For this look at Saturn-Uranus conjunction patterns a model will be proposed, then the planetary data compared to it to see how good a match it is – or not. This post follows on from two recent posts which can be found here and here.

The model will be based on the orbit period of Uranus and the Saturn-Uranus conjunction period.

The planetary data is from NASA-JPL.

As many will know, the Fibonacci number series starts with:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233.

Each number is the sum of the two numbers before it, except 0 and the first 1.

The ratio of two consecutive numbers converges towards the ‘golden ratio’, phi.

For Uranus the notional orbit period will be 84 years (JPL value: 84.016846y).

For the Saturn-Uranus conjunction period the figure will be 45.3333 years ( JPL-derived value 45.338381y).

Saturn and Neptune orbit periods will be derived from the other (notional) data.

Anyone with limited time or a dislike of numbers, or both, may wish to skip to the discussion below.

**Model:**

102 (34 x 3) Uranus = 8568 years

52 (13 x 2²) Neptune = 8568 years

102 – 52 = 50 so:

50 Uranus-Neptune conjunctions = 8568y = 34 x 21 x 3 x 4y

Neptune orbit = 8568y / 52 = 164.76923y

U-N = 171.36y

This is a Uranus-Neptune conjunction cycle where a complete number of both planetary orbits has occurred.

8568 / 45.3333 (Saturn-Uranus) = 189 so:

189 S-U = 8568y (189 = 21 x 3²)

For 50 U-N and 189 S-U the Saturn-Neptune figures are:

239 S-N = 8568y (50 + 189 = 239)

S-N = 35.84937y

From the above model data we can derive:

63 S-U = 8568y / 3 = 2856y (34 x 21 x 4y)

34 U = 2856y (34 x 84)

therefore

34 U = 63 S-U = 97 S (34 + 63 = 97)

Saturn orbit = 2856y / 97 = 29.4433y

291 S (97 x 3) = 2856y x 3 = 8568y

This is a repeating pattern of 63 (21 x 3) Saturn-Uranus conjunctions.

The 63 S-U figure breaks down further:

21 S-U = 8568y / 9 = 952y (34 x 7 x 4y)

3 S-U = 8568y / 63 = 136y (34 x 4y)

7 S-U = 8568y / 3³ = 317.333y (= 952 / 3)

That concludes the model.

The period of 7 S-U conjunctions corresponds closely to that discovered in raised beaches in the Hudson Bay area, as noted by Dr. Rhodes Fairbridge here:

http://www.mitosyfraudes.org/Calen2/Rhodes.html

Quoting from the caption to a picture of some raised beaches:

‘The Hudson Bay “staircase”, a typical series of 184 successively uplifted strandlines, situated in Richmond Gulf on the eastern side of Hudson Bay, Canada. The sand gravel beaches are preserved by permafrost, and recur with great regularity about every 45 years, representing the cycle of storminess. There are longer cycles of 111 years and 317 years evident in the beaches, which are linked with planetary cycles.’

Dr. Fairbridge comments: ‘Their extraordinary regularity is duplicated in other parts of the Arctic, which denies any theory of randomness in storminess cycles.’

Turning to the JPL-derived data (model data value for comparison in brackets):

102 Uranus = 8569.7 years (8568)

50 Uranus-Neptune = 8570.31 years (8568)

52 Neptune = 8569.15 years (8568)

This shows the model parallels reality closely so far (about 99.98%).

189 S-U = 8568.95y (8568)

239 S-N = 8569.24y (8568)

291 Saturn = 8569.22y (8568)

Comparison of JPL-sourced values with derived model data (in brackets):

63 S-U = 2856.32y (2856)

21 S-U = 952.106y (952)

3 S-U = 136.01514y (136)

7 S-U = 317.369y (317.333)

1 S = 29.447498y (29.4433)

1 U = 84.016846y (84)

1 N = 164.79132y (164.76923y)

S-N = 35.85455y (35.84937y)

U-N = 171.36y (171.4062y)

**Discussion**:

This shows an extremely close correlation between actual orbital data values and the Fibonacci-based model (better than 99.98% in most cases).

For example we can see that 3 Saturn-Uranus conjunctions take almost exactly 34 x 4 (or 34 x 2 x 2) years:

3 x 45.338381 (S-U) = 136.01514y (34 x 4 = 136)

Note also:

3 S-U / U = 1.6189031 (Fibonacci comparison: 136/84 = 34/21 = 1.6190476)

3 S-U / S = 4.6189031 (1.6189031 + 3)

Thus the ratio of 3 Saturn-Uranus conjunctions to one Uranus orbit is almost exactly 34:21, very close to phi:1.

More could be said but for now that’s probably enough to digest.

The Fibonacci model mirrors the observed motion of Saturn and Uranus very well.

Thus it can be a useful tool in analysing the data as well as suggesting how planets may be organising themselves.

The next post in the series will contain a model for Jupiter-Uranus and a summary – hopefully easy to follow – modelling all the outer planets on a Fibonacci basis, drawing on the recent ‘giant planet’ posts.

***

Footnote: readers may notice the frequent appearance of ‘x 4y’ in the notes.

This may well be because 4 years is an exact number of Earth days i.e. an exact number of rotations (365.25 x 4 = 1461).

In the two previous ‘giant planet’ posts the periods discussed were 1768 years (34 x 13 x 4y) and 4628 years (89 x 13 x 4y). Here we have 8568 years (34 x 21 x 3 x 4y) so the pattern is there: Fibonacci numbers x 4.

Reference data: http://solarsystem.nasa.gov/planets/charchart.cfm/

The Fibonacci number sequence is explained in some detail here.

Nature loves Fibonacci sequences and series. They’re everywhere.

http://www.inspirationgreen.com/fibonacci-sequence-in-nature.html

I hope to show a comprehensive model of the orbits and synodic periods of the outer planets can be achieved using only Fibonacci numbers. It should closely mirror the ‘real-life’ data.

Details to be drawn mainly from the three posts so far and brought together in the next one.

oldbrew,

This is a very good explanation of the mathematical process involved but you have missed out the part about actually describing the model. What is your model?

You should be able to break down your explanation into a few dot points. I understand that you are using Fibonacci numbers and I understand that this particular piece of information is important:

“In the two previous ‘giant planet’ posts the periods discussed were 1768 years (34 x 13 x 4y) and 4628 years (89 x 13 x 4y). Here we have 8568 years (34 x 21 x 3 x 4y) so the pattern is there: Fibonacci numbers x 4.”

4628 is the grand planetary cycle for the Jovian planets but what are the other two in the real world?

Sorry for being a bit obtuse but I would like to more fully understand what yo are saying in these posts.

IW: the model is an attempt to match a consistent pattern to the existing data of the outer solar system.

It’s intended as an aid to see what’s really going on. I may expand on that a bit in the next post.

If I can find a good format I’ll include a small spreadsheet to try and summarise everything so far.

1768 is 89 Jupiter-Saturn conjunctions, where 60 Saturn = 149 Jupiter orbits (very close).

8568 is 50 Uranus-Neptune conjunctions, where 52 Neptune = 102 Uranus orbits (very close).

In reality it’s nearer to 8570y but it’s the pattern I’m after so a 99.97% match is adequate.

102 x 84 = 8568 but Uranus’ orbit is a shade more than 84 years (a few days extra).

I’m coming round to the idea that the orbit of Uranus is a key to understanding the system.

4628y is considered a grand cycle but in the earlier post I proposed that a ‘grander’ cycle exists:

89² J-S = 34 x 3³ U-N

4628 / (89/34) = 1768 but Saturn-Uranus aligns to 4624y not 4628y.

That’s because:

8568 / 3 = 2856 y = 34 Uranus = 97 Saturn = 63 S-U (21 x 3)

and

2856 x (34/21) = 4624 (34 x 3 S-U)

I’ve got a model for Jupiter-Uranus and another for Uranus-Neptune-Pluto so I’ll include those in the next post – all based on the same ideas.

oldbrew

Thank you. That helps me see what you are trying to do with these conjunctions. It makes you wonder why Uranus is so special?

In the model the main conjunction periods: 1768, 4628 and 8568 – are all Fibonacci multiples x 4.

Uranus is too: 21 x 4 (plus a few days).

83 Uranus-Earth conjunctions = 84 years.

The sum of the conjunctions is closer to the period in years than the orbit period in this case.

“The period of 7 S-U conjunctions corresponds closely to that discovered in raised beaches in the Hudson Bay area, as noted by Dr. Rhodes Fairbridge..”

That’s because it is the synodic cycle of Uranus, Saturn and Jupiter. 7, or any number of S-U synodic periods on its own is essentially meaningless without the reason for every 7th one creating a cycle. Except for one S-U synod, where if you carefully inspect each inferior conjunction rather than the average period, you will see that Jupiter is also very regularly in syzygy or quadrature with N or S/U at the same time. Meaning that there are major Jovian events occurring at every S-U inferior conjunction, which should be what the 45y pattern in the Hudson staircase is about.

Of course you would need to know why a quadrature matters to appreciate this, which I will cover in due course.

Where the slip in 317.7y J-S-U cycle gets taken up by a shorter 179y step in the 4627y grand cycle should also be evident in the Hudson staircase.

As for your 8568y model, I don’t see any point in it, especially with the wrong Saturn orbital period value, it’s about 7 years too short.

UL: I’ve used the figures in the dataset I quoted and the results are in accordance with that.

In any case the differences with your preferred version of the orbital data are in the order of 1 in 1000, which is OK for a model. Saying something is the ‘wrong’ value is a personal opinion when there are two versions of the data.

Paul Vaughan tells me this is the right version to use, so whatever I do somebody is going to be complaining.

https://tallbloke.wordpress.com/2014/10/23/evidence-of-correlation-lod-and-solar-magnetic-cycles/comment-page-1/#comment-91342

You can also find the same data here, which PV described as ‘more precise elements’.

It lists the source of each item of data e.g. [D] is Seidelmann.

http://ssd.jpl.nasa.gov/?planet_phys_par

UL: ‘As for your 8568y model, I don’t see any point in it’

What do you get for 83 x 102 Uranus-Earth conjunctions?

And 8277 Saturn-Earth conjunctions?

If those two are near 8568 then so must Saturn-Uranus be, within 1-2 years.

With the Saturn figure that I am using, 189 U-S synods is 8573.39yrs.

Either way, the 8568 is an abstraction, it serves no purpose.

Let’s try it another way. There are 83 U-E conjunctions in 84 years.

83 x 102 = 8466

84/83 = 1 conjunction period

84/83 x 83 x 102 = 8568y

1 conjunction = 8568/8466 = 1.0120481y

(U / (U-1) = 1.0120457y but the result is almost the same)

You can’t make it 8573+ years, it’s impossible: five years is nearly five extra U-E.

102 (U) + 189 (S-U) = 291 = Saturn orbits

With your numbers:

8573 / 291 = 29.46048

29.46048 / 28.46048 = 1 S-E = 1.0351364y

8573 / 1.0351364 = 8282 S-E

8573 / 1.0120481 = 8471 U-E

(check: 8471 – 8282 = 189)

So you’ve got too many U-E and the equation can’t work.

PS try 52 Neptune too.

189 U-S synods is 8573.3892 yrs

Which is 8471.33798 U-E synods

and 8282.33798 S-E synods

A difference of exactly 189, which it should be.

UL: that’s exactly the problem right there – too many synods of U-E.

You’ve got more than 83.05 per Uranus orbit and there aren’t that many, it should be 83.

102 x 0.05 = 5.1 so you’re 5 over at 84 years per Uranus, or about 4 over compared to the actual Uranus total, which on your NASA fact sheet is (by my reckoning) 84.012046 x 102 = 8569.2286y

Your synod number needs to be about 8467 not 8471, because 8467 + 102 = 8569.

I’ve just noticed the NASA fact sheet gives a figure of 369.66 days for U-E.

8467 x 369.66d = 8569.2298y which confirms my calc.

It also says the Uranus orbit period is 30685.4 days so:

30685.4 / 369.66 = 83.009792 (U-E per U orbit)

83.009792 x 102 = 8466.9987 i.e.

8467.How do you justify 83.05?

OB:

“UL: that’s exactly the problem right there – too many synods of U-E.”

You miss the point entirely, there are also 5 extra S-E synods.

“You’ve got more than 83.05 per Uranus orbit and there aren’t that many, it should be 83.”

With your choice of Uranus orbital period, there are 83.01358 per Uranus orbit,

and with the figure that I am using, there are 83.01058 per orbit.

“Your synod number needs to be about 8467 not 8471, because 8467 + 102 = 8569.”

Nonsense, the U-E and S-E synods have to be exactly 189 difference, the same as in your figures, the absolute difference being due to the two wildly different Saturn orbital period values.

OK, so your figures won’t give 102 Uranus = 189 S-U = 291 S and mine will.

http://space-facts.com/saturn/

Neither are exactly 102, 189 and 291, it’s not as if there was supposed to be a perfect fit at those numbers using either orbital period values anyway. And what of it, at 8568 or 8573.39 yrs, it’s meaningless.

Every pair of planets has a ‘closest match’ to whole orbit numbers. On the data I referred to that closest match is 34 U : 97 S which is 1/3rd of 102:291.

Again, this is from the data. The model is my own idea and if you don’t see anything in it, fair enough, that’s up to you.

And even closer matches will be found at larger numbers using the same orbital values. While with the alternative Saturn value, it leads to a completely different set of close match numbers, interestingly 1 U-S synod off from the 2224y period.

Try 102*S-U and 233*J-S using your figures. You should find that they are 4 years apart. That would demolish the 4627yr grand synod.

OB: I’m coming round to the idea that the orbit of Uranus is a key to understanding the system.Uranus’ unusual tilt is a hint that forces are brought to bear on it by it’s interactions with the other gas giants which are resolved by a revolution of it’s axis rather than by an adjustment of its orbital eccentricity, which seems to be the first ‘escape route’ resorted to by planets that are being pushed around by a larger neighbour.

Wayne Jackson commented some time ago that Venus’ orbit is almost circular because it is being acted on by more than one neighbour (mainly Juputer and Earth, whose gravitational effect on Venus is the same within an order of magnitude).

Venus has an unusual direction and rate of rotation and a conventional axial orientation.

Uranus has an unusual axis of rotation and a conventional spin rate.

Rick Salvador found that incorporating the 1/4 period of Uranus orbital period (Thanks Sparks) into his planetary solar model improved it greatly. That may be linked with Ulric’s ideas about the importance of quadratures, which I hope he’ll get around to explaining to everyone else, so I can discuss openly what he told me in private.

Exciting times for the solar-planetary theory.

UL: ‘Try 102*S-U and 233*J-S using your figures. You should find that they are 4 years apart. That would demolish the 4627yr grand synod.’

I explained that in the earlier post: 89² J-S = 34 x 27 U-N.

Nothing is demolished: 4628y is 27 U-N, 1768 is 89 J-S and they eventually equalize.

U and N orbits align at 50 U-N in 8569-8570 years to give this line-up:

52 N – 102 U – 291 S

1/27th of that corresponds to the period of the beach ridges identified by Fairbridge.

(291 – 102 = 189 / 27 = 7 S-U)

TB: ‘Rick Salvador found that incorporating the 1/4 period of Uranus orbital period (Thanks Sparks) into his planetary solar model improved it greatly.’

That would be 21 years 😉

I’ll cover that in the next post: a Jupiter-Uranus model – stay tuned!

PS thanks for the tip.

OB, as I said, just calculate 233 J-S, and 102 S-U, and you’ll find that they are 4yrs apart, hence no 4327y grand synod using your choice of orbit values.

And 27*317.7y does not exist astronomically, and it certainly cannot be as short as 317.3 because of the length of 16 J-S and 23 J-U.

https://tallbloke.wordpress.com/2014/11/18/why-phi-giant-planets-a-saturn-uranus-model/comment-page-1/#comment-93019

UL: I think you’re creating a problem, S-U is a bit of a red herring at 4628 years. Think about it: is Saturn-Uranus as significant as J-S and U-N, or J and anything for that matter?

It’s the main conjunctions of J-S and U-N that matter there IMO, and the JPL data makes them about half a year apart. Your version does too I believe.

That’s why I find the real meeting is later: 34 grand synods removes the ‘rump’ J-S:

34 x 233 = 7922 and 89² = 7921.

Re: ‘does not exist astronomically’ – again it’s not an objective term for me.

Geoff Sharp has an interesting graphic here, you’ve probably seen it:

Website: http://www.landscheidt.info/

” Think about it: is Saturn-Uranus as significant as J-S and U-N, or J and anything for that matter?”

There is no 317.7yr cycle without Jupiter, think about it:

https://tallbloke.wordpress.com/2014/11/18/why-phi-giant-planets-a-saturn-uranus-model/comment-page-1/#comment-93019

“It’s the main conjunctions of J-S and U-N that matter there IMO, and the JPL data makes them about half a year apart. Your version does too I believe.”

As I have shown you, with your choice of orbital values, 233 J-S, and 102 S-U are 4yrs apart.

With the values that I am using they are 0.129 yrs apart.

“Re: ‘does not exist astronomically’ – again it’s not an objective term for me.”

Read comment-93019 again, the explanation is there.

“Geoff Sharp has an interesting graphic here, you’ve probably seen it:”

The very first thing that I ever said to him when I saw his N-U ideas, was that it was much more likely to be colder when Neptune and Uranus are in quadrature. I still stand by that, and can now confirm that Neptune-Uranus in inferior conjunction, is actually when solar activity can be at its highest for that pair of bodies. It is highly dependent on where the other two are though, which makes it very difficult to tease the puzzle apart. I seem to remember that Geoff’s idea was that it tripped up solar activity a decade or two later, but maybe not always, etc.

‘As I have shown you, with your choice of orbital values, 233 J-S, and 102 S-U are 4yrs apart.

With the values that I am using they are 0.129 yrs apart.’

It’s the same in reverse with S-U, U-N and S-N. Your values are 4 years apart and mine line up.

Can’t have it both ways.

Nonsense, they are 4627.43y, 4626.908y, and 4627.017y.

Centered at the inferior conjunction of Uranus and Saturn, April 8 1307:

And 1690000d later:

4627.43y – 4626.908y = 0.522y

4627.43y – 4627.017y = 0.413y

That’s what I said: ‘It’s the main conjunctions of J-S and U-N that matter there IMO, and the JPL data makes them about half a year apart. Your version does too I believe.’

Btw the JPL data gives 23 J-U as 317.69679y if that’s any help. Fairbridge mentions 17 lunar declinations but that’s a year less.

You actually said:

“Your values are 4 years apart and mine line up.

Can’t have it both ways.”

Which I proved to be false.

And so what about your J-S and U-N, it doesn’t change the fact with your choice of orbital values, 233 J-S, and 102 S-U are 4yrs apart, thereby trashing any grand ~4627y cycle.

No Ulric, perhaps you misread it. Here’s what I said:

‘It’s the same in reverse with S-U, U-N and S-N. Your values are 4 years apart and mine line up.’

Saturn, Uranus, Neptune. No Jupiter – I was referring to the ~8569 year period where your S-U value was 8573. Maybe I should have made that clearer.

I would just add that the nearest multiple of Uranus is around 4621 years. That’s going to drift off your 4627 year timescale anyway, so talk of ‘trashing’ something is a bit over the top surely?

Add in that 28 Neptune (55(U) – 27) is only 4614 years and the ‘grand synod’ doesn’t quite cover all the bases.

The fact is the best U-N alignment is at 50 U-N (maybe 25 as well but that excludes Saturn as the ‘third party’) and 27 is not a sub-division or multiple of 50 or 25.

So even when U-N and J-S do align as pairs at around the same time every 4627-8 years, it must be pot luck whether they’re anywhere near alignment to each other.

Back to the Sharp graphic above.

OB, you are conflating two different items. The 4 years out was with your figures on 233 J-S and 102 S-U.

OB said

“I would just add that the nearest multiple of Uranus is around 4621 years. That’s going to drift off your 4627 year timescale anyway, so talk of ‘trashing’ something is a bit over the top surely?”

That has nothing to do with the grand syzygy, as none of the bodies does exactly a whole number of obits at that period.

“The fact is the best U-N alignment is at 50 U-N (maybe 25 as well but that excludes Saturn as the ‘third party’) and 27 is not a sub-division or multiple of 50 or 25.”

In fact if you go 8573yrs ahead from 1307, N-U-S will line up well, but Jupiter is at quadrature with them.

“So even when U-N and J-S do align as pairs at around the same time every 4627-8 years, it must be pot luck whether they’re anywhere near alignment to each other.”

It’s closer with the figures that I am using. And calling it pot luck is definitely my calling to take leave from this thread.

“Back to the Sharp graphic above.”

I’ve said all I need to on that.

Model seems to fit to about 3 significant digits.

tallbloke says:

“Rick Salvador found that incorporating the 1/4 period of Uranus orbital period (Thanks Sparks) into his planetary solar model improved it greatly. That may be linked with Ulric’s ideas about the importance of quadratures, which I hope he’ll get around to explaining to everyone else, so I can discuss openly what he told me in private.”

A quadrature takes at least two bodies, in which case it would be half synodic periods. For three bodies it’s a whole number of synods for one pair, and say 1.5 and 3.5 for the other two pairs. Such as Jupiter opposite Uranus both square to Saturn on their ~69yr quadrature return. I did go into some detail of the apparent values of various syzygies and quadratures a while back. The comments where I stuck the copyright symbol. There are some more add, and one correction to make.

Based on extensive observations, this is what I am repeatedly finding, when in isolation from any clear additional syzygy or quadrature from either other body, in terms of a stronger or weaker solar signal:

Jupiter opposite Neptune weak

Jupiter opposite Uranus strong

Saturn opposite Neptune strong

Saturn opposite Uranus weak

Jupiter quadrature Neptune strong

Jupiter quadrature Uranus weak

Saturn quadrature Neptune weak

Saturn quadrature Uranus strong

Saturn opposite Jupiter weak

Saturn quadrature Jupiter strong

Given that set of logic, Jupiter opposite Uranus both square to Saturn, is very warm signal indeed.

In that particular Jovian configuration, at the scale of weather, warmer periods commence from when the Earth-Venus bisector is towards Saturn, and cooler from when towards the J-U line.

Transposing Uranus for Neptune, introduces two weak aspects, and also shifts the warm and cold positions for the Earth-Venus bisector through 90°, with the colder periods now starting when the Earth-Venus bisector is towards Saturn (on either side of the Sun). As is happening from late 2015:

Another clue is that an inferior conjunction of Uranus and Jupiter in quadrature to Saturn, also shifts the warm and cold positions for the Earth-Venus bisector through 90°, with the colder periods starting from when the Earth-Venus bisector is towards Saturn.

UL: ‘The 4 years out was with your figures on 233 J-S and 102 S-U.’

That resolves at 13 grand synods: 351 U-N (27 x 13) = 1327 S-U = 1678 S-N

To put it another way: it’s the 9:34:43 ratio with 1 extra S-U and S-N every ~61000 years.

The S-U-N match at 8569+ years doesn’t happen with your data – 4 years out is true for S-U there as you said: 8573+.

That period is whole numbers of orbits, but 4627/8 is not for Uranus and Neptune, so it’s not a like-for-like comparison.

Any comments or questions Rog? There’s a whole heap of predictive power there, it’s not just numbers. And it provides all the right clues to the actual mechanisms.

Rog, I think it’s better to air this first before showing my findings on the sunspot cycles and grand minima progression that I discussed with you. It will help make more sense of it.

[…] Why Phi? – giant planets: a Saturn-Uranus model […]

A quick look at 7066 Nessus, ‘the third centaur discovery’ in 1993.

‘7066 Nessus has an orbital period of 122.4 years, an eccentricity of 0.52 and an inclination to the ecliptic of 15.6 degrees. At perihelion, it moves much closer to the Sun than Uranus, while at aphelion it moves out well beyond the orbit of Neptune.’

‘The orbits of centaurs are unstable due to perturbations by the giant planets.’

http://en.wikipedia.org/wiki/7066_Nessus

It turns out that 60 km. diameter Nessus does 70 orbits of 122.42245 years every 8569.57 years. That puts it right in the timeframe of 52 Neptune:102 Uranus:291 Saturn and fits very well with the model (8568 years) – see post above.

Also, since the Nessus:Uranus ratio is 70:102 (or 35:51) it follows that in Fibonacci terms:

21 x 5 x 2 (210) Nessus = 34 x 3² Uranus (306) = 13 x 3 x 2² Neptune (156)

So maybe not as ‘unstable’ as suggested?

Tallbloke said

“..Ulric’s ideas about the importance of quadratures, which I hope he’ll get around to explaining to everyone else..”

And I hope that you respond to the examples that I gave above, with interest and with pertinent comments and questions.

Judging by the lack of response, including unanswered email from four years ago, it doesn’t seem that tallbloke is that exited or interested in the observed logic of the planetary ordering of solar activity. How sad.

excited*

This paper: http://www.aanda.org/articles/aa/full/2002/11/aah2799/aah2799.html

says:

‘Figure 5 shows the variation of the Earth’s precession cycle over the last 2 million years. The cycle is rather stable with a maximum difference of only about 800 years, or 3%.

The mean precession cycle length is 25709 yr.’50 Uranus-Neptune conjunctions = 8570.31 years (compared to the 8568 year model above)

3 x 8570.31y = 25710.93y

In that number of U-N conjunctions there would be, in theory:

306 Uranus orbits = 25709.15y

156 Neptune orbits = 25707.45y

306 – 156 = 150 U-N = 3 x 50

(3 x 8568 = 25704y)