Our friend and regular Gray Stevens has been researching and publishing his observations and ideas on his own site at Jupiters Dance for a long time now. I’m delighted he has asked me to showcase his most recent work here, which investigates planetary harmonics and their possible correlations with solar activity. This is a huge piece of work which has taken a lot of effort and time to concieve and compile. Please show Gray your appreciation by taking time to study and digest the material, and do post your thoughts and observations.
Synodic Cycles of Jupiter and the other planets of the Solar System
Introduction
Movements of the planets and potential influences on the Solar activity cycle.
Review
The earlier work by P D Jose (1) on a 178.7 year solar activity cycle, and I Charvatova (2) regarding a 2402 year solar activity cycle, showed long term periodicity in the Sun’s movement around the Solar System Barycentre and related cold and warm climate periods. A further 4627 year period consisting of 2402 years and 2225 year periods was also considered (3). This paper is to focus on the influences that may create the 11.171 year Wolf and 22.235 year Hale cycle in solar activity as well as linking with the longer periods.
Material
Each of the planets forms a synodic cycle with Jupiter which contains the largest mass and magnetic field of all of the Solar System planets.
Each of the planets form close to a whole number of synodic cycles around their orbits with a fairly small amount of prograde or retrograde motion.. In each case we are looking at the number of synodic cycles taken to complete a whole orbit. As the synodic cycles are only an average time the variation between each cycle and thus the exactitude of each cycle is not considered here. A figure is included for each cycle to show the average difference.
Neptune and Jupiter have 13 synodic cycles taking 12.782 x 13 = 166.168 years (see diagram).
188 cycles are timed at 2403 years. 13 synodic orbits 166.168. Neptune’s orbit 164.785
Uranus has six synodic cycles of 13.81 years taking 82.87 years to complete six conjunctions around its orbit (see diagram).
It takes 174 cycles to complete 2403 years.
6 synodic orbits 82.8717
Uranus’ orbit 84.0106
Jupiter and Saturn have three synodic cycles to a basic unit of three conjunctions taking 59.5742 years (see diagram).
9 conjunctions equals 178.7226 years
121 cycles equals 2402 years. 112 cycles equals 2225 years. 233 cycles equals 4627 years.
The conjunctions occur in reverse order.
3 synodic orbits 59.5742
2 Saturn orbit’s 58.9133
Mars and Jupiter form five conjunctions taking 11.1772 years (see diagram).
80 such conjunctions form a cycle of 16 x 11.1772 = 178.8352 years.
215 x 11.1772 cycles equals 2403.01 years.
5 synodic orbits 11.1772
Jupiter’s orbit 11.8617
Earth and Jupiter form a basic cycle of 11 conjunctions at 1.0921 of 12.0127 years. (see diagram).
2200 synodic cycles equals 2403.808 years.
11 synodic orbits 12.0127
Jupiter’s orbit 11.8617
The Venus and Jupiter cycle produces 18 synodic cycles in one orbit over a period 0.6488 x 18 = 11.679 years.
18 synodic cycles 11.679
Jupiter’s orbit 11.8617
Mercury and Venus form 48 cycles in 11.800 years
Jupiter’s orbit 11.8617
With the synodic period at 0.2458 years.
Conclusion
Mars and Jupiter are phased so that the five conjunction cycles of 11.177 years occur 16 times in 178.83 years. This may in some way define the sixteen peak solar activity cycle which we recognise. Notably, Mars reaches its highest and lowest conjunction points with Jupiter over a 22.354 year cycle which is close to the Hale cycle of 22.341 years, the cycle of the Sun’s polarity change. The 11.177 year cycle is close to the recognised sunspot frequency of 11.171 years. The overall 178.832 year cycle is close to the recognised 178.730 year period of sunspot cycles. The close to transit period for Mars and Jupiter is 35.765 years (16 synodic cycles), five such periods equals 178.825 years.
Two further notable points are that the periapsis of Mars is the first in orbital direction compared to the remaining planets and that Mars’ orbit is considerably elliptical thus its tidal force on the Sun is virtually doubled from apoapsis to periapsis.
With regard to the characteristics of Jupiter and Saturn’s synodic cycles over 4627 years and related periods of 2402 and 2225 years the following observations are made:
233 is the number of synodic cycles of Jupiter and Saturn in the 4627 year period and suggests a mathematical foundation to the cycles in that it is a very unusual number having the following properties amongst others; it is a Prime Number, the 13th Fibonacci Number and a member of the 3,4,5 Pythagorean Triplets 105, 208, 233. The two associated periods of 2402 years and 2225 years produce cycles of 121 and 112 which also show unusual properties.
121 is a square and is the sum of three consecutive primes (37 + 41 + 43).
112 is the sum of six consecutive primes (11 + 13 + 17 + 19 + 23 + 29).
To follow on from the conclusions posted above: Each Jupiter and Mars conjunction and opposition were numbered in sequences of ten (11.171 years avg.) throughout the sunspot record 1749-2009. Each position was then averaged for the entire period.
Whilst the sample shows a uniform peak centred on the 11.171 year period this feature might be dismissed as simply coincident upon the existing sunspot peak frequency. However, measuring the distance of Mars from the sun in AU at conjunction only, shows a notable imbalance with a lower sunspot count for the closer approach and a higher count for a distant approach.
Range 1.3814 – 1.6659 = 52.43
Range centre = 1.52365 AU
Less than 1.52365 AU = 43.91
More than 1.52365 AU = 61.71
Distance Variation Percentage 17.08
A look at the Jupiter distance for the sample:
Range 4.9456 – 5.4540 AU = 52.43
Range centre = 5.1998 AU
Less than 5.1998 AU= 45.35
More than 5.1998 AU= 58.44
Distance Variation Percentage 9.33
The graph depicts the latitude of Mars at conjuncton with Jupiter set against the sunspot record. As expected we do not see a precise alignment of the sunspot record with the relatively regular rise and fall of the Mars and Jupiter conjunctions however it should be noted that 17 of the 23 solar maxima fall predominantly during either the extremes of negative or positive latitudes. The alignments are seen to drift both away from and towards the latitude peaks not randomly but in gradual steps. This advancing and retardation of the maxima relative to the relatively consistent Mars and Jupiter alignments is suggestive of a relationship between the sixteen peak sunspot cycle and the Mars and Jupiter conjunctions.
Below are two additional graphs aligned with the sunspot record. The first shows a representation of Neptune’s changing distance from the Sun at each conjunction point with Jupiter. The last is a representation of the solar distance for Uranus whilst at successive Jupiter conjunctions.
Neptune distance
Uranus Distance
Whilst the graphs are very much open to interpretation it should be noted that the most stable section of the solar record occurs whilst Neptune is at its closest approach to the Sun with the solar peaks coincident with the Mars and Jupiter conjunctions The most variable timings fall during the two periods when Neptune is furthest from the Sun. It should also be noted that the three occasions when a maxima occurs fully at the negative latitude, 1770, 1829 and 1947, occur when Neptune is at distance. The Uranus graph shows that the sunspot peaks coinciding with maximum and minimum distance for Uranus and Jupiter conjunctions are generally diminished peaks often with a flattened top and singular spike.
Saturn Jupiter Conjunctions
The above graph shows a representation of the solar distance of Saturn whilst at conjunction with Jupiter. The one notable feature shows that Saturn at its greatest solar distance coincides with the minima between peaks at the four data points shown (the vertical bars are to aid here). The period between the three data points is 178.659 years raising the possibility that Saturn and Jupiter thus punctuate the solar cycle. There are some notable similarities in the solar peaks surrounding the Saturn maximum distance. In three of the cases (sections are shown below) the reverse latitude peak occurs one peak before Saturn is at maximum distance, the following peak is high with a slow decay and the next peak is diminished and also with a slow decay. This pattern however does not occur around the 1901 cycle whilst Neptune is closer to the Sun and does not appear to be happening ahead of the next Saturn conjunction in 2020 as Neptune closes again. Solar cycle 24 would be expected to end at around 2021 as the next data point in the series shows…
The starting position for Saturn for the initial synodic cycle with Jupiter is close to its perihelion, with Jupiter moving away (the left hand margin). The end position of this synodic cycle is two solar peaks later with Saturn close to its aphelion and with Jupiter coming to conjunction. (red bar). This is close to the longest synodic cycle Jupiter and Saturn can produce in each case.
Initially Saturn is at its perihelion and accelerating whilst Jupiter is slowing. This is due to the relative positions of the perihelion of Jupiter (first) and Saturn (second). As Jupiter moves ahead the first solar peak is initiated whilst the first solar peak is reached shortly after Saturn reaches its perihelion and begins thereafter to fade. Jupiter now leaves Saturn behind and continues on its orbit before approaching Saturn once more. The first peak is generally diminished.
As Jupiter closes on its conjunction point with Saturn the inner planets are making conjunctions with the pair as they orbit, first Jupiter then Saturn. Because of the relative positions of the perihelion it now occurs that Jupiter begins accelerating as Saturn is still slowing during Saturn’s approach to its aphelion. Therefore the successive conjunctions of the inner planets with Jupiter and Saturn are occurring with increasing frequency thus increasing the activity cycle and advancing its arrival. This can be seen in the abruptness of the rise of the leading slope of the second peak and the shortened period from the previous peak.
As Jupiter passes Saturn before the third peak Saturn is still moving slowly whilst Jupiter accelerates and the time between successive conjunctions begins to extend, thus the solar activity reduces and prolongs. This is seen in the less steep leading slope of the third peak, its extended decay and its extended period from the second peak.
It is also noted that the second peak occurs some four to six years before the actual Saturn and Jupiter conjunction. It is a possibility that as the most potent Jupiter and Saturn conjunction approaches so a similar process is occurring with all of the other planets. Considering specifically the inner planets. As Mars approaches Jupiter; Earth, Venus and Mercury form multiple conjunctions with increasing rapidity with Mars, Jupiter and Saturn in sequence. Mars takes a little over 2 years to complete its Jupiter conjunction cycle and it appears the optimum position occurs when Mars is around 60-70 degrees from Jupiter and Jupiter 60-70 degrees from Saturn. This happens about two Mars and Jupiter synodic cycles earlier than the actual conjunction point with Jupiter and Saturn. Once the angle between Jupiter and Saturn begins to close the optimum is passed and the peak is decaying. The subsequent peak is weaker because Saturn is no longer at its optimum position. It would take about 60 years before a close to repeat position (the case in 1829) might be obtained and about 180 years before a more precise repetition (1947).
The outer planets would be expected to help form a maximum peak should they be positioned ahead of the Jupiter Saturn conjunction.
The above Jupiter and Saturn graph distance graph set against the sunspot record as it is known back to 1610 illustrates how the conjunctions lined up. Interestingly, the number of sunspot peaks between the furthest Saturn and Jupiter conjunctions are seen as either five or six. It is anticipated that the current series until 2020 will be five. Looking back to the beginning of the record the series 1723 – 1782 contained six peaks. The two periods spanning the Maunder Minimum cannot be determined due to the paucity of spots and record keeping but it raises the possibility that the series sequences 5-5-6-5-5-6-5-5 with the Maunder period two collapsed 5 periods. This would indicate we are to see only ten peaks between 1961 and 2081. Given that this then spaces the cycles at 12 years we may expect reduced amplitude peaks during the period and possibly a collapse of the cycles. However, the distance of the conjunction points is constantly changing and so the pattern may falter as subsequent conjunctions move closer or further from the Sun.
The researcher Timo Niroma (4) demonstrated the bi-modal nature of the sunspot peak with a probability distribution graph showing two peaks one at 10.38 years and a second at 12 years. Similar figures have been produced by Ray Tomes (5) another researcher of solar cycles.
This can be explained by the synodic cycles of the inner planets with Jupiter as follows:
Earth Jupiter synodic cycle = 1.0921 years
1.0921 x 11 = 12.031 years (11 is a prime)
Venus Jupiter synodic cycle = 0.6488 years
0.6488 x 16 = 10.3808 years (16 is a square)
Mercury Jupiter synodic cycle = 0.2458
0.2458 x 49 = 12.0442 (49 is a square)
0.2458 x 42 = 10.3236
Mars Jupiter synodic cycle 2.23544
2.23544 x 5 = 11.1772 (5 is a prime)
The graph above shows how the timing of the various inner planet conjunctions with Jupiter align with the distribution of solar cycle lengths. This provides a clear indication of the impact of the planetary positions on the solar cycle. It further shows a clear relationship of the planets with Jupiter rather more so than with each other. It must be noted the Mercury conjunctions are particularly closely spaced at 0.2458 of a year so would fall close to the marked Venus and Earth conjunctions in any case and would have to be studied at a daily resolution for clarity.
From the evidence it is suggested that a perfect entrainment of the planets would occur as follows: The conjunction of the innermost planet with Jupiter occurs before the next conjunction of the next outer planet with Jupiter. This process is followed by succeeding outer planets, So that, the Mercury conjunction at the peak’s apex occurs before the next Venus Jupiter conjunction. Venus then become conjunct before the next Earth Jupiter conjunction. Then Earth before the next Mars Jupiter conjunction and Mars before the next Jupiter Saturn conjunction. In turn these fall ahead of the upcoming Uranus Jupiter conjunction and the following Neptune Jupiter conjunction.
This would define the highest peaks of the solar cycle and it is thought that imperfect positioning of the planetary conjunctions with Jupiter would result in weaker solar peaks. This is a slow progression which ultimately will reverse. However, at this point this must remain conjecture and it is beyond the scope of this article to investigate further. A full investigation may reveal a quasi-periodic nature to the progression and there is some suspicion that relative position of the Galactic centre may be a feature over multi-millenia cycles.
The examples of 1778 and 1957, which were described here in detail, fall short of perfect in that Mars is phased slightly before this optimum position. In 1778 it forms a second conjunction with Jupiter and then several Earth Jupiter conjunctions occur just before the Jupiter Saturn conjunction of 1782 . In 1957 the peak comes shortly after the ultimate Mars conjunction, but only barely, followed by an additional Earth conjunction. It would seem that Neptune and Uranus are too far behind at this current time.
To conclude: There is evidence that Mars is influential in the 16 peak 178 year sunspot record although its signature is overwhelmed at intervals by the positions of the outer planets according to a slowly shifting pattern. The inner planets show a closely timed positioning with regard to the bi-modal nature of the sunspot cycle which can be enhanced by the further optimum timing of Mars, Jupiter and Saturn. The evidence indicates a clear relationship of the planets with Jupiter in their influence on the Solar activity cycle.
It was always Jupiter’s Dance.
References:
Thanks to Rog Tallbloke for advice, encouragement and a constant supply of relevant information through his blog at: https://tallbloke.wordpress.com/
(1) Paul D Jose – Sun’s Motion and Sunspots (1965) – http://adsabs.harvard.edu/full/1965AJ…..70..193J
(2) I. Charvatova – Can origin of the 2400 year cycle of Solar activity be caused by Solar Inertial Motion? Geophysical Institute Prague, Czechoslovakia.
(3) Planetary Motion and Solar Activity – are they linked? – http://www.jupitersdance.com/TheLastTango/
(4) Timo Niroma http://personal.inet.fi/tiede/tilmari/sunspots.html#tdist
(5) Ray Tomes Cycles Research Institute http://cyclesresearchinstitute.wordpress.com/
gray@jupitersdance.com
Copyright Jupiter’s Dance January 31st 2010. Updated July 25th 2010. Author G. Stevens http://www.jupitersdance.com/thefinalwaltz/
Tallbloke's Talkshop 
Gray has added a lot to this since the draft I saw a few days ago. Can’t wait to have time to re-read it all. Enjoy!
Very interesting. Looking forward to the knowledge base to weigh in here!
Gray,
Thanks for the post – you have done a lot of work here! Very interesting there is a lot to digest. I am just now reading Landscheidt’s book. Fascinating stuff.
There is so much in this piece of work to think about, it’s going to take a bit of time to work out a coherent response. The same is probably true for others, so Gray should be patient here.
Cherry-picking items to agree or disagree with would not do justice to this well integrated piece of work. Much food for thought.
One thing I noticed with regard to Mars/Jupiter is that 3 of the ~22 year cycles bring them back to conjunction in the same part of the sky, in a slowly precessing ‘reverse’ gyration similar to 3 Jupiter/Saturn conjunctions.
Great presentation…. my only comment would be to remove the Jose reference. His 178.7 period for the gas giants is incorrect and should not be compared with synodic cycles of other planet groups.
Thanks for the comments everybody. I understand it will take a while to absorb the material in detail.
Certainly the wider implications are yet to be explored. The Saturn Jupiter conjunction of 1604 for example was 357 years before the 1961 cycle, 2 x 178.5 periods approx. The synodic cycle to the 2000 conjunction was the shortest in 400 years.
If the assertion that this is an entrainment of the planets based on their Jupiter conjunction periods is correct, and that it is therefore the key to the solar activity cycle, then there is a need to understand that process fully and perhaps urgently.
There’s something going on in this I can’t quite see. I’m going to sleep on it and read it all again tomorrow.
Thanks Gray for a most interesting approach to presenting the planetary relationships. It really helps to get a look at fresh ways of coming at it in order to jog new ideas out of ones own schemata.
tallbloke says:
July 28, 2010 at 11:13 pm Some “pillow thinking” is always fruitful. It seems that when an issue is too “spicy” it takes longer to properly digest. Quite differently to the common light and fast food.
Thanks, Gray, for some useful information about the planets. I will have to do some hard thinking before understanding all you have shared with us.
I wonder if you have looked at the role of Mercury in this planetary dance?
Although small it has a very eccentric and rapid orbit with its distance from the Sun ranging from 46 to 70 million kilometre and taking only 88 days to complete an orbit. Another oddity is that if you consider the plane of the Earth’s orbit to be 0° then Mercury’s orbit is inclined at 7°. It’s axial tilt is only 0.01° and it is the densest of all the planet after compression caused by gravity is taken into account. Mercury consists of around 75% metals, mostly iron and has a weak magnetic field.
Hi Tenuc. It’s worth pointing out that the Sun is also inclined at ~7 degrees to the plane of invariance most of the other planets stay near. This would indicate that the Sun and Mercury are in a tidal resonance with each other. Indeeed Mercury revolves on its own axis three times for each two orbits of the Sun, proving the existence of a coupling on a 3-2 resonance.
Also, Mercury’s magnetosphere ain’t all that weak for a planet of its size. And it gets up to 10 times more reconnections between its magnetosphere and the Sun compared to Earth.
Thanks for more interesting facts about Mercury TB. This got me thinking (always dangerous!) about harmonics…
Length of solar day (=SD) is between 27 and 31 Earth days or about 29 average.
Length of Mercury year (=MY) is 88 Earth days.
SD=MY/3 = 29.3
TBWUWT?
Tenuc/tallbloke
I think the Mercury connection is a given, it is marked just before the major peak on Timo’s graph. The figures for the first peak are 42 synodic cycles and for the second 49 synodic cycles. So, 6 x 7 and 7 x 7.
Hi Gray,
There sure is a very good resonance at 104 Venus/Earth synods (c.60728days), with everything but Saturn, this why I refer to SC9 as an analogue for SC24;
http://landscheidt.auditblogs.com/2008/06/03/the-sunspot-cycle-and-c24/
The 179yr return was spotted a very long time ago in the harmonies of Venus, Earth, Mars, Jupiter and Saturn. The Chinese have old records of it for weather/climate cycles. Volcanoes occur at a similar location in 179yr strings, so do extreme weather events.
{112 Earth/Venus synods}
I`m sure people have been watching for a long time when Jupiter, Mars, Earth and Venus are on the same side of the Sun, it is a basic weather calendar. Every 4th Earth/Venus synod, Mars joins in (one circuit), every 28th Earth/Venus synod, returns all three back with Jupiter too. (7 circuits on your labyrinth)
28 being a triangular number, and a perfect number.
{4627/28}
The nature of the Mars/Earth/Venus cycle is worth noting, I call it a modal cycle. The E/V conjuncts go from conjuncting Mars, to opposing Mars, then back to conjuncting Mars over a 299yr cycle.
The Mercury/Venus synods have a strong resonance with most things;
3 V/M = 433.7d Chandler
4 V/M = 4.99 E/M and 1 E/V synod – 5.65d
19 V/M = 3.998 Mars sidereal orbits.
28 V/M = 1 average solar cycle
30 V/M = 1 J orbit + 4.8d
35 V/M = J/U synod + 14d
43 V/M = 1 coronal hole cycle
47 V/M = LNC (46.995)
48 V/M = 234.986 Lunations, 18.999 solar years
The c.317.66yr J/S/U cycle that King-Hele noted, seems to be apparent in storminess, but it is only good with temperatures at every third step, at 953 yrs. This is not only good with the E/V synod, but also the solar cycle and the coronal hole cycle too. Such that 1963 is a good analogue for 1010AD, many cold winters can be found on this interval as well as the 179.
“Mercury and Venus form 48 cycles in 11.800 years” ??
Mercury and Jupiter.
tallbloke says:
July 29, 2010 at 2:23 pm
That 3:2 resonance is a perfect fifth, and the entire solar system should be a perfect octave, however it is not, as far as I know. The moon is too big a satellite for the earth.
Any thoughts?
Hi Ulric
Thanks for your interesting response. The figures emphasise how closely synchronised the labrynth is. I agree that SC9 and SC24 are similar in many ways although with each cycle there are small advances in position so not much is certain. I also note from Geoff’s work with the angular momentum graph that it predicts five peaks for the next 3 Jupiter Saturn synods from 2020.
It seems to me that all of the planets are involved but certainly that Venus and Earth are major players. The bi-modal graph figures show that is probably via a link with Jupiter. I also think that there is a geometric solution here.
It should be Jupiter, thanks Ulric
tallbloke
When you say 3:2 resonance are you referring to JS?
Hi Gray,
I said “Indeeed Mercury revolves on its own axis three times for each two orbits of the Sun, proving the existence of a coupling on a 3-2 resonance.”
That was all I was referring to for Mercury, though I’m sure we’ll find other examples in the solar system, probably in the Jovian moon system?
I have a copy of ‘A little book of coincidences’ on it’s way to me from the States, recommended by Lucy Skywalker. We’ll see what pops out of that that might help.
Another low whole number resonance I just spotted is the 5:4 resonance between Saturn-Neptune and Saturn-Uranus synodic periods.
171.4442476 = 1 U,N
178.7298381 = 9 J,S
178.9506166 = 14 J,N
179.5553461 = 13 J,U
179.3493935 = 5 S,N
181.4409144 = 4 S,U
Tallbloke, it was said that `only Pythagorus could hear the music of the spheres`!
I don`t think simple harmonic ratios found in music are the way to go. My own studies. as well as key studies throughout history, reveal a wealth of triangular numbers in planetary harmonics. I showed my works to John Martineaux about 5 years ago, he didn`t konw what to make of it at the time and said they were `rather large numbers` as he was concentrating on musical ratios. I have since heard through the grapevine that he now sees I am on to something.
Have a look at the fractal generator on http://www.hermetic.ch examples and see the galactic spiral pattern produced from triangular numbers. Also check out the subatomic importance of these numbers on http://www.blazelabs.com
If you would like to befriend me on facebook, I have written a piece there on the astronomy of the Mayan Long Count, and also an analysis of the Magic Square of the Sun and how the 666 day count would have been used as a solar and lunar/solar calendar.
Thanks Ulric, that’s very interesting. I don’t have a facebook account, but I’ll get my lady to sign me in later on hers.
Phi turns up a lot in subatomic physics too. The Fibonacci series ratios are common in the solar system as well. There is a lot to consider, my poor peabrain is overstuffed at the moment!
Thanks for the links though, I didn’t spot the fractal generator, but I did find this nice page on Ulams Spiral
http://www.hermetic.ch/pns/pns.htm
@Gray says:
August 2, 2010 at 1:00 am
“I also think that there is a geometric solution here.”
There most definitely is, in `magnetic` angles, as Kepler said.
I have the `rules` established well enough to hindcast all anomalies on CET. (MWP/LIA/Modern Warming explanation is all part and parcel of it)
tallbloke says:
August 2, 2010 at 11:05 am
The Fibonacci series is very much a growth factorial, the are not that common in orbital integer ratios (21 and 55 are triangular as well). If I had to explain resonance in the solar system by these numbers alone; …89, 144, 233, 377, 610, 987, 1597, 2584 etc,
I would have examples that are less than the fingers on one hand.
Phi is a geometrical proportion and not an integer, and so not valid as harmonies are whole number ratios.
The fibonacci series tends closer and closer to phi (The golden section: 1.618:1) as the numbers get bigger
2/1=2 (Approx orbital period ratio U:N )
3/2=1.5 (Sun, Mercury orbit/axial rotation)
5/3=1.66
8/5=1.6 (Earth, Venus synodic)
13/8=1.625
21/13=1.615
34/21=1.619 (Earth, Venus orbital period ratio)
If you plot it, you get a nice decay curve.
x-axis numbers represent the position in the series, not magnitude. i.e. 2 is 3/2, 4 is 8/5 etc
Hi tallbloke/Ulric
I definitely think that this is indeed where it’s headed:
Fibonacci sequence 0,1,1,2,3,5,8,13,21,34,55,89,144,233,377
1/1 =1
2/1 = 2
3/2 =1.5
5/3 =1.667
8/5 =1.60
13/8 = 1.625
21/13 = 1.6153
34/55 = 1.6176
89/55 = 1.6181
144/89 = 1.6179
233/144 = 1.6180
Golden Ratio is 1.61803398875
Fibonacci triangles
Starting with 5, every other Fibonacci number {0,1,1,2,3,5,8,13,21,34,55,89,144,233,…} is the length of the hypotenuse of a right triangle with integral sides, or in other words, the largest number in a Pythagorean triple. The length of the longer leg of this triangle is equal to the sum of the three sides of the preceding triangle in this series of triangles, and the shorter leg is equal to the difference between the preceding bypassed Fibonacci number and the shorter leg of the preceding triangle.
The first triangle in this series has sides of length 5, 4, and 3. Skipping 8, the next triangle has sides of length 13, 12 (5 + 4 + 3), and 5 (8 − 3). Skipping 21, the next triangle has sides of length 34, 30 (13 + 12 + 5), and 16 (21 − 5). This series continues indefinitely and approaches a limiting triangle with edge ratios: sqrt(5) : 2 : 1
2.235445 is the Mars conjunction time with Jupiter. Being that this is also years, Earth is linked by a figure very close to the square root of 5.
sqrt(5) = 2.2360679775
This in turn is part of the equation for the Golden Triangle a + sqrt(5)/b = 1.61803398875
If you now take the relationships of the inner planets you get for their orbital times:
Mercury 260, Venus 104, Earth 64, Mars 34.
If you scale the ratios down you get:
Mercury 260/52 = 5
Venus 104/8 = 13
Earth 64/8 = 8
Mars = 34
Multiply Earth 64 x 2.235445 = 143 close to 144 another number in the Fibonacci series and possibly a Kepler Triangle. We are very much in his footsteps here.
Jupiter Saturn conjunctions 233 for 4627 year period
The outer planets conform to the sequence as well:
Neptune/Uranus 1: 2 = 2 orbits Uranus = 1 synodic period
Uranus Saturn 2: 3 = 1.54 orbits Saturn = 1 synodic period
Jupiter/Saturn 3: 5 = 1.67 orbits Jupiter = 1 synodic period
The inner planets being inside Jupiter’s orbit follow a different interlock.
This is an interesting pic of a Golden triangle fitted to a Fibonacci Spiral:
http://en.wikipedia.org/wiki/File:Golden_triangle_and_Fibonacci_spiral.svg
Page on the Golden Triangle:
http://en.wikipedia.org/wiki/Golden_triangle_(mathematics)
I should have known Gray would be three steps ahead of me. 🙂
Here’s you wiki image:
From Wikipedia on Orbital Resonance:
“The presence of a near resonance may reflect that a perfect resonance existed in the past, or that the system is evolving towards one in the future.”
For anyone who hasn’t sussed it, the fibonacci series is generated by adding the previous number to the current number:
1+0=1
1+1=2
2+1=3
3+2=5
5+3=8
8+5=13
13+8=21
As you can see, each column become a fibonacci series – it’s an analogy for organic growth, as Ulric said.
This thread is starting to warm up. 🙂
Hi tallbloke
It’s a labrynth one could get lost in…
3,5,8,13
Triangle 25,39,64
39/3 = 13
25/5 = 5
64/8 = 8
While your contemplating the solar system planetary distance spaceing, remember that the system has been disturbed several times and is trying to reestablish order.
The earth/moon pair is quite unique and not an original creation in place or form. pg
Hi PG,
Yes, Miles Mathis calculates that Saturn is trying to go into an orbit below Jupiter, and that the last time it tried, it come pretty close to hitting the big boy. According to Mathis’ gravitational theory, there is a repulsion component hidden in Newton’s equation for gravity. Under certain circumstances, this can overcome the tendency for massive objects to come together and it is this which prevents the planets hitting each other, and also explains why the moon is the same size as the sun from earth, and why the planets in the most stable orbits all look the same size from the sun. His theory, when applied to the spacings of the planets, ends up with a better overall result than the Bode-Titius Law. The ‘bounce-off’ Saturn got from his big brother means Saturns orbit is currently getting bigger as he strays further out from the Sun.
http://milesmathis.com/bode.html
The key point about Mathis’ gravitational theory is that the planets are active in maintaining their orbital distances from the sun and each other. This makes more sense to me than the traditional explanation that they got given their orbits at the creation of the solar system, and forever keep the same angular momenta. Entropy dictates otherwise. The further implication is that energy is feeding into the Sun and out to the planets to maintain the solar system.
It is known that in the deep past, the sun had a considerable energy coupling with the planets via the solar wind. Leif Svalgaard says that stopped a long time ago. I’m not so sure.
tallbloke says:
August 2, 2010 at 3:26 pm
“It is known that in the deep past, the sun had a considerable energy coupling with the planets via the solar wind. Leif Svalgaard says that stopped a long time ago. I’m not so sure.”
We know that there is an Earth/sun connection several time a day from the NASA CLUSTER mission:-
“…On the day-side of Earth (the side closest to the sun), Earth’s magnetic field presses against the sun’s magnetic field. Approximately every eight minutes, the two fields briefly merge or “reconnect,” forming a portal through which particles can flow.
The portal takes the form of a magnetic cylinder about as wide as Earth. The European Space Agency’s fleet of four Cluster spacecraft and NASA’s five THEMIS probes have flown through and surrounded these cylinders, measuring their dimensions and sensing the particles that shoot through. “They’re real,” says Sibeck…”
I’m sure that the ‘magnetic cylinders’ that NASA identified are in fact Birkland currents and that the ‘reconnect’ events are actually electrical in mature and not magnetic. It is possible that these connections focus fast plasma flow to the Earth, with a back EMF towards the sun when the connection breaks. We need to know how much energy is transferred by these events and what impact they have on Earth and solar weather mechanisms.
I also suspect that other planets are connected to the sun in the same way that Earth is. Perhaps this is the mechanism that forces the planet’s orbits to be entrained at the nodes of a sinusoidal current sheet which permeates the heliosphere and which weakens the further out from the sun it goes?
TB – Could this be a shadow of your harmonic decay graph which you posted above?
Sorry, forgot to post the link to the NASA quote 🙂
Here it is now:-
http://science.nasa.gov/science-news/science-at-nasa/2008/30oct_ftes/
Tenuc says:
August 2, 2010 at 5:04 pm
These portals, as tradition calls them, are: The Assura Loka (The Devil’s gate) and the Deva Loka (The Gods’ gate).
Rene Guenon “Symbols of Sacred Science”
mmmm, interesting that every other Fibonacci is the hypoteneuse on a Pythagorus triangle, but this is not the triangular numbers I am talking about;
1,3,6,10,15,21,28,36,45,55,66,78,91,105.120,136,153,171,190,210,231,253,276,300,325,351,378,
406,435,465,496,528,561,595,630,666,703,741,780,820,861,903,946,990,1035,1081 etc….
My original approach to finding the best harmonies was to create a multiplication table on `Mathmatica` up to 6400 and multiply by the simple ratio and look for whole numbers. Eg 365.242189/29.530595 for the Earth and Moon.
An easier way is to take the first two close matches, and add them together in appropriate multiples to get the best close matches, so at 11yrs we have close to 136 Lunations (16th triad), and at 8yrs we have close to 99 Lunations (1.5x 11th triad)
Add the 8 and 11 and a closer fit appears at 19yrs = 235 Lunations.
Carry further on adding 11`s and 8`s and all the finer harmonies can be found, such as 334yrs = 27×153(t) Lunations (discovered by an Arabic in the middle ages), or 315yrs (half of 630) = 8×487 Lunations, 487 being the days in 1.33333yrs.
This technique can be used on any pair or triplet of harmonies to readilly find the best harmonies up to high numbers, such as;
48×48 sidereal Earth years = 35×35 sidereal Mars years, x4 = 777 Jupiter orbits.
35×35 = 1225, the 49th triangular number.
1225×4 = 4900, the only doulble tetrahedral* number to also be a square (*if you imagine a triangular pyramid of cannon balls {a la Kepler} with and edge of 24 balls, the stack contains 2600, the 23rd tetrahedron contains 2300, imagine now turning the 23 stack upside down, and putting it on the bottom of the 24 stack, voila, the double tetrahedron.
“48×48 sidereal Earth years = 35×35 sidereal Mars years, x4 = 777 Jupiter orbits.”
48+1=7^2
35+1=6^2
777+7=28^2
Intriguing.
I also suspect that other planets are connected to the sun in the same way
Tenuc:
” Perhaps this is the mechanism that forces the planet’s orbits to be entrained at the nodes of a sinusoidal current sheet which permeates the heliosphere and which weakens the further out from the sun it goes?
TB – Could this be a shadow of your harmonic decay graph which you posted above?”
Dunno yet. The other graph I made today was one which plots Orbital distance against orbital period. As you’ll know, Kepler had something to say about this. It looks like the curve needs an equation.
Excellent stuff.
I think there is going to be a number of ways to analyse the relationships Ulric. For example. series of Fibonacci numbers are divisible by 11 with another Fibonacci number as the result. Also, these number series are linked to primes.
The limiting factor is interesting in that they oscillate down to a precise geometric relationship. Any cross relationship ultimately adds to our understanding of the process and some may be better than others.
I would be interested to see your Mayan article, is it postable here? Jupiter’s Dance started as a sideways look at the Mayan calendar. However, their Long Count is very applicable in this area.
tallbloke, that’s an interesting graph. However, I’ve just done an orbit of my local hostelry and I’m going to crash.
I’ll repost Ulric’s article if he gives permission. Nicely done with sneaking in comment number 42 on this thread Gray. 😉
I knew The Hitchiker’s Guide to The Galaxy was onto something…
42 also happens to be the long term average sunspot number since 1750, and the ocean equilibrium value at which it neither gains nor loses heat energy from the Sun. Why would this be? Does the cloud albedo and other water vapour effects work to keep the ocean near equilibrium?
You’ve got to watch these numbers they are seductive:
However, the Markov Number is interesting:
http://en.wikipedia.org/wiki/Markov_number
42 ? that`s “all sixes and sevens” !
are there 8/7 or 7/6 ratios in musical intervals?
Or, 21×2, 14×3, 7×6
Musical Intervals = 2 3 5 7 11 13 17 19
In the chapter nine of this book you´ll find the law of three and the law of the octave:
Click to access Ouspensky-In-Search-of-the-Miraculous.pdf
And right here you will find a marvelous image of the “All suns conected to the central Sun”
@Gray says:
August 7, 2010 at 4:48 pm
Musical Intervals = 2 3 5 7 11 13 17 19
…………………………………………………
How`s that?
What about the harmonic series that the diatonic and chromatic scales are derived from?
2/1, 3/2, 4/3, 5/4, 6/5, 9/8, 16/15/, 45/32, and their inversions, no sevens.
I think you’ll find that the series you quote are derived from the intervals I’ve listed. There are major and minor sevenths I believe.
There are for example 39 Mercury orbits in 5 Mars orbits and 19 Mars orbits in 3 Jupiter orbits. It might be interesting to build a matrix of orbital timings based on such ratios.
Hey Tallbloke, do you know if anyone in Cycles Research has spotted the perfect harmony of Lunar anomalistic (749), sidereal (746), and perigee (740) cycles at 20381.96 days? {exactly 3 Lunar Nodal Cycles}
The period is highly interesting as regards Me/V/E/Ma/J/S/U synods, and close to 5 solar cycles.
@Gray says:
August 8, 2010 at 10:19 pm
I think you’ll find that the series you quote are derived from the intervals I’ve listed. There are major and minor sevenths I believe.
…………………………………………
I can`t see your list??
Major 7th is the inverse of a semi-tone.
Minor 7th is the inverse of a tone.
6th is the inverse of a major 3rd.
Hi Ulric, I’ve asked your question here:
Sorry Ulric we may be slightly at cross purposes here. This link lists musical intervals as I described.
http://en.wikipedia.org/wiki/List_of_musical_intervals
@Gray says:
August 8, 2010 at 11:46 pm
Sorry Ulric we may be slightly at cross purposes here. This link lists musical intervals as I described.
http://en.wikipedia.org/wiki/List_of_musical_intervals
………………………………………………………………
Ah prime limit is what you are refering to, higher number, more dissonance.
Fascinating page, looks a bit like TB`s planet period/distance graph at the foot !
Pythagorean scale with frequency ratios
1:1 Unison
256 : 243 2^8 : 3^5 Pythagorean minor second
9 : 8 3^2 : 2^3 Pythagorean major second
32 : 27 2^5 : 3^3 Pythagorean minor third
81 : 64 3^4 : 2^6 Pythagorean major third
4 : 3 2^2 : 3 Pythagorean perfect fourth
3 : 2 3 : 2 Pythagorean perfect fifth
128 : 81 2^7 : 3^4 Pythagorean minor sixth
27 : 16 3^3 : 2^4 Pythagorean major sixth
16 : 9 2^4 : 3^2 Pythagorean minor seventh
243 : 128 3^5 : 2^7 Pythagorean major seventh
This may something or nothing, but it reminds me of the fibonacci decay curve I graphed upthread. It might work better with inclination to plane of invariance rather than ecliptic.
tallbloke,
Interesting ratio from the Pythagorean Scale: 256:243
243 = The number of Earth Days for the planet Venus to complete one Venetian day, one revolution, 243 years between Venus/Earth Transits
256 square of 16
The decay plot is interesting too.
How to apply this as a predictive method, the big question?
Gray,
Notice also the 243 and half of 256=128 showing up in the ratio for the major seventh!
And 128:81 for the minor sixth, 3×81=243=3^5
In fact, if you step diagonally down the ratios you get a series of powers of 3 starting on one side, and a series of powers of 2 on the other.
here is the sequence of powers 3 is raised by starting from the minor second:
5,2,3,4,1,1,4,3,2,5 – a mirror image about the centre.
And the powers 2 is raised by starting from the minor second:
8,3,5,6,2,1,7,4,4,7,
Predicting what? The orbital parameters of an as yet undiscovered planet? 🙂
I’m still pondering this sequence tallbloke. If you took the Sunspot cycle vs Jupiter orbital ratio of 16:15 how would it fit with the sequence?
I’m dealing with Planet X on another thread… 🙂
16 : 15 2^4 : 3 x 5 Just diatonic semitone, major semitone, or limma
Or, perhaps that should be the JS synodic cycle vs. sunspot cycle ratio of 9:16
Which is:
16 : 9 2^4 : 3^2 Pythagorean minor seventh
The music of the spheres indeed!
By the way Gray, the Just Semitone is only 1:600 away from the
2187 : 2048 = 3^7 : 2^11 Pythagorean augmented prime, Pythagorean chromatic semitone, or Pythagorean apotome
So, add Mars/Jupiter synodic cycle 25 x 2.235445
= 55.886125/ 5 = 11.177225 years
80 MJ cycles : 9 JS cycles
Hang on to that ~55/5=~solar cycle thought, I’ll have a new post up in the next couple of days which will blow your hat off. 8)
I’m hanging…
[reply] Refresh the front page of the blog in your browser and hold onto your hat!
I have lot’s of new insights for this thread too Gray, so don’t worry, plenty to chew on in the coming days. See the new post too!
I just read the Roy Martin paper, very interesting.
Small question tallbloke, what do 2187 : 2048 refer to?
Memory is going 🙂
2187 : 2048 37 : 211 Pythagorean augmented prime, Pythagorean chromatic semitone, or Pythagorean apotome. Very close to the 16:15 Just intonation semitone
http://en.wikipedia.org/wiki/List_of_musical_intervals
Pleae let us have your obs on the Roy Martin paper on his thread. Ta.
My Father, Frederick Bailey, discovered some time ago the link between planatery positions (movements) and comprehensively described the mechanism in his first book, “Who is listening”, further more he is able to predict sunspot cycle changes for 100’s of years to come (a diagram showing future cycles is in the latest book).
Although this article is correct in stating that the Sun’s orbit is chaotic and ever changing, it is incorrect to say that sunspot cycle changes are therefore unpredictable.
Following directly on from this work, Bailey discovered that the Earth’s AU of 1 is incorrect and does in fact vary all the time and it is this variation that causes major climate changes. All this is detailed in the new website to be made public about end September 2010 and in his third book to be released ASAP.
Please study the methodology put forward and see for yourself.
Regards
Howard Bailey
It seems that our old Pythagoras was right …..after all. His hypotenuse (wavelength) grows or shrink as cathets grow or shrink, as the sin and cosine. The shorter wavelength the higher the energy, the higher the pitch…
What is more important for you interest: We see an vibrational descending octave at C1 B0 (DO-SI), having a wavelength 1050-1110; avg:1,100
-Then we have an interval, a gap, at the Sun´s corona, where it receives energy from the outside.
-Going down we found the equivalent wavelength of the Earth, at F0 (FA, of 1,580
-Then, so: As 12,760 km it is to 1,580, thus 1,100 it is to……: 8,844 kms. The Sun´s diameter.
Then, it follows that Gravity it is not the more important force directing planets but electromagnetic fields and its harmonic development. You can dig in these.
Adolfo Giurfa says:
November 17, 2010 at 5:02 pm
“Then, it follows that Gravity it is not the more important force directing planets but electromagnetic fields and its harmonic development. You can dig in these.”
Gravity and the EM bombardment field are both needed to maintain the solar system balance – Yin / Yang have opposite natures without which there can be no dynamic harmony.
Without this constant dynamic, kinematic behaviour the universe would not exit. Life itself ceases to exist once this quasi-cycling symphony stops. We need to look within ourselves if the simple rules which sit behind the apparent complexity of the universe will be revealed.
Understood.
It seems what keeps the square triangle being square is Magnetism-Electricity, this angle would never change , leaving to change just the lengths of the legs.
Gravity is an effect that results from the electrical activities of all of the “stuff” of the universe.
A part of Aldolfo’s connectivity of everything. Concentration of matter causes local electrostatic warpage of the stuff of space, Aether. pg