . . . . . . . . . 41045.524193709601873536174321D / (22)

(J / 91) x (S / 226) / (J / 91 – S / 226) = 796656.310487 / 475 =

. . . . . . . . . . . . . . . 113209.0564815263157894784416D x (2 / 135)

If we experimented with any of the 90 beats in our table (using the adjusted S & J)

they would all show the same great results. But… we can do even better than

this if we adjust the orbital periods to be more in line with the actual values for

Jupiter and Saturn (J = 11.862 and S = 29.457184).

. . . . . . . . . . . . . . . . . . . . . . . . . . . .We’ll do that next…..

Now, let’s experiment with commensurate orbital periods that are more

in line with those found at nssdc.gsfc.nasa.gov/factsheet (Dr D.R. Williams):

. . . J = 11.862 . . . . . . S = 29.457184 . . . .

Let’s use the ratio (1841074 : 741375)

. . . 11.862 x 1841074 = 21838819.788

. . . 29.457184 x 741375 = 21838819.788

21838819.788 years:

. . . / 1099699 = 19.858906653547925 = S x J / (S – J)

. . . / 383051 = 57.01282541489253 = . . J x S / 3 / (J – S / 3)

. . . / 358324 = 60.9471310545763 = . . . S / 2 x J / (S / 2 – J)

. . . / 24727 = 883.19730610264083 = . . J / 2 x S / 5 / (J / 2 – S / 5)

. . . / 453 = 100408.36684137931034 / 2 = J / 60 x S / 149 / (J / 60 – S / 149)

. . . / 11711 = 41025.876128084706686 / 22 =

. . . . . . . . . . . . . . . . . . . . . . . . . . . . S / 221 x J / 89 / (S / 221 – J / 89)

. . . / 12146 = 1798.0256700148196937 = S / 72 x J / 29 / (S / 72 – J / 29)

. . . / 12146 = 25771.70127021241561 x (3 / 43) ‘ axial precession

. . . / 13016 = 113254.481844652735095 x (2 / 135) =

. . . . . . . . . . . . . . . . . . . . . . . . . . . . J / 91 x S / 226 / (J / 91 – S / 226)

Notice that when we are more in line with the Dr Williams orbital periods

for Jupiter and Saturn, the axial precession value is closer to 25772 years.

Dr J.L. Hilton estimated axial precession to be approximately 25772 years.

Hilton, J.L., et al., 2006. Report of the International Astronomical Union

. . Division I Working Group on Precession and the Ecliptic. Celestial

. . Mechanics and Dynamical Astronomy 94, 351-367.

When: . . . J = 11.862 . . . . . . S = 29.457184 . . . ratio: 2.48332355

. . . S / 72 x J / 29 / (S / 72 – J / 29) = 1798.0256700148 years

When: . . . J = 11.862242 . . . S = 29.457784 . . . ratio: 2.48332347

. . . S / 72 x J / 29 / (S / 72 – J / 29) = 1798.321064019 years

This 1798 year period is the Keeling and Whorf oceanic tidal cycle.

Keeling, C.D., Whorf, T.P., 2000. The 1,800-year oceanic tidal cycles:

. . . A possible cause of rapid climate change.

. . . Proc. Natl. Acad. Sci. 97(8), 3814 – 3819.

The 1798 year oceanic tidal cycle is linked to the axial precession cycle

and there is a very good reason why this is so. In the next posts I hope

to explain this.

. . . . . . . . . . . Please stick around . . .

using: . . . . . . J = 11.862242 . . . . . . . . . . . S = 29.457784

Jupiter is approximately 72% of the mass orbiting the Sun. Because of

this, Jupiter and the Sun share a binary attribute, they always oppose one

another. Jupiter is a massive planet, but this is more about percentages

than about mass. To share this binary attribute with the Sun, a planet need

only be more than 50% of the mass orbiting the Sun. Saturn is approximately

21% of the mass, so consequently Saturn will be regularly found on the

same side of the center of mass as our Sun. But… if we were to remove Jupiter

from our solar system, Saturn would then be 66+% of the mass and would

develop a similar binary relationship with the Sun. Our sun would no longer

orbit the center of mass in 11.862242 years but in 29.457784 years.

The Sun’s orbital pattern is not usually viewed as an 11.862242 year 360 degree

trip around the center of mass. The Sun orbits the center of mass in a looping

pattern called an epi-trochiod which is a 19.8593122389 year 602.6982425434

degree excursion.

. . . . (19.8593122389 / 11.862242) 360 deg = 602.6982425434 deg.

. . . . . . . 602.6982425434 deg – 360 deg = 242.6982425434 deg

The Sun’s pattern of motion rotates ~242.6982425434 degrees in a

counter-clockwise direction every 19.8593122389 years (Jupiter/Saturn

synodic period). This could also be viewed as an ~117.30175745651 degree

clockwise rotation.

Because they are separated by ~117.30175745651 degrees, three successive

synodic loops form the distinct shape of a three leaf clover. But this tri-synodic

period of 59.57793671687 years does not complete a full 360 degree

rotation.

. . . . . . . . 360 deg – (117.30175745651 deg) 3 = 8.09472763044 deg

Each successive tri-synodic pattern rotates ~8.09472763044 degrees in

a counter-clockwise direction every 59.57793671687 years, eventually

turning 360 degrees in 2649.63297065 years.

(360 deg / 8.09472763044 deg) 59.57793671687 = 2649.63297065322 yrs

We could also have calculated the number of years that

pass with each degree of rotation:

. . . . . 59.57793671687 / 8.09472763044 deg = 7.360091586 years/deg

. . . . . (7.360091586 years/deg) 360 deg = 2649.63297065322 years

The 2649.63297065322 year cycle belongs to an exclusive group of

frequencies that have a 360 degree rotation characteristic. There’s a

patterned formula for viewing these frequencies in pairs and the

2649.63 year cycle is one of these significant periods.

continued . . .

using: . . . . . J = 11.862242 . . . . . . . S = 29.457784 . . . . . . .

There is an exclusive group of frequencies that have a 360 degree

rotation characteristic. We can view these frequencies in pairs with

these formulas:

. . . (a) 19.8593122389 x N x 360 / (117.3017574565 x N – 360 x M)

. . . (b) 19.8593122389 x N x 360 / (242.6982425434 x N – 360 x M)

. . . where: 360 x M reduces the denominator so as to fall within

. . . a range of 0 to 360 degrees

when N = {3, 6, 9, 12, 15, . . . 132} using formula (b) we get

2649.63297065322 years

when N = {2, 4} using formula (b) we get 114.02975542582 years

when N = {1, 2, 3} using formula (a) we get 60.94838271 years

when N = {43, 86, 129, 172, . . .} using formula (a) we get

77327.805752832 years = 1798.321064019 (43) ‘ Keeling & Whorf

77327.805752832 years = 25775.935290544 (3) ‘ axial precession

If we take the first N from each set we can find the root of any

period that is derived using these formulas:

2649.63297065322 / 3 = . (J / 2)(S / 5) / (J / 2 – S / 5)

114.02975542582 / 2 = . . J (S / 3) / (J – S / 3)

60.9483827100845 / 1 = . (S / 2) J / (S / 2 – J)

77327.805752832 / 43 = . (S / 72)(J / 29) / (S / 72 – J / 29)

When N = {132, 264, 396, . . .} using formula (a) we get

246273.06727448875 years = 1865.70505510976 (132)

1865.70505510976 (22) = 41045.51121241479 years ‘ obliquity

246273.06727448875 / 132 = (S / 221)(J / 89) / (S / 221 – J / 89)

. . . . continued . . .

using: . . . . . J = 11.862242 . . . . S = 29.457784 . . . . .

. . (a) 19.8593122389 x N x 360 / (117.3017574565 x N – 360 x M)

. . (b) 19.8593122389 x N x 360 / (242.6982425434 x N – 360 x M)

when N = {89, 178, 267, . . . } using formula (b) we get

4431425.94338327044742 years = 49791.302734643488 (89)

49791.302734643488 (2) = 99582.605469286976 years ‘ earth’s eccentric orbit

4431425.94338327044742 / 89 = (J / 60)(S / 149) / (J / 60 – S / 149)

Hans Jelbring found that his commensurate orbital periods had the ratios:

. . . 11.862242 (149) ~ = 29.457784 (60) ~ = 19.8593122389 (89)

I hope that folks following these posts will agree that the Milankovic

cycles belong to an exclusive group of frequencies that have a 360

degree rotation characteristic.

Milankovic theory is not universally accepted and for good reason. In my

estimation, the current view of this theory is a bit turned around. The

actual role that these cycles have in climate is so much more beautiful

than the oversimplified version that is served up.

. . . We’ll go there next . . . please stick around . . .

The Milankovic cycles belong to an exclusive group of frequencies

that have a 360 degree rotation characteristic. This has significant

importance when we consider how the sun moves around the solar

system’s center of mass.

When the sun decelerates, it moves in closer to the center of mass.

And when the sun accelerates, it moves away from the center of mass.

The sun has an inwardly directed deceleration and an outwardly directed

acceleration.

The Milankovic cycles derive their power from the 360 degree rotation of

the sun’s outwardly directed acceleration. Because the Milankovic cycles

describe physical motions of the earth, it is widely accepted that these

cycles are exclusively ‘earth’s cycles’. But this is simply not true. The

Milankovic cycles are the sole property of the sun and all of the sun’s

satellites feel the same accelerations of the sun.

Among the sun’s satellites, the earth is unique in having a single large

moon. Our 25775.9 (77327.8 / 3) year axial precession cycle is a result

of being caught up between an accelerating sun and a large moon ( see

the june 23, 9:25 post above). But… all of the sun’s satellites receive the

same 77327.8 year pulse that we get from the sun. We may all have

different precession rates but we all get our marching orders from the

same place, the sun.

continued . . .

In my estimation, Milankovic theory ‘is’ completely turned around

backwards.

The earth’s inner core is continually cranked by an

accelerating sun and a large moon. It’s axis swings up and down

every 41000 years while it precesses (25772 yrs) like a football

and i’ts eccentric orbit expands and contracts (100000 yrs). These

are just a few of the motions the earth has inherited from an

accelerating sun. They all have something in common, they cause

the earth to produce an incredibly strong magnetic field.

The most plausible explanation for re-occurring ice age cycles is:

the substantial loss of magnetic field. Current Milankovic theory

does not address the magnetic field. How light changes with a

weaker field. How the chemistry of the atmosphere changes with

different light. ( for more on this visit Reality348)

One of the contradictions raised by Milankovic theory is the issue of

eccentricity. Milankovic theory suggests that every 100000 years the

earth’s eccentric orbit will increase and the sun’s light will be diffused

enough to initiate an ice-age. Also… the severity of this ice-age will be

determined by many other factors including obliquity and axial precession.

So… this presents a problem, can the very same motions that are

responsible for creating our magnetic field also be responsible for

an ice-age cycle? Probably not.

Even though Milankovic got it wrong, eccentricity for other reasons is one

of the most important factors involved in the ice-age cycle.

We’ll go there next, please stick around.

Can the very same motions that are responsible for creating our

magnetic field also be responsible for an ice-age cycle? Only if

we’re talking about the loss of obliquity, the loss of axial precession

and especially the loss of eccentricity.

Where there is eccentricity there is acceleration and where there is

acceleration there is magnetic field production. When acceleration

diminishes so does magnetic field strength. When a bodies eccentricity

value goes to zero, it’s magnetic field is weakened.

The sun orbits the solar system’s center of mass in a looping pattern

called an epi-trochoid. We don’t normally look at the sun’s orbit as

having eccentricity, but it most certainly does and it gets this eccentricity

almost entirely from the gas giants. This eccentricity is manifested as

acceleration and distance from the center of mass. If the gas giants

were to down shift into zero eccentricity values, the sun’s orbit would

look much different. It’s smaller loop would be much broader and rounded.

The two open ends would not extend out as far from the center, due to

the decrease in acceleration. The magnetic field strength of the gas giants

and the sun would all be decreased. The sun’s solar cycle would be extended

out to about 11.86 years from 11 years. Also… solar minimum would occur

at the same position on the ecliptic most of the time.

It’s not a large eccentric value for earth that we should be concerned about.

It’s a solar-system-wide loss of magnetic field strength.

continued . . .