View Full Version : Spiral Model of Solar System
Robert Tulip
2008Oct23, 10:54 AM
Here is a way to present a simple model of the solar system showing the spiral paths of the gas giants in relation to the path of the sun around the galaxy, using the following parameters to represent Jupiter, Saturn, Uranus and Neptune as spiral coils with radius and frequency/wavelength relative to their actual orbits. Any assistance in either referring me to such a model, or in building one would be welcome.
Planet Wavelength Radius
Jupiter 1 1
Saturn 2.501 1.853
Uranus 7.110 3.680
Neptune 13.896 5.577
Robert Tulip
2008Oct23, 01:17 PM
Attached is a rough schematic of the relative orbits and a rough superimposition on each other.
ToSeek
2008Oct23, 08:08 PM
Moved from General Science to Astronomy.
Robert Tulip
2008Oct23, 09:40 PM
Thanks ToSeek. A spiral model is here (http://www.ehuh.com/animations/currentsheet2.html). What I have proposed is actually a helix model, understanding helix as a three dimensional spiral with constant amplitude. A working model would show the paths of the planets along each line of the helix.
PraedSt
2008Oct23, 10:05 PM
Robert, excuse my ignorance, but what are these models for exactly? Navigation? Observation?
01101001
2008Oct23, 10:44 PM
Robert, excuse my ignorance, but what are these models for exactly? Navigation? Observation?
Robert Tulip's first BAUT topic: Science and Astrology (http://www.bautforum.com/againstmainstream/50974scienceastrology.html). Coincidence?
PraedSt
2008Oct23, 11:00 PM
Lol!
Off topic: How do you keep coming up with these past threads? Encyclopaedic memory? :)
01101001
2008Oct23, 11:17 PM
Off topic: How do you keep coming up with these past threads? Encyclopaedic memory? :)
Everything I need to know I learned through Googling.
I was an incoming freshman when ToSeek got his PhD at Google University. I had him as a TA first semester.
01101001
2008Oct23, 11:38 PM
Suddenly, I have this irresistible urge to play with my Slinky (http://en.wikipedia.org/wiki/Slinky).
orionjim
2008Oct24, 01:14 AM
Hmmm,
His link looks like our solar systems "current sheet" to me.
See this NASA link:
http://ulysses.jpl.nasa.gov/science/monthly_highlights/2002July2001JA000299.pdf
Jim
Robert Tulip
2008Oct24, 06:25 AM
Robert, excuse my ignorance, but what are these models for exactly? Navigation? Observation?
It is about observation. Two dimensional models show the spatial relation between the planets but do not incorporate their cyclic relations, as shown in the attached 3D model. This representation is helpful if we want to understand the solar system as a whole.
PraedSt
2008Oct24, 08:33 AM
It is about observation. Two dimensional models show the spatial relation between the planets but do not incorporate their cyclic relations, as shown in the attached 3D model. This representation is helpful if we want to understand the solar system as a whole.
Thanks Robert. But you know I'm going to ask you: how is it helpful in understanding the system? :)
Robert Tulip
2008Oct24, 09:59 AM
Thanks Robert. But you know I'm going to ask you: how is it helpful in understanding the system? :)It is useful to incorporate time into models of space. This model takes the two dimensional XY plane ellipses of the gas giants and introduces the third Z dimension of movement along the vertical axis of the sun to represent the paths of the planets in space. It is a simplified model  in reality the Z axis is not vertical because the solar system plane is not orthogonal to the path of the sun around the galaxy. The model presents interesting questions in astrophysics. It can be analysed to portray the exact path over time of all objects in the system. For example, the path of the sun can be analysed against the overall helix structure to show how the position of the sun relates to a central axis line and to the centre of mass. It can be shown how far off a straight line/even curve the planets pull the momentum of the sun. If this model was the diameter of a coin the near star Alpha Centauri would be one hundred metres away. This is a model of our galactic environment.
PraedSt
2008Oct24, 11:08 AM
I once spent a year doing something similar. For pretty much anything that has a market (adequate volumes), if you plot volume on the x axis, price on the y axis and time on the z, you get lots of pretty spirals. It's my own little economics ATM theory: one day I'll discover why spirals exist, and publish. ;)
Yeah, right I hear you say..
Anyway, the only tiny flaw in my otherwise cunning plan, was that this presentation/model was completely and utterly useless in making money. :rolleyes:
Robert Tulip
2008Oct24, 11:29 AM
.. if you plot volume on the x axis, price on the y axis and time on the z, you get lots of pretty spirals... the only tiny flaw in my otherwise cunning plan, was that this presentation/model was completely and utterly useless in making money. :rolleyes:The stars put on a show for free. The advantage of this model over economic models is that it is a permanent environmental feature which can be accurately plotted into the future.
This model reflects the planetary musical composition here (http://www.purevolume.com/RobertTulip). The notes on this composition are built from the positions of Jupiter, Saturn and Neptune over 179 years with every fourth note a JupiterSaturn conjunction/unison. These notes can be mapped as vectors between the planetary helixes.
tusenfem
2008Oct24, 01:55 PM
It is useful to incorporate time into models of space. This model takes the two dimensional XY plane ellipses of the gas giants and introduces the third Z dimension of movement along the vertical axis of the sun to represent the paths of the planets in space. It is a simplified model  in reality the Z axis is not vertical because the solar system plane is not orthogonal to the path of the sun around the galaxy. The model presents interesting questions in astrophysics. It can be analysed to portray the exact path over time of all objects in the system. For example, the path of the sun can be analysed against the overall helix structure to show how the position of the sun relates to a central axis line and to the centre of mass. It can be shown how far off a straight line/even curve the planets pull the momentum of the sun. If this model was the diameter of a coin the near star Alpha Centauri would be one hundred metres away. This is a model of our galactic environment.
You also easily forget that the planet's orbits are inclined with respect to the Zaxis, which means that there is also a periodic motion "upanddown" along the Zaxis. So even more deviation from a nice spiral.
Also, the location of the barycentre of the solar system moves at the most 2 Rsun away from the centre of the sun, which in your coin analogue would mean the following:
Solar system = 6 1012 meter (Pluto's orbit) = 1 Euro (1 cm radius)
2 Rsun = 14 108 m / 6 1012 m = 2 104
This means that "our galactic environment" sortof "wiggles" at 0.0002 cm with the 100 m location of Alpha Centauri. Now, I have no idea what exactly you are trying to say here, but I seriously doubt that there is something significant here.
For sure, there is a wiggly line "left behind" by the Sun in her path around the centre of the galaxy, but the beautiful thing is that the barycentre of the solar system does no such thing, but has a very smooth path.
01101001
2008Oct24, 02:33 PM
The advantage of this model over economic models is that it is a permanent environmental feature which can be accurately plotted into the future.
Do you plan to do so, or are we just going to get the crude schematics of the initial articles?
I like pretty pictures.
Robert Tulip
2008Oct24, 08:14 PM
the planet's orbits are inclined with respect to the Zaxis, which means that there is also a periodic motion "upanddown" along the Zaxis. So even more deviation from a nice spiral.This is in agreement with my comment that "It is a simplified model  in reality the Z axis is not vertical because the solar system plane is not orthogonal to the path of the sun around the galaxy." It means the Z axis pushes the slinky spiral at an angle. I could not find the value of this angle in a quick look on the internet, but I am sure it is readily available. I am not sure how the angle of the Z axis equates to an 'up and down' motion of the XY plane of the planets, as this plane moves at fixed pace through time.
Also, the location of the barycentre of the solar system moves at the most 2 Rsun away from the centre of the sun, which in your coin analogue would mean the following:Solar system = 6 1012 meter (Pluto's orbit) = 1 Euro (1 cm radius)2 Rsun = 14 108 m / 6 1012 m = 2 104This means that "our galactic environment" sortof "wiggles" at 0.0002 cm with the 100 m location of Alpha Centauri. Now, I have no idea what exactly you are trying to say here, but I seriously doubt that there is something significant here. For sure, there is a wiggly line "left behind" by the Sun in her path around the centre of the galaxy, but the beautiful thing is that the barycentre of the solar system does no such thing, but has a very smooth path. Thanks very much. It illustrates that the central axis of the helix model is the solar system barycentre, while the sun moves around this position  as shown here (http://www.orbitsimulator.com/BA/sbc4.GIF ) and here (http://www.bnhclub.org/JimP/jp/comp1.JPG). A sine wave model of the contribution of Jupiter, Saturn and Neptune to this path is here (http://www.bautforum.com/attachments/questionsanswers/8500d1218818604solarsystembarycentregravityjsnssbsinefunction.gif ).
Robert Tulip
2008Nov03, 01:52 AM
Attached (http://www.bautforum.com/attachment.php?attachmentid=8972&d=1225677002) picture shows the solar system as a set of sine waves mapped on a cylinder. Sine waves with periods corresponding to Jupiter, Saturn, Uranus and Neptune are mapped with equal amplitude. Contact points between these functions mark the conjunction points between the planets when the sine waves are viewed as a 2D representational of a 3D cylinder. The 52 Jupiter Saturn orbital relation over each sixty years is clearly apparent by viewing the sequence of the waves at the top and bottom of the diagram.
Edit to add  Cylindrical sine wave solar system model (http://www.bautforum.com/attachment.php?attachmentid=8973&d=1225683728) puts bars connecting equivalent points on the cylinder. The JupiterSaturn 52 pattern from the sine wave image is illustrated on the purple bars on the central spiral, while periodic patterns in the outer planets are roughly indicated in the red green and blue bars.
01101001
2008Nov03, 07:17 AM
picture shows the solar system as a set of sine waves mapped on a cylinder
Very poorly, without any apparent value, with neither rhyme nor reason.
Is this presentation of a solar system model good for anything practical? How is it superior to previous presentations? What advantages come to those who use it? What are its strengths? The strengths come from a tradeoff for what weaknesses?
Why should this be taught in schools? Why should NASA include it in educational materials about the solar system? Why are you teaching it to us? What are the top three facts you think we should know about it? How is it best taught? To what age groups? Why?
PraedSt
2008Nov03, 07:26 AM
01101001, Robert was kind enough to explain earlier.
This model reflects the planetary musical composition here.You can make sweet music with this.
Robert Tulip
2008Nov03, 10:04 AM
without any apparent value, with neither rhyme nor reason.These models may be rough but they are empirically accurate, showing the rhyme and reason of the cosmos. The apparent value is years  if by 'apparent value' you mean unit of measurement. Apologies that my crude initial models do not all have axes. The first model shows the years, so these can easily be added to the rest. For example, the JupiterSaturn 5:2 ratio is close to 59 years. If by 'apparent value' you meant intrinsic worth, then the value is the addition of the dimension of time to the depiction of the relative orbits of the gas giants.
Is this presentation of a solar system model good for anything practical? Picture two from the OP fits 500 years of data into a very simple diagram. It is mainly a more informative way to present relative orbits. Looking for nonastronomical practical uses, it may be useful for historical timelines.
How is it superior to previous presentations? It expands the horizons of modelling the solar system by showing the relative dimensions of the gas giants in temporal as well as spatial terms. Previous presentations usually just show orbits by distance, a method which does not show that for example, Jupiter orbits the sun about fifteen times for each Neptune orbit, as is readily apparent from this model.
What advantages come to those who use it?They can see the overall shape of our solar system through time.
What are its strengths?This model is a constant depiction of the solar system's main features  the models here are nearly equally accurate for now and for a million years ago. They can readily summarise all the main orbital data in our solar system over centuries into a page showing how the system as a whole relates to the galaxy. Comets could be added to show how they relate to the gas giants regarding distance, ellipticity and period. A logarithmic scale could add the inner planets and the centre of mass, or could just show earth and asteroids with near earth orbits.
The strengths come from a tradeoff for what weaknesses?A three dimensional working model gives the benefit of presentation over time in a single diagram, at the cost of the increased complexity of a helix compared to an ellipse. A simple moving two dimensional elliptical model of the solar system can show the relative speeds of the planets over time, but cannot capture dynamism in a static drawing as this model does. The multihelix has the advantage of capturing these relative speeds in a single still picture.
Why should this be taught in schools?I think it would be great to use this method for students to build a clear temporal model that would show students both how isolated our system is in the galaxy, and how what seem to be long periods to us, eg Neptune's 162 year period now just coming round since its discovery, are very short compared to universal time scales. As well, the sine wave function is useful in geometry to see how it collapses a cylinder into two dimensions.
Why should NASA include it in educational materials about the solar system?Once cleaned up it would be an easy way to teach information about the relative motions of the main objects.
Why are you teaching it to us?The solar system is where we live :) The harmonic relations between the gas giant orbits are intrinsically interesting.
What are the top three facts you think we should know about it?For starters, (1) OP diagram two, once refined, captures all the relative positions of the gas giants over 500 years; (2) It can readily be analyzed to see simple repetitive patterns which are not well described by other models, such as the 179 year relation between Jupiter, Saturn and Neptune; and (3) it depicts the main forces operating on the solar system centre of mass, which scribes an exact arc through space.
How is it best taught?Building the model is a useful way to understand the relative dimensions of the solar system. To build the simple pictures here, I started to work out how to draw a spring using excel, and found that I had to also use paint, and then I had to work out how much to stretch the first Jupiter spring to get the others. CAD software could present this very well.
To what age groups?Who ever is interested in solar system celestial mechanics
Why?To help understand our physical place in the cosmos.
Centaur
2008Nov03, 06:15 PM
Robert, are you referring to Kepler’s Third Law which states that the cubes of the planets’ orbital semimajor axes are proportional to the squares of their orbital periods? Are you seeking something like the flawed TitiusBode Law of orbital sizes? http://en.wikipedia.org/wiki/Titius%E2%80%93Bode_law
PraedSt
2008Nov03, 07:00 PM
Attached (http://www.bautforum.com/attachment.php?attachmentid=8972&d=1225677002) picture shows the solar system as a set of sine waves mapped on a cylinder.
I like your sine wave diagram actually. Brings out orbital resonance quite clearly. Unfortunately, I went and did some reading, and it turns out that most orbital resonances involving planets are illusions. At least according to wiki (http://en.wikipedia.org/wiki/Orbital_resonance):
A number of nearintegerratio relationships between the orbital frequencies of the planets or major moons are sometimes pointed out. However, these have no dynamical significance because there is no appropriate precession of perihelion or other libration to make the resonance perfect.
Such nearresonances are dynamically insignificant even if the mismatch is quite small because (unlike a true resonance), after each cycle the relative position of the bodies shifts. When averaged over astronomically short timescales, their relative position is random, just like bodies which are nowhere near resonance.
For example, consider the orbits of Earth and Venus, which arrive at almost the same configuration after 8 Earth orbits and 13 Venus orbits. The actual ratio is 0.61518624, which is only 0.032% away from exactly 8:13. The mismatch after 8 years is only 1.5° of Venus' orbital movement. Still, this is enough that Venus and Earth find themselves in the opposite relative orientation to the original every 120 such cycles, which is 960 years. Therefore, on timescales of thousands of years or more (still tiny by astronomical standards), their relative position is effectively random.
BUT, luckily for you, it goes on to say:
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.As for your 3D attempts, I think you're running into the same problems as I had with mine (see above post (http://www.bautforum.com/1349851post14.html)). You need a 3D display to fully bring out their advantages. On a 2D surface, it just looks confusing. Stick to 2D as much as possible is my advice.
Robert Tulip
2008Nov18, 02:58 AM
Continuing my research, please see attached (http://www.bautforum.com/attachment.php?attachmentid=9060&stc=1&d=1226976113) a pair of charts that correlate the positions of the four gas giants (notation: Jupiter, Saturn, Uranus, Neptune = JSUN) and the position of the solar system barycentre (SSB) over the period 18822061. This period is typical for the 179 year JSN cycle. Planetary periods are shown in actual temporal relation, but with equal radius for greater ease of interpretation. The sine waves are a 2D representation of orbits mapped onto a cylinder. All inferior conjunctions are marked, eg JS, SN, etc.
The following observations are of interest.
1. SSB maxima generally coincide with JS inferior conjunctions, and SSB minima generally coincide with JS superior conjunctions (as noted by Newton).
2. Deviations from this pattern are explained by the influence of Neptune and Uranus. For example,
the long maximum at 18961903 correlates to the JN, SU and JU conjunctions preceding the JS conjunction;
the greatest minimum at 1990 matches J opposite SUN;
the 1919, 1958, 1998 and 2037 maxima precede JS due to JN and/or JU; and
the 1943, 1982 and 2022 maxima follow JS due to JN and/or JU.
3. The wiggles in the graph are where J conjuncts U and N in between the JS cycle, at 1970 and at present.
Robert Tulip
Robert Tulip
2008Nov19, 12:24 AM
Robert, are you referring to Kepler’s Third Law which states that the cubes of the planets’ orbital semimajor axes are proportional to the squares of their orbital periods? Are you seeking something like the flawed TitiusBode Law of orbital sizes? http://en.wikipedia.org/wiki/Titius%E2%80%93Bode_lawHi Centaur, no, this is nothing to do with Bode's Law or Kepler's Law. It is just about finding more informative ways to depict the long term structure of the solar system. Thanks for your question.
John Jaksich
2008Nov19, 02:06 AM
This is very intriguing...after learning the basics of Kepler and others mentioned above ... I have been under the impression that "chaotic" models have also been mentioned as possible models that could better explain the motion of the starry wanderers.
see:
Chaotic Motion in the Solar System
Rev Mod Phys
Volume: 71
Year 1999
page: 835
Author: Jack J. Lissauer
Robert Tulip
2008Nov22, 01:12 PM
The attached diagram (http://www.bautforum.com/attachment.php?attachmentid=9125&stc=1&d=1227359300) adds to the previous depiction of the solar system’s main structure by illustrating how the Fourier decomposition of the solar system barycentre wave function maps to the sine curves of the four gas giants. The wave in the upper picture is composed primarily of the four waves in the lower picture. Groups of planetary conjunctions pull the SSB maxima forward and back in time as shown by arrows and ovals in the attachment. This is a purely mathematical illustration of the composition of the centre of mass. Minor apparent errors in the alignment of ovals and arrows in the attached picture should be readily corrected by more exact data.
Robert Tulip
frankuitaalst
2008Nov28, 05:29 PM
Hi Robert .
I'm wondering how you create these wonderful diagrams .
Is it a product of the r=a.cos(wt+fi) relationships of our solar system or is it a product of integration of the movements of the planets within our solar system ?
novaderrik
2008Nov28, 10:03 PM
Hi Robert .
I'm wondering how you create these wonderful diagrams .
Is it a product of the r=a.cos(wt+fi) relationships of our solar system or is it a product of integration of the movements of the planets within our solar system ?
i'd bet that he uses a spirograph (http://en.wikipedia.org/wiki/Spirograph) set.
when i was a kid, i made a LOT of diagrams of the orbits of the planets, but i just thought i was making some neat looking squibbles on paper using plastic gears with holes in them and a pencil.
Robert Tulip
2008Dec03, 07:30 AM
Hi Robert .
I'm wondering how you create these wonderful diagrams. Is it a product of the r=a.cos(wt+fi) relationships of our solar system or is it a product of integration of the movements of the planets within our solar system ?Hi Frank. On the most recent diagram, the top part is from JPL data of the solar system centre of mass, while the bottom part is an excel spreadsheet as follows.
1. Enter
A1: 11.8592
A2: 1
A3: =A2+1/A$1
B1: Jupiter
B2: =SIN(A2)
C1: 29.657296
D1: Saturn
E1: 84.323326
f1: Uranus
G1: 164.79
H1: Neptune
2. Copy the formulas to all columns then copy down the spreadsheet for several hundred rows
3. Chart columns bdfh to get four sine waves with periods corresponding to the gas giants.
4. Add arrows and ovals and text use the miraculous excel draw function.
5. Print screen, paste into paint and crop.
6. Make sure jpeg size is within BAUT attachment limits, if not, select all and shrink.
:)
Robert
Robert Tulip
2008Dec11, 09:40 AM
Here (http://www.bautforum.com/attachment.php?attachmentid=9254&stc=1&d=1228987468) is a further illustration of the helix pattern of Jupiter, Saturn and Neptune. This diagram is a composite sine wave, adding the sine waves of Jupiter, Saturn, Uranus and Neptune over 800 years. In addition, sine waves of Saturn and Neptune are shown, with the five successive cycles of conjunctions, occurring with Jupiter (not shown) each 179 years, at the five different coloured sets of arrows. It can readily be seen that the composite wave (green  SSB JSUN) has very similar shape at each same coloured arrow. This is just a schematic built as a mathematical model, with effects of each gas giant set at equality in order to highlight the input of the further planets. In reality the shape of the barycentre wave function is much more similar at the arrow points than is shown here. If this twodimensional sine wave were presented in three dimensions as a cylinder, each arrow would take about eleven points to circumnavigate the ecliptic, in families of JupiterSaturnNeptune conjunctions moving into and out from exactness over the millennia, with the twelfth point about one twelfth further around the ecliptic. By an interesting coincidence, the lunisolar precession of earth's equinox each ~25764 years takes very close to 144 of these arrows. These are rough calculations. I hope there are astronomers with interest in this cyclic pattern of our solar system who could verify my numbers and model. If anyone can suggest a web location where I could put a better version of the attached picture, or if you have questions about it, please let me know.
Robert Tulip
2008Dec12, 12:08 AM
Attached version shows the model I am describing. It just shows the 35.8 year conjunction cycle of Saturn and Neptune, occurring in five sets of cycles, shown here over 800 years, in a permanent structure of the solar system. These cycles are moderated by the position of Jupiter (not shown), which stands at the same angle to each fifth SN conjunction every 179 years, indicated by arrows. The precession period of 25764 years is 144 times the 178.9 year JSN cycle. Every second SN conjunction (71.6 years) occurs after one degree of lunisolar precession of the equinox.
Robert Tulip
Apologies that shrinking this jpeg to within BAUT attachment limit makes it hard to read. Please let me know if you would like the excel original.
Robert Tulip
2008Dec13, 12:10 PM
A further diagram here (sun.http://www.bautforum.com/attachment.php?attachmentid=9266&stc=1&d=1229169920) illustrates the relative influence of the gas giants on the sun in terms of the position of the barycentre. Rather than varying the amplitude of the orbits with their relative distance from the sun, the amplitude of the sine waves are weighted to show their relative effect on the solar system centre of mass.
ETA
At any two points separated by 179 years on the x axis, Jupiter, Saturn and Neptune should be in the same positions.
The word 'gravitational' in the title of the attachment is not correct, as the ratio J:S~=3:1 is a function of mass not gravity.
Robert Tulip
2009Feb12, 05:27 AM
In the Direction of Sun Q&A, a respondent (Hornblower) provided this picture of the solar galactic vector over 750,000 years (http://img102.imageshack.us/img102/5503/sunapexmotionyf3.jpg), showing the direction and pace of movement of the sun against the galaxy. The vector in this picture could be presented as a helix, as discussed in this thread, made up primarily of the orbits of the sun and gas giants. Connecting the dots for the JupiterSaturnNeptune conjunction every 179 years, another helix is described that advances close to 30 degrees per instance and circles the vector about once every 2150 years, 300 times in the course of this 50 light year movement of the sun. A logarithmic scale could depict both the helix and the vector in one picture.
Robert Tulip
2009Apr15, 09:25 PM
I have now built a prototype model of the solar system to illustrate the permanent relations between Jupiter, Saturn and Neptune in their 179 year conjunction cycle. On a flat board, three coils of wire illustrate the three planets, with 1.08 coils for Neptune, 6.08 coils for Saturn and 15.08 coils for Jupiter. The coils are held in place with 15cm vertical dowel sticks with holes drilled where the wire passes through. Wool is used to join planets at conjunctions, with planets made of polystyrene balls stapled to the wire. Orbit scales are Jupiter = 10 cm, Saturn = 20 cm, Neptune = 40 cm
This model produces a series of ladders similar to the DNA double helix. The JupiterSaturn ladder rungs are separated by 59.3 years and the JN and SN ladder rungs, in an extended model, are separated by 179 years.
This model shows the locations of these gas giants every 179 years, with the starting point advancing 1/12 of the circle of the ecliptic, as a permanent model. For example, it shows the positions of the planets after two current sets of conjunctions beginning in the following years.
Year
126 629
53 808
232 987
411 1166
590 1345
769 1524
948 1703
1127 1882
1306 2061
1485 2240
1664 2419
1843 2598
2022 2777
A number of interesting astronomical features can be seen from this model. For example, the current JSN cycle that began in 1882 also includes the conjunction in 2022 in the other family. This 2022 event is spread over about six years, and is at the end of a family of conjunctions which was exact* in 769. The 1882 family was close to exact in 1524.
*JSN reached the same point within three days from 1720 July 769.
The five SN points every 35.8 years mark five simultaneous helical families of JSN conjunctions, with the JS point drifting slowly against the SN cycle.
Stacking twelve 179 year periods on top of each other will reveal these slower Neptune cycles, with the twelve JSN ladder rungs on the triple helix forming a full circle around the ecliptic every 2148 years.
These bodies are the main influence on the distance between the sun and the system centre of mass. The barycentre can be included as a central dowel.
Uranus is not included because it is not part of this permanent cycle.
Wire, dowel, polystyrene and wool are crude materials to model the solar system. I would like to make an exact model using design software showing how these patterns develop over longer periods. This would make an excellent thesis topic for a university science student. I would be happy to assist anyone interested to pursue this fascinating project. I will send photographs of the model to anyone who asks by private message.
Robert Tulip
Robert Tulip
2009Apr17, 06:01 AM
http://img24.imageshack.us/img24/904/solarsysteminrthands.jpg
Other images here (http://profile.imageshack.us/user/Robert_Tulip)
Robert Tulip
2009Apr18, 01:27 AM
The purple threads show conjunctions between Jupiter and Neptune, the black threads show conjunctions between Saturn and Neptune, and the red, green, orange and blue threads show conjunctions between Jupiter and Saturn over 179 years. The JupiterSaturn ladder has two rungs between the JSN triple helix rungs at the base and top. Over 2148 years, there are twelve rungs of the triple helix, in five simultaneous groups around SN, fourteen around JN and three around JS.
These photos (http://img24.imageshack.us/img24/904/solarsysteminrthands.jpg) are of a beta version. I have since corrected errors which keeneyed observers may have detected. The purple thread at the top joins Jupiter and Neptune. It should pass beneath the Saturn orbit rather than above as shown. The SaturnNeptune black threads should be separated by fifths of the orbit to mark true relation to alignments with JN. Saturn has a widening gyre in the model, and needs the wire pulled in to correct the orbit. The barycentre can be shown with the central wire forming a helix with outer turning points at the JS conjunctions and midpoints close to the sun. Styrofoam planets are needed to mark Jupiter on the second and third JS ladders, which also need to be added to show the full braid of the system.
The following table compares each set of conjunctions. The third column of each group shows the symmetrical axis of the planetary conjunctions around this basic cycle, which describes the structure of time for the solar system.
Years JN SN JNSN JN JS JNJS SN JS SNJS
12.79 12.79 19.86 7.07 19.86
25.57 25.57
38.36 35.80 2.56 38.36 39.71 1.35 35.80 39.71 3.91
51.14 51.14
63.93 63.93 59.57 4.36 59.57
76.71 71.60 5.11 76.71 79.42 2.71 71.60 79.42 7.82
89.50 89.50
102.29 107.40 5.11 102.29 99.28 3.01 107.40 99.28 8.12
115.07 115.07 119.13 4.06 119.13
127.86 127.86
140.64 143.20 2.56 140.64 138.99 1.65 143.20 138.99 4.21
153.43 153.43
166.21 166.21 158.84 7.37 158.84
179.00 179.00 0.00 179.00 178.70 0.30 179.00 178.70 0.30
real x
2009May06, 03:12 AM
4dsolarsystem.com has a simulated 20 month long exposure of the entire solar system.
Robert Tulip
2009May07, 05:50 AM
4dsolarsystem.com has a simulated 20 month long exposure of the entire solar system.
Thanks, this is nice. The sine wave patterns of the planets illustrate their orbital periods, with Mars completing nearly one orbit, Earth 1.6, etc. The outer planets seem only to go to Uranus and not to include Neptune or Pluto.
Comparing to the 179 year model I presented above, the period shown at 4dsolarsystem.com is an extremely short picture of the overall system. By taking longer snapshots, and paring back to recurrent patterns such as the JSN cycle, we can examine the temporal structure of the solar system.
Appleblythe
2009May09, 05:35 PM
Highly informative. Great read.
Robert Tulip
2009Jun25, 11:06 PM
If this twodimensional sine wave were presented in three dimensions as a cylinder, each arrow would take about eleven points to circumnavigate the ecliptic, in families of JupiterSaturnNeptune conjunctions moving into and out from exactness over the millennia, with the twelfth point about one twelfth further around the ecliptic. By an interesting coincidence, the lunisolar precession of earth's equinox each ~25764 years takes very close to 144 of these arrows. These are rough calculations. I hope there are astronomers with interest in this cyclic pattern of our solar system who could verify my numbers and model. If anyone can suggest a web location where I could put a better version of the attached picture, or if you have questions about it, please let me know.
Taking further this analysis of how the JupiterSaturnNeptune cycle is 1/144th of the earth's Great Year, I have built a diagram (http://img530.imageshack.us/i/precessionyuga.jpg/) illustrating the relation between the Great Year, the movement of the South Celestial Pole, and the Indian theory of the Yuga. I am not sure about the scientific status of the Yuga diagram, but it does have a primafacie match with the cycle of precession.
4dsolarsystem.com has a simulated 20 month long exposure of the entire solar system.I made more detailed diagrams of similar cyclic periods of the solar system, for example a geocentric model of the 1960s (http://img7.imageshack.us/img7/9551/1960s.jpg).
mugaliens
2009Jun27, 10:50 PM
Here (http://www.bautforum.com/attachment.php?attachmentid=9254&stc=1&d=1228987468) is a further illustration of the helix pattern of Jupiter, Saturn and Neptune.
And so it is! We had a poster here a while back, from Australia, if I'm not mistaken, who touted this information all the time.
He was largely dismissed, and towards the end, his disgruntlement with the negativism became cause for his demise.
It's nice to see this idea resurfacing, but it's a shame what happens to early proponents.
PraedSt
2009Jun27, 11:07 PM
Robert, think you could look over this paper (http://www.bautforum.com/astronomy/90059sunpotscausedkboimpacts.html) I posted? It tries to tie in orbital resonances of the outer planets with our sunspot cycle. I thought you might be interested, and that you might also check their workings. :)
Robert Tulip
2009Jun29, 06:41 AM
And so it is! We had a poster here a while back, from Australia, if I'm not mistaken, who touted this information all the time.
He was largely dismissed, and towards the end, his disgruntlement with the negativism became cause for his demise. It's nice to see this idea resurfacing, but it's a shame what happens to early proponents.You might be talking about Ray Tomes from New Zealand. Ray was banned from BAUT for issuing legal threats, and was indeed disgruntled at the lack of interest in astronomical cycles. He was not aware of the 179 year JSN cycle that I have discovered and described here, but rather thought that the barycentre followed cycles of differing lengths. So he did not tout this information, let alone all the time, as he was not aware of it.
See http://www.bautforum.com/againstmainstream/71027jupiterinfluencingsunspots4.html#post1207894
Robert Tulip
2009Jun29, 09:04 AM
Here (http://img12.imageshack.us/img12/4575/solarsystemjsnverticalv.jpg) is a view from the future back along the galactic path of the sun showing Jupiter, Saturn and Neptune relative frequency, diameter and position over 179 years. I have since done more work on this model to make it more complete and accurate.
Here (http://img150.imageshack.us/i/neptunezodiacage.jpg/) is a diagram showing the sign position of Neptune from 53AD to 2201AD. The large numbers are the years when Neptune was conjunct Jupiter and Saturn in that sign, showing how this conjunction cycle advances by 30° per time.
The circle with Neptune dates can be placed on the spindle of the model. The large year aligned to the base of the triple planet spiral shows the conjunction dates of Jupiter, Saturn and Neptune for the following 179 year period. A problem with this Neptune date wheel is that it uses the tropical signs as they were in 53AD and does not correct for precession of the equinox. So the dates for more recent cycles are sidereally incorrect by 2.5° per cycle, adding to 30° over the entire period. The designation "Age of Pisces" refers to the period when the position of the sun at the March equinox is in Pisces.
Robert Tulip
2010Jan06, 06:21 AM
http://rtulip.net/yahoo_site_admin/assets/images/Solar_System_Planet_Clock.4225703_std.JPG
Solar System Planet Clock (http://rtulip.net/yahoo_site_admin/assets/docs/Solar_System_Planet_Clock.4205909.pdf)
Note: while this post may relate to material against the scientific mainstream, it does not contain any ATM content and I do not wish to engage in discussion of material against the scientific mainstream here. This post continues the purpose of this thread, building an accurate temporal model of the solar system.
The solar system planet clock, shown above, is a schematic empirical diagram of the solar system enabling ready calculation of the positions of Jupiter, Saturn and Neptune over the 2148 years of the period known as the Age of Pisces. The diagram also shows how the 25765 year Great Year axial cycle of terrestrial lunisolar torque maps to a pattern of the solar system gas giants.
The twelve joined diamond wedges in the diagram, one for each hour of the clock, each consist of two isosceles triangles joined at the base, with head angle thirty degrees. Each of the twelve diamonds of the clock has one mark at the centre, then two, three and so on to twelve at its mirror axis half way to the star point. The mirror axes of the twelve diamonds form a circle with 144 points. The number of marks on each star point descends arithmetically from twelve at the joining circle to the single mark at each star point.
The diagram depicts a number of temporal cycles. The twelve points of the star are marked with the numbers one to twelve in the central spiral, indicating both a regular clock and longer term patterns of the earth and the gas giants. These longer patterns are the Great Year of 25765 years, the Zodiacal Age of Pisces, and the gas giant conjunction cycle. The twelve points of the clock mark the triple conjunction dates of the three heaviest gas giant planets, Jupiter, Saturn and Neptune, over the period of the earth’s Zodiacal Age. By coincidence these cycles of the gas giants and the earth align almost perfectly.
The Age of Pisces, one twelfth of the Great Year, is roughly equal to the period in which the position of the Sun at the March equinox has precessed through the constellation of Pisces over the last two thousand years. The average length of an Age, 2148 years, is the same as the period required for Jupiter, Saturn and Neptune to complete twelve conjunctions in a grouped cycle. Over a longer period the gas giants move into and out of alignment, forming families of conjunctions. One conjunction family has its centre in the year 769 and the next is centred in the year 1524. These overlapping cycles are separated by 755 years. The next such cycle appears to be centred in about 2636, but I have not yet obtained data this far in the future.
The stability of the component orbital periods of the gas giants and the earth means that the components of this clock diagram can describe any time in the earth’s future and past, for millions of years at least. Such stability appears to have been in evidence for billions of years, and is likely to persist into the far future.
The planet clock depicts the Age of Pisces against the regular cycle of the gas giants in each of the twelve ‘hours’ at the points of the clock. The years 53 to 2201 around the outer spiral are the dates when the gas giant planets Jupiter, Saturn and Neptune form a triple conjunction, once every 179 years. 179 years forms the ‘hour’ of the clock when the Zodiacal Age is considered as the twelve hour circle. Within each 179 year ‘hour’, more frequent planetary meetings are shown dividing the hour. Each hour is divided in three by JupiterSaturn, in five by SaturnNeptune, and in seven by JupiterNeptune conjunctions. These divisions enable ready calculation of the approximate date and position of all gas giant conjunctions for the last two thousand years with the exception of Ouranos (Uranus) which is irregular.
The signs of the zodiac are shown in each hour to indicate a surprising empirical fact: that Jupiter, Saturn and Neptune begin and end each ‘hour’ of the Age in or close to that tropical sign. This match is exact for the fourth and fifth ‘hours’ of the clock, but drifts slightly out of alignment the further in time one gets from 1720 July 769, when the triple conjunction was most exact. This three day period is the cusp of the ‘hours’ of Cancer and Leo and the planetary conjunction occurred at the cusp of these tropical signs.
I would welcome assistance in comparing this tropical depiction against a sidereal version of this diagram, as a way to help visualize the process and rate of precession of the equinox around the zodiac and to define the historic positions of the gas giants against the background stars.
The three JupiterSaturn conjunctions shown in each ‘hour’ at the third marker of each star point occur every 59.6 years. These conjunctions occur physically at the points shown. For example, between the JupiterSaturnNeptune triple conjunctions at 0° Leo in 769 and 30° Leo in 948, actual positions of JupiterSaturn conjunctions are shown at 10° Leo in 829 and 20° Leo in 888. Jupiter and Saturn meet every 19.85 years. The other two JupiterSaturn conjunctions between each one shown occur at points equally spaced around the ecliptic, ie at 3° Sagittarius and 7° Aries etc. To calculate the position of these JupiterSaturn conjunctions, the time between two events spaced by 19.85 years is given as 37/108ths of the circle, or four hours of the clock plus one point at the ring of nine marks per hour.
The five SaturnNeptune conjunctions in each ‘hour’ are of particular interest as a model of our sixtybase clock. SaturnNeptune conjunctions occur every 35.8 years, dividing the Zodiacal Age by sixty (2148/60 = 35.8), and forming the minutes and seconds when the diagram is used as a normal clock. The actual locations of the planetary conjunctions for the four points shown between each ‘hour’ are each 13 ‘minutes’ (13/60) further around the clock, at the thirteenth SaturnNeptune point, ie 2.6 signs further on along the ecliptic. Each fifth conjunction is exactly one ‘hour’ later, once Neptune has completed 13/12 orbits and Saturn has completed 73/12 orbits.
JupiterNeptune conjunction points are shown in each ‘hour’ by each row of six conjunctions between the JupiterSaturnNeptune points at the seventh line. These points indicate the fourteen JupiterNeptune conjunctions from each triple conjunction to the next, with each second event shown. The actual distance between each conjunction is 13/168 of the ecliptic, or 6.5 points along the circle of seven shown with Jupiter and Neptune, making fourteen meetings per ‘hour’, one per 179/14 = 12.8 years. The JupiterNeptune cycle embodies the number of hours in a week, 168, as the denominator of its fractional distance around the ecliptic.
The planet clock shows how our familiar twelve and sixty based time systems are embedded in the structure of the solar system through the ratio between earth’s spin wobble period and the orbital pattern of the three heaviest planets. This orbital pattern finds a unity in the effects of the planets on the position of the sun in relation to the centre of mass, the arc that the solar system follows around the galaxy. Planetary influence on the centre of mass is shown by the barycentric formula r = a/(1+m1/m2), where r is the radius of the sun, a is the distance from the sun to a planet, m1 is the mass of the sun and m2 is the mass of the planet. The relative effects of the planets on the barycenter given by this formula are Jupiter 49%, Saturn 27%, Neptune 15% and Ouranos 8%. The four inner planets in total have 0.1% of Jupiter’s effect on the barycenter. These relative planetary effects are readily seen by examining a graph of the barycentersun distance over time, in which the three biggest planets produce a wave function with period 179 years, or 1/144th of the Great Year of the earth.
Robert Tulip
January 2010
Hornblower
2010Jan06, 07:43 PM
Another graphical variation on the same tired old theme of numerical curiosities.
A.DIM
2010Jan07, 02:48 PM
So this is mere numerology, astrology or tired ol curiosity?
Personally, I rather like how what Robert has here ties in with some ancient and ATM ideas ...
but is it empirical?
Robert Tulip
2010Jan07, 08:18 PM
So this is mere numerology, astrology or tired ol curiosity? Personally, I rather like how what Robert has here ties in with some ancient and ATM ideas ... but is it empirical?Thanks A.Dim. This is 100% empirical. As I explain in my text above, it provides a method to find the positions of the three described gas giants any time over the last 2000 years, and over longer time horizons as well, as this model is accurate over millions, possibly billions, of years.
The link to terrestrial cycles is a coincidental bonus.
I grant that the association with folk traditions has a 'yuk' factor for scientists, which may explain Hornblower's "tired" comment, but the fact is that this cyclic temporal model of the solar system is entirely new and entirely scientific.
Hornblower
2010Jan07, 11:10 PM
Thanks A.Dim. This is 100% empirical. As I explain in my text above, it provides a method to find the positions of the three described gas giants any time over the last 2000 years, and over longer time horizons as well, as this model is accurate over millions, possibly billions, of years.
The link to terrestrial cycles is a coincidental bonus.
I grant that the association with folk traditions has a 'yuk' factor for scientists, which may explain Hornblower's "tired" comment, but the fact is that this cyclic temporal model of the solar system is entirely new and entirely scientific.
Are you taking orbital eccentricity into account?
Robert Tulip
2010Jan08, 12:20 AM
Are you taking orbital eccentricity into account?Orbital eccentricity may be a possible tiny refinement, but is so small (see table (http://hyperphysics.phyastr.gsu.edu/Hbase/Solar/soldata.html#c1)) that it really does not affect this model.
Precession is a far bigger effect, in that the data I have used is tropical rather than sidereal, so the locations given are measured against the earth's seasonal framework rather than against the stars. The tropical and sidereal locations were previously the same (in about year 200AD?), but the tropical zodiac has since precessed by about 24° of arc.
To illustrate this problem of precession, the diagram dates could be shifted to centre in 1524, the middle of the next 'family' of conjunctions when Jupiter Saturn and Neptune were closely conjunct, but the sign locations would either be in tropical Pisces or sidereal Aquarius. The diagram could equally be used to calculate cycles for any other 2148 year period in the future or past for which ephemeral data for the gas giants is available.
Hornblower
2010Jan08, 03:30 AM
I don't know whether to laugh or cry when you blow off the eccentricity like that. Let's consider Jupiter for example. If we ignore its eccentricity and assume it will just move at its average speed from one opposition to the next, we will have a position error of some 3 degrees when near perihelion or aphelion. If that is your idea of being accurate, I do not want to trust your work for any practical purpose such as navigation or planning a mission like Voyager or Galileo.
Robert Tulip
2010Jan08, 06:48 AM
I don't know whether to laugh or cry when you blow off the eccentricity like that. Let's consider Jupiter for example. If we ignore its eccentricity and assume it will just move at its average speed from one opposition to the next, we will have a position error of some 3 degrees when near perihelion or aphelion. If that is your idea of being accurate, I do not want to trust your work for any practical purpose such as navigation or planning a mission like Voyager or Galileo.
The main purpose of this diagram is to depict the stable long term helical cycle of the three shown gas giants in schematic form. Against human time scales this pattern is in permanent repeat, showing cycles that have existed for millions or billions of years. It does not aim for the level of accuracy required to navigate a spacecraft, although doubtless such data could be used to refine it.
I'm surprised to see your comment that position error for Jupiter due to orbital eccentricity speed variability could be up to three degrees, and confess I haven't thought about this issue until you brought it up. I would be interested to understand why the figure for Jupiter's eccentricity of 4.8% from circle to max/min would shift its conjunction points with Saturn and Neptune by 3%. It indicates the need for an overlay of perihelion/aphelion points on the diagram, so that some conjunction points are grouped tighter and some further apart. The eccentricity for Saturn is 5.56% and for Neptune is 0.86%.
I have checked a number of the planetary positions indicated by this diagram against ephemerides. Taking precession into account, they are within one degree of where I had expected, which is fairly close for a one page diagram condensing more than two thousand years of data. I will keep checking this.
Robert Tulip
2011Jun14, 02:43 PM
15108
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A further way to illustrate the gas giant conjunction cycle is shown in the attached diagrams using the solar system simulator at http://dd.dynamicdiagrams.com/wpcontent/uploads/2011/01/orrery_2006.swf
These diagrams show JupiterSaturnNeptune triple conjunctions every 179 years from 1345 to 2060, with Saturn slowly drifting back against the other two planets. It can also readily be seen how each successive conjunction is thirty degrees of arc further around the ecliptic. These three planets have the strongest effect on the position of the center of mass of the solar system.
Hornblower
2011Jun14, 09:53 PM
15108
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A further way to illustrate the gas giant conjunction cycle is shown in the attached diagrams using the solar system simulator at http://dd.dynamicdiagrams.com/wpcontent/uploads/2011/01/orrery_2006.swf
These diagrams show JupiterSaturnNeptune triple conjunctions every 179 years from 1345 to 2060, with Saturn slowly drifting back against the other two planets. It can also readily be seen how each successive conjunction is thirty degrees of arc further around the ecliptic. These three planets have the strongest effect on the position of the center of mass of the solar system.
No, they have the same effect as all of the other planets, which is none. In keeping with conservation of momentum, the barycenter remains stationary or moves at a constant velocity, depending on the inertial frame of reference chosen. What they do is cause the Sun to move around with respect to the barycenter.
Robert Tulip
2011Jun14, 11:53 PM
No, they have the same effect as all of the other planets, which is none. In keeping with conservation of momentum, the barycenter remains stationary or moves at a constant velocity, depending on the inertial frame of reference chosen. What they do is cause the Sun to move around with respect to the barycenter.
Thanks Hornblower for the clarification, of course you are correct, what I meant was "the position of the center of mass with respect to the sun". However, the barycenter is a function of all the mass of the system, so it does make sense to that extent to say that the planets have an effect on it. If there was no mass there would be no center of mass.
Robert Tulip
2011Jun15, 10:40 PM
15108
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15107
A further way to illustrate the gas giant conjunction cycle is shown in the attached diagrams using the solar system simulator at http://dd.dynamicdiagrams.com/wpcontent/uploads/2011/01/orrery_2006.swf
These diagrams show JupiterSaturnNeptune triple conjunctions every 179 years from 1345 to 2060, with Saturn slowly drifting back against the other two planets. It can also readily be seen how each successive conjunction is thirty degrees of arc further around the ecliptic. These three planets have the strongest effect on the position of the center of mass of the solar system.
Please look at all five attachments in order. What they show is that Jupiter, Saturn and Neptune come together like the hour hand of a twelve hour clock face, with their successive conjunction points at the hour points of the clock. What I find very interesting in this observation is that the twelve 'hours' of the clock match closely to the 2148 year period of precession of earth's equinox by one ecliptic sign, thirty degrees.
Robert Tulip
2011Jun18, 02:02 AM
Putting this 'solar system planet clock' into an even simpler format, the attached diagrams add an hour and minute hand to the successive diagrams of the solar system over 2500 years to show how closely the successive Jupiter Saturn Neptune conjunctions form a bigger cycle in which they return close to their original positions after twelve 'hours', or 2148 years.
This solar system planet clock is an empirical way to understand the solar system as a temporal whole. The cycle described here is a rhythm of the entire system, seen in the way these three gas giants shift the sun in a regular pattern against the center of mass, which is the point around which the whole system moves in its majestic arc around the galaxy. To note, Uranus does not visibly affect the main pattern of the barycenter to anywhere near the extent that Neptune does, because Neptune is so much further away. The main barycenter cycle is caused by Jupiter and Saturn, which as Newton discovered cause a twenty year wave pattern of the barycenter. The material I am presenting shows how this main JS pattern is modulated into families of similar wave patterns by Neptune.
The same twelve hour clock pattern which is the basis of our ordinary clock is embedded in the entire system at this level.
It opens the speculative possibility, although this is something that I cannot prove, that the earth is in harmonic resonance with the entire solar system, with the precession of the equinox nested within the twelve 'hour' period of the solar system gas giant planet clock. This idea of a terrestrial resonance is only speculative, but the fact is that the regular pattern of the earthmoon system has existed within this larger regular pattern of the whole solar system since the solar system stabilised nearly four billion years ago. I do not offer this speculation of a possible resonance as in any way against the mainstream, but rather just as a question, asking if it helps to explore how the whole solar system is a temporal unity with a definite structure. The period and dynamics of terrestrial wobble are fairly well understood, but this material does open the intriguing question of whether the lunisolar torque framework of precession has a larger systemic context in which it is nested.
In astronomy, cycles such as this one that involve multiple objects often drift in and out of phase. A good example is the eclipse cycle of the moon, known as the Saros cycle, whereby eclipses form overlapping families of eclipses separated by eighteen years, beginning with weak eclipses, growing to exact alignment, and then moving again out of alignment. There are exact resonances, such as between Jupiter's moons, but this one here between the gas giants is a bigger and more complex wholistic description of the temporal structure of the entire solar system.
The diagrams below illustrate how the JupiterNeptune conjunction cycle forms the 'hour hand' of the solar system planet clock, with Saturn drifting in and out of alignment in long cycle families. The two families of conjunctions that currently exist are centered respectively on near exact alignments in 591 AD, for cycle 1, and in 1523 AD for cycle 2. Looking at the diagrams, readers can see that the further in time from these central points, the further Saturn is from exact alignment, and how over time Saturn drifts across the JN conjunction point. Every 179 years there are 9 JS conjunctions, 5 SN conjunctions and 14 JN conjunctions. The diagrams here could have equally been presented using the SaturnNeptune exact alignment as the hour hand, with Jupiter drifting in and out of alignment, or less exactly, with the JupiterSaturn alignment as the hour hand, with Neptune drifting across.
The minute hand of the clock, moving only about 25 minutes in 2500 years, illustrates how very close this cycle is to a precise marker of terrestrial precession, with the triple conjunction every 179 years occurring close to thirty degrees after the last one, such that 12 of these recurring twelve 'hour' stable patterns are very close to equal to the 25,765 year period of terrestrial spin wobble.
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Robert Tulip
2011Jun18, 02:06 AM
Continuing previous post, attached diagrams are for the cycle 2, centered in 1523. Attachments to previous post are for cycle 1, centered in 591 AD.
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Robert Tulip
2012Aug23, 11:35 AM
Using Fourier Transform I have produced the attached Spectrum of the Solar System Barycentre ephemeris over 4096 years from 3000 BC (http://cosmoquest.org/forum/attachment.php?attachmentid=17455&stc=1&d=1345721023), using JPL data.
We see here the following primary barycentric frequencies of the solar system in peak order, with their apparent planetary drivers.
1. 19.85 years: Jupiter Saturn Cycle
2. 12.8 years: Jupiter Neptune Cycle
3. 13.8 years: Jupiter Uranus Cycle
4. 35.9 years: Saturn Neptune Cycle
5. 11.9 years: Jupiter Cycle
6. 7.8 years: unknown
7. 45.5 years: Saturn Uranus Cycle
8. 9.9 years: 1/2 Jupiter Saturn?
9. 8.2 years: unknown
10. 29.5 years: Saturn cycle
11. 171 years: Uranus Neptune cycle
I thought the triple cycle of JupiterSaturnNeptune at 178.9 years would appear in this spectrum. It does not appear because it is a near exact multiple of cycles 1, 2 and 4.
I would be grateful if more informed readers could help me to help understand this material. My statistician friend tells me I can plug the exact numbers in to the fourier transform to refine the analysis. I would be interested in opinion regarding causes of peaks 6, 8 and 9 in the list above.
We see here that Fourier Transform is well suited to depict the barycentric cycles of the solar system. I would be interested in references to similar analysis.
Shaula
2012Aug24, 08:55 AM
What windowing function did you use? What size window? Did you use any post processing?
Robert Tulip
2012Aug24, 12:58 PM
What windowing function did you use? What size window? Did you use any post processing?
Shaula thanks.
I come at these issues from quite an unusual position, in that my academic study was in philosophy, not physics, but I approach philosophy from the viewpoint that astronomy is the foundation of truth. So this thread is about the structure of the solar system, as the context of real time, to use some more abstract concepts. So please bear with my very limited grasp of physics terminology.
I just read Ice Ages and Astronomical Causes by Muller and MacDonald. That was really the first time I had any detailed exposure to Fourier Transform. I come at these ideas as a rank amateur, but with an interest in the scientific explanation. My hope is that if I can understand it so can anyone.
What that book suggested to me was that the wave function of the solar system barycenter data would produce spectral peaks at the main planetary pairs. And indeed it does.
I took the JPL SSB data, which are monthly, and selected just the first data point for each year from 3000 BC to 1095 AD. This annual sampling makes no difference to the result because the curve of the annual data will produce the same Fourier Transform chart as the monthly data. The program I used had a limit of 4096 data points, so I wanted to get years rather than months. 4096 months = 341 years, so the 172 year UranusNeptune cycle might not show as strongly if I used months. I could have used a longer period to make use of the full 6000 years of data available from the Jet Propulsion Laboratory, but considered 4096 years would be a good sample.
I looked up Window function (http://en.wikipedia.org/wiki/Window_function) in response to Shaula's question, and am really not sure how it is relevant as I am not using any zero valuing.
In producing the transform, I got a friend who is a statistician to help me. There is no post processing as far as I understand it; I just gave him a spreadsheet with 4096 data points and he sent me back a spreadsheet with columns headed Fourier Transform; Modulus; Real; Imag; 4096 * freq; freq; Period. He told me to chart the modulus column as Y against Period as X. I will give the spreadsheet to anyone who wants it.
Earlier in this thread I have discussed the effects of the outer planets on the barycenter, so I know what to look for in terms of precise planetary periods that should make the main peaks in the graph. The transform produces these peaks quite beautifully and precisely, showing the strength of influence of each planetary pair and planet on the barycenter movement.
But there are also small peaks which look significant but do not match to any of the main planetary factors as far as I can tell. Hence my question here and in Q&A.
ETA: This spectrum of the central function of the solar system shows planetary patterns that are very slow to change, possibly existing over millions or billions of years.
Shaula
2012Aug24, 06:04 PM
No windowing? Then I have concerns. Windowing functions are essential to prevent Gibbs wiggles.
As Tusenfem said in the other post we need to know certain parameters before we can speculate on what the peaks are. Is it a 4096 point FFT?
Robert Tulip
2012Aug24, 10:10 PM
Replying here to Q&A comment

Depending on your sampling frequency of the data f_s, there is the socalled Nyqvist frequency f_ny = 0.5 f_s, telling you the highest frequency that you can measure in your power spectrum. As you put in period on the xaxis this translates in the lowest period you can measure.
Now one interesting thing is, that if you have a signal with higher frequencies in it than the Nyqvist frequency, you can still get information on these frequencies, as they will be "folded around" f_ny, which means if you have a frequency in your signal that is df higher than f_ny, then you will see a peak in your power spectrum at f_ny  df.
Maybe the periods that you looked at result from folded frequencies.
http://en.wikipedia.org/wiki/Nyquist_frequency and http://en.wikipedia.org/wiki/Aliasing#Folding refers to an effect that causes different signals to become indistinguishable (or aliases of one another) when sampled. Aliasing refers to the appearance of higher frequencies when the sampling rate is lower.
In this example, the sampling rate is one year, and the shortest peak frequencies have period seven years, up to the slowest frequency of period 172 years (Uranus Neptune conjunction). Nyqvist frequency is not relevant in such a case, as I understand it.
The deleted monthly data makes no difference to the peaks, because the wave function is so slow, with the main cycle in the SSB the 20 year JupiterSaturn cycle. In this case the monthly data could easily be interpolated in between the annual points.
No windowing? Then I have concerns. Windowing functions are essential to prevent Gibbs wiggles. As Tusenfem said in the other post we need to know certain parameters before we can speculate on what the peaks are. Is it a 4096 point FFT?
Gibbs wiggles are discussed at http://en.wikipedia.org/wiki/Ringing_artifacts : "The main cause of ringing artifacts is due to a signal being bandlimited (specifically, not having high frequencies) or passed through a lowpass filter; this is the frequency domain description. In terms of the time domain, the cause of this type of ringing is the ripples in the sinc function,[1] which is the impulse response (time domain representation) of a perfect lowpass filter. Mathematically, this is called the Gibbs phenomenon (http://en.wikipedia.org/wiki/Gibbs_phenomenon)."
There are no significant artifacts in this data, which precisely matches and illustrates prediction. The order of peaks reflects the size and distance of the gas giants in their effect on the position of the sun. The beauty of this example is that the Newtonian mechanics of planetary orbits produces continuous wave functions without the type of signal problems of ringing seen in other fields.
The chart above produced from the 4096 years of continuous SSB data from 3000 BC shows the interesting part with the real peaks between 172 and 7 years. There is also a long tail to the graph going down to two years which I can also provide, but I deleted it from the shown illustration as it is mainly just a flat line.
Shaula
2012Aug24, 10:30 PM
There are no significant artifacts in this data, which precisely matches and illustrates prediction. The order of peaks reflects the size and distance of the gas giants in their effect on the position of the sun. The beauty of this example is that the Newtonian mechanics of planetary orbits produces continuous wave functions without the type of signal problems of ringing seen in other fields.
The ringing effects are simply due to the fact that your signal is not infinite in length. A pure sinusoidal signal is only possible in an infinite length signal and so the HF noise comes from terms that are added in to cause your sinusoids to cut off  at the edges of your data set. So it is good practise to window your data. The HF artefacts would not create the new peaks but would modify the background.
If this data precisely matches predictions then surely you know what the peaks you have asked about are? After all, it matches predictions perfectly.
If you could ask your friend what was the FFT size he used that would help in understanding this.
Robert Tulip
2012Aug25, 12:21 AM
The ringing effects are simply due to the fact that your signal is not infinite in length. A pure sinusoidal signal is only possible in an infinite length signal and so the HF noise comes from terms that are added in to cause your sinusoids to cut off  at the edges of your data set. So it is good practise to window your data. The HF artefacts would not create the new peaks but would modify the background.
If this data precisely matches predictions then surely you know what the peaks you have asked about are? After all, it matches predictions perfectly.
If you could ask your friend what was the FFT size he used that would help in understanding this.
Thanks again, I appreciate your interest and help.
As I stated above, the main peaks have obvious planetary causes. It is these smaller peaks 6, 8 and 9 that are a mystery to me, hence my question to try to understand it. I will provide the spreadsheet with the details of the FFT data.
We see here the following primary barycentric frequencies of the solar system in peak order, with their apparent planetary drivers.
I have added in the power of each peak, as can be readily seen against the chart, with the percentages of each peak against the sum of these 11 peaks, and the actual orbital periods, which match the peaks as shown. The unknown peaks are 8% of the total power.
Cycle FFT Peak in years A B Power % Actual Period
1 19.85 Jupiter Saturn 983 40.9% 19.85
2 12.8 Jupiter Neptune 419 17.4% 12.78
3 13.8 Jupiter Uranus 190 7.9% 13.81
4 35.9 Saturn Neptune 189 7.9% 35.87
5 11.9 Jupiter Cycle 137 5.7% 11.86
6 7.8 unknown 128 5.3%
7 45.5 Saturn Uranus 96 4.0% 45.37
8 9.9 Jupiter Saturn? 75 3.1% 9.93
9 8.2 unknown 72 3.0%
10 29.5 Saturn cycle 59 2.5% 29.46
11 171 Uranus Neptune 57 2.4% 171.37
2405 100.0%
It is interesting that the JupiterNeptune peak is double the power of the JupiterUranus peak. Neptune is so much further away that it 'pulls' the barycenter more than Uranus does.
Robert Tulip
2012Aug25, 06:45 AM
The spreadsheet with the data for this material is at Solar System Barycenter Fourier Spectrum.xlsx (http://rtulip.net/yahoo_site_admin/assets/docs/Solar_System_Barycenter_Fourier_Spectrum.236231301 .xlsx). (1MB)
The steps to produce the graph were
1. Obtain JPL SSB Sun Distance data for 4096 years from 3000BC to 1095 AD. (Column A)
2. Subtract mean from each data point. (Column B)
3. Fourier Transform (Column C)
4. Extract Modulus from imaginary number (IMABS function) (Column D)
5. Add Column E showing years (3000 BC = 0, 1095 AD = 4096)
6. Determine period for each row (4096/year) (Columns F G)
7. Chart modulus as Y axis, period as X axis for first 600 rows.
This process provides a clear visual indication of the main planetary influences on the system barycenter.
Shaula
2012Aug25, 07:33 AM
Step 6 implies you took a 4096 point FFT.
Why are you taking the modulus of the real part? Normally to establish power you take the sum square of the two components. You are not plotting power you are plotting the modulus of the coefficients of the cosine components of the Fourier series. Your power column should be the Fourier term squared. Might explain why your signal is so clean!
Robert Tulip
2012Aug25, 09:15 AM
Step 6 implies you took a 4096 point FFT.
Yes, as I mentioned at #63 I selected just the first data point for each year from 3000 BC to 1095 AD.
Why are you taking the modulus of the real part? Normally to establish power you take the sum square of the two components. You are not plotting power you are plotting the modulus of the coefficients of the cosine components of the Fourier series. Your power column should be the Fourier term squared. Might explain why your signal is so clean!
I don't think it is the modulus of the real part. For example in Row 2 we have (rounded) Fourier Transform of 0.5+7i and modulus of =IMABS(0.5+7i) = 0.513. IMABS function returns the absolute value (modulus) of a complex number in x + yi text format. I do not understand your comment about power.
The signal is so clean because these planetary cycles are the physical cause of the barycenter function, and this decomposition of the solar signal is just a way to illustrate the strength of the inputs.
On a further question, could the single planetary peaks (eg Jupiter 11.85 years) just be due to eccentricity?
Shaula
2012Aug25, 09:54 AM
OK, was assuming that the abs function worked like a basic abs function. I should have spotted that it had IM in front of it. A lot of built in ABS functions are actually doing a REAL() on imaginary numbers. Either way your 'power' column is not a power spectral density. That is a squared term. It is a useful comparison term though  I was just pointing out that the terminology is slightly off.
Yes, as I mentioned at #63 I selected just the first data point for each year from 3000 BC to 1095 AD.
You have 4096 data points. There are numerous ways to FFT them. You can take one 4096 FFT (usually the noisiest way but give the greatest frequency range), you could take multiple windows of 256 points, of 128 points or any other number (but powers of two are neatest) and combine them. These smaller window FFTs give less of a range of frequency but are useful for generating smoother results. That is what I am getting at. I think you have opted for the one huge FFT approach.
The signal is so clean because these planetary cycles are the physical cause of the barycenter function, and this decomposition of the solar signal is just a way to illustrate the strength of the inputs.
I am surprised at how smooth the background is. That is what I mean by clean. It has little to do with the physical mechanism and more to do with the sampling method, data errors and so on.
Robert Tulip
2012Aug25, 01:14 PM
your 'power' column is not a power spectral density. That is a squared term. It is a useful comparison term though  I was just pointing out that the terminology is slightly off.Being primarily self taught in these matters means I sometimes use words wrongly. Here, especially given the clean background, it looks like the power of the spectral lines is strong, but I'm not sure if that is the right way to describe it.
You have 4096 data points. There are numerous ways to FFT them. You can take one 4096 FFT (usually the noisiest way but give the greatest frequency range), you could take multiple windows of 256 points, of 128 points or any other number (but powers of two are neatest) and combine them. These smaller window FFTs give less of a range of frequency but are useful for generating smoother results. That is what I am getting at. I think you have opted for the one huge FFT approach.
But would smaller windows disemphasise the slowest cycles, such as the 171 year UranusNeptune cycle? I don't see any advantage in multiple windows in this instance since there is so little noise, but will have a look.
I am surprised at how smooth the background is. That is what I mean by clean. It has little to do with the physical mechanism and more to do with the sampling method, data errors and so on.
I disagree that it has little to do with the physical mechanism. The SSBsun distance is a sine function composed of these planetary effects, and pretty well nothing else. The planetary cycles are very stable, so we should expect the narrow peaks as shown in the FFT chart. The conformance of this chart with the expectation (except for the minor peaks which I have asked about) indicates the causality is clear and the calculation is correct. There is little reason to expect data error in the JPL ephemeris for the SSB as it provides a core integrating measure of all the motion of the solar system over historical time frame.
I've just read a fascinating book called The Neptune File, about the discovery of Neptune, which shows how tiny errors in prediction of planetary positions provided the basis for our current accurate model of the solar system. That is the great beauty of Newtonian celestial mechanics, its wonderful accuracy.
Yes there is small accumulative error in this data which reconstructs the situation back to 5012 years ago, but that error is not the cause of the smooth background of this FFT.
tusenfem
2012Aug25, 02:20 PM
Yes, as I mentioned at #63 I selected just the first data point for each year from 3000 BC to 1095 AD.
I don't think it is the modulus of the real part. For example in Row 2 we have (rounded) Fourier Transform of 0.5+7i and modulus of =IMABS(0.5+7i) = 0.513. IMABS function returns the absolute value (modulus) of a complex number in x + yi text format. I do not understand your comment about power.
I do hope that you have a typo there in your complex number 0.5 + 7i, because that has not a "modulus" of 0.513.
I assume you just took the points (each first point of the year) and put that list into an FFT, with a data set of 4096 point that is childs play for a normal software.
The FFT gives you a transform, with the length of the data set and the sampling rate you get your frequency estimates, and the FFT will give you conjugate values for the results, so you throw away half of the information, because that belongs to negative frequencies.
So you have your frequency step df = 1 / total interval (= 1/4096), and you have the Nyqvist frequency as 0.5 sampling frequency (= 2 years), now talking in units of years.
Then you take for the positive frequencies FFT^2, which in frequency space gives you the power of the peaks (note that these are complex numbers, so you multiply a+bi with abi, and thus have a^2+b^2) in unit^2/Hz (if you would do this in real units for frequency and not "per year"), as shaula also told you.
I don't know what IMABS does, but I assume you had a typo there, however also wit 0.5+0.7i the modulus would still not be 0.513, however that is a problem you will have to solve for yourself.
I am not at work now, so I don't have my spectral analysis tools (Matlab) at hand. However, it is usual to use a window to get rid of boundary effects and is it also ususal to average over at least 7 spectral estimates.
However, I don't see why only take one data point for each year. That will undersample the inner planets, albeit at small mass, they will still have an influence on the barycentre. So the first thing to do is make your data set monthly at the least.
In my personal opinion (and my papers) I want at least an interval in which three periods of the longest signal that I am interested in fit in.
And then to know whether your power spectrum peaks are significant, then you will have to look at your data set, look at the standard deviation of the set, subtract a fit of the background on which the peaks are superimposed and then using the standard deviation find the 95% confidence level of the peaks in your spectrum (which is roughly 3 times the standard deviation, but is dependent on sampling rate, number of points etc.)
FFT is a wonderful tool, but it does come with some nooks and crannies.
Robert Tulip
2012Aug25, 03:21 PM
I do hope that you have a typo there in your complex number 0.5 + 7i, because that has not a "modulus" of 0.513.
Yes, I misread the cell. It was 0.511057160381806+7.01209504964108E002i and the modulus is 0.515845295. Sorry, and thanks for checking.
I don't see why only take one data point for each year. That will undersample the inner planets, albeit at small mass, they will still have an influence on the barycentre. So the first thing to do is make your data set monthly at the least.
Okay will look at that. There is a good Orbit Simulator website which successively subtracts each planet from the SSB function (http://www.orbitsimulator.com/gravity/articles/ssbarycenter.html). It shows the gas giants at scale of million km and inner planets at scale of 100 km, which is why I ignored the inner planets and assumed annual data is accurate for this purpose.
I am having trouble finding the SSB dataset at http://ssd.jpl.nasa.gov/?horizons There's got to be a pony in there somewhere.
In my personal opinion (and my papers) I want at least an interval in which three periods of the longest signal that I am interested in fit in.
And then to know whether your power spectrum peaks are significant, then you will have to look at your data set, look at the standard deviation of the set, subtract a fit of the background on which the peaks are superimposed and then using the standard deviation find the 95% confidence level of the peaks in your spectrum (which is roughly 3 times the standard deviation, but is dependent on sampling rate, number of points etc.)
FFT is a wonderful tool, but it does come with some nooks and crannies.
I would need help to follow up with such analysis. But I am looking at it as a simple depiction of the integrated patterns of the solar system, and for that purpose I think the method I have used is sufficient.
Robert Tulip
2012Aug26, 02:20 AM
Here we see the SSB spectrum using 25 day steps (http://cosmoquest.org/forum/attachment.php?attachmentid=17463&stc=1&d=1345946963) based on 4096 data points from 3000 BC to 2720 BC.
This chart confirms the shape of the annual graphing, with the peaks again matching to the same gas giant cycles as listed above, as well as the unknown peak at 7.8 years, but with the slowest cycle (UranusNeptune) not picked up except by the rough first number at 140 years.
I don't think the 7.8 year peak matches to anything from the inner planets, so it remains a mystery.
All the information in this model is in the first 40 points of the chart. I assume that windowing would provide more detailed analysis.
Shaula
2012Aug26, 07:49 AM
Windowing would drive down the background. Which you have plenty of there. You need to so this to work out how significant those peaks are. Personally I am not sure they are significant enough to call features in the FFT (look to be 2 sigma or so). Because you have not done any windowing, and because this is a one shot 4096 point FFT. When I am looking at features like this I often use multiple FFT windows and look for these peaks in all appropriate FFTs. Frequency space artefacts are a real pain.
tusenfem
2012Aug26, 08:23 AM
Here we see the SSB spectrum using 25 day steps (http://cosmoquest.org/forum/attachment.php?attachmentid=17463&stc=1&d=1345946963) based on 4096 data points from 3000 BC to 2720 BC.
How can you have 25 day window when your data are yearly?
Apart from that I use an extra window in the fourier domain to get rid of sidebands of the fft, willl give a description of the routine tomorrow when I am back at my desk.
Robert Tulip
2012Aug27, 01:32 AM
The JPL data is for every 25 days. In presenting the data I initially selected yearly datapoints because the SSB position barely changes in a year. In response to your suggestion I redid the analysis using the more detailed 25 day data over a shorter total time period.
tusenfem
2012Aug27, 01:33 PM
Okay just to give a short overview of what I (would) do with the data set.
As said before I would use monthly points, that will give you enough resolution to also find the minor components. The interesting thing is that it comes (most likely) from a model at JPL, which means that you have a rather clean dataset.
FFT works best on 2^n data points, but differing from that is not too much of a problem, but take at least an interval that has 3 periods of the longest period you deem interesting in your work.
Here is the Matlab setup that I use.
Then take your data set "data" and create fdata = FFT(data).
Then on fdata you put a "geo filter" which takes away the side bands. My colleague who made this filter took it from "Otnes & Enochson: Digital time series analysis" and had the following form of the filter:
fil = [.1476, .1707, .1817, 1.0, .1817, .1707, .1476];
and then run the "filter" function of Matlab to "smooth" the fdata.
Then you get the power through: P = fdata.*conj(fdata)
Then you do a running average over nh harmonics of the power P to smooth the result: smP
In order to find whether the peaks that you have are significant or not, I take the smP and make a 3rd order polynomial which I subtract from the smP, smPmin. I also calculate the standard deviation of smPmin: std.
Then to find the 95% significance level you take about a factor 2, so v = 2 * std.
And to get the confidence level you need to take the square root so conf = sqrt(v).
Then one takes the average of smPmin: mean(smPmin)
And then you plot the smPmin versus frequency and the line mean+conf, which will show which peaks can be trusted in your signal.
Hope this helps.
Robert Tulip
2012Aug31, 11:45 AM
Windowing can't be expected to add much since this spectrum is derived from calculation rather than observation. JPL used the observed positions and movements of the planets to compute the position of the sun over the last 5000 years, unlike most wave functions which are collected from observation. Windowing is most relevant, as I understand it, when a wave function is from real data. Here, the described planetary pairs are the main input to the calculation of the barycenter function, so the spectral peaks are expected as a product of the inputs to the calculation. The order of peaks is just as expected.
The point here is just to illustrate the main planetary inputs for the barycenter in a simple graphic presentation.
Windowing should confirm the relative size and position of the spectral peaks, so I will analyse the data further from different time periods.
The problem remains that the peaks at 7.8 and 8.2 years do not match any planetary cause as far as I can see. If readers here cannot explain these anomalies, perhaps you can recommend experts who could?
Shaula
2012Aug31, 11:51 AM
Windowing is important. You have two people with experience in frequency analysis telling you this. You have said you have no background in this. Why do you keep arguing that it is unimportant? Please justify your stance on this and explain in detail the reasons behind your position. References would be nice. To signal processing papers or books, not Wikipedia.
tusenfem
2012Aug31, 08:30 PM
when I get back from my conference (I am at the 11th international conference on substorms next week) why don't you send me your data set and I will run it through my programme to see what result I get. Spectral analysis is not so easy if you want to do it right.
I don't known what would be the two periods 7.8 and 8.2, however, that looks like one broad peak to me and not two separate peaks in your last figure. However, it could well be some beat frequency that you have not thought of.
Robert Tulip
2012Aug31, 11:23 PM
Windowing is important. You have two people with experience in frequency analysis telling you this. You have said you have no background in this. Why do you keep arguing that it is unimportant? Please justify your stance on this and explain in detail the reasons behind your position. References would be nice. To signal processing papers or books, not Wikipedia.
Shaula, no disrespect at all intended. I should have phrased my last comment as a question rather than an assertion. I appreciate your help.
The reason I wonder about the value of windowing in this instance is that in my limited reading, it appears windowing is most useful when you are working with actual data  an ice core record or a mass spectrometric ion analysis or an audio signal. But in this case there is little actual data  the numbers from before discovery of Neptune are entirely calculated from Newtonian formula. The inputs to the formula are the planetary positions which cause the sun to move with respect to the barycenter.
Adding together a bunch of sine waves, a spectral analysis of the resulting wave will just give the original inputs. That is all that is happening here, as far as I can tell.
The cleanness of the original background indicates that the formula used by JPL is derived from these main planetary patterns. Newton proposed this basic method in his Principia using just Jupiter and Saturn to calculate the barycenter. So this spectrum is just a way to illustrate what is there in the method used to derive the numbers, showing the system planetary influences on the barycenter in order of their power. It is just illustration, not discovery, because these wave functions were the basis for NASA to calculate the dataset.
I am going to proceed with comparing the spectrum in different millennia, with the expectation there will be very little difference.
Here is the SSB data from JPL at 25 day steps from 3000 BC to 1485 AD (http://rtulip.net/yahoo_site_admin/assets/docs/SSB_Radius_3000bc1485ad.243172925.xlsx). (Excel spreadsheet 1.5 MB)
Robert Tulip
2012Sep01, 02:34 AM
17475
Using 50 day steps so the 4096 data points each provide a period of 540 years, three times the maximum planetary period under study (Uranus Neptune 171 years), this SSB Spectrum chart shows six spectral lines for successive 540 year periods (http://cosmoquest.org/forum/attachment.php?attachmentid=17475&d=1346466724).
It shows that the peaks are precise, and that the mysterious twin peaks at 7.8 and 8.2 years appear with granulated data.
I have emailed the JPL contact at http://ssd.jpl.nasa.gov/horizons.cgi to ask about how to define parameters to extract this data from horizons ephemeris and why these short wave peaks appear.
Robert Tulip
2012Sep01, 03:29 AM
The NASA person I emailed has kindly got back to me, and recommended this link to discussion on Newhall et al : DE102 numerically integrated ephemeris (http://articles.adsabs.harvard.edu/cgibin/nphiarticle_query?bibcode=1983A%26A...125..150N&db_key=AST&page_ind=3&plate_select=NO&data_type=GIF&type=SCREEN_GIF&classic=YES).
As well, the following advice: "The planetary ephemerides are not derived from a formula (in which periodicities might be "put in"). We are oblivious to periodicities when solving for planetary orbits. Instead, orbit solutions come from a numerical integration of 2nd order differential equations of relativistic gravitational motion in which periodicities are emergent properties of the physics and a fit to measurement data. You might be interested in work by Bretagnon; he and others deliberately fit periodic functions afterthefact to the numerically integrated planetary ephemerides so, in a sense, they deliberately "put in" periodicities as necessary to approximate the actual result."
Robert Tulip
2012Sep02, 11:13 AM
Relating this material on spectral analysis of the barycenter to the topic of this thread, the primary cyclic structure of the solar system, the attached diagram provides a helpful way to illustrate the long term patterns. The spectral analysis has proved the identity of the main planetary causes. These can be shown in their combined effect.
Each line of the graph provides a successive wave function of the distance from the sun to the barycenter over 179 years (http://cosmoquest.org/forum/attachment.php?attachmentid=17481&d=1346584000). The bottom line shows the SSB distance from 3000 BC to 2821 BC, while the top row shows the distance between 1294 AD and 1473 AD. This form of presentation was designed (http://plasmaresources.com/ozwx/SSB/images/SSB_179y_cycles_9952985AD.jpg) by the late Carl Smith (http://astrosage.blogspot.com.au/2009/07/carlbsmithseptember071952june24.html). Each row is almost identical to the adjacent rows, showing how similar the pattern is every 179 years, but over the 4000 years of the chart there is considerable change.
Why 179 years? Building on my table at #67, 179 years is the smallest number that is near a common multiple of the planetary combinations that drive the barycenter position. The table below shows the % variance in each planetary cycle after 178.9 years (http://cosmoquest.org/forum/attachment.php?attachmentid=17480&d=1346583999). Removing UranusNeptune (row 11) as the outlier at 4.5% (but only 2.4% of the spectral peak total) leaves all the stronger spectral wave functions as close divisors of 179, with level of variance as indicated.
What this means is that every 179 years, the gas giants are close to the same relative positions to each other, so the SSB Sun distance will always be close to the same as it was 179 years before. The minor difference between the gas giant orbital cycles over this period is the cause of the very gradual change seen in the wave pattern.
With the wave chart, a further point of interest is that each row has a vertical axis of symmetry. The reason for this is that considering JS, JN and SN as the primary drivers, with their triple conjunction every 179 years, any number of years before or after this triple conjunction will shift the barycenter by an almost equal amount.
17480
17481
Robert Tulip
2013Jan07, 12:23 PM
17861
In studying this helix model of the solar system, the method of graphing the solar barycenter function pioneered by the late Carl Smith continues to intrigue me. Here is an empirical rendering that could be called Throb of the Sun, Pulse of the Solar System, Structure of Time. It depicts the distance from the sun to the solar system center of mass over 6000 years, 179 years per line, to show the 179 year wave function produced by the orbits of the gas giants. (http://rtulip.net/yahoo_site_admin/assets/docs/6000_years_SSB_chart2.641508.xlsx)
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