Spiral Model of Solar System

[Robert Tulip]

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]

Attached is a rough schematic of the relative orbits and a rough superimposition on each other.

[ToSeek]

Moved from General Science to Astronomy.

[Robert Tulip]

Thanks ToSeek. A spiral model is here. 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]

Robert, excuse my ignorance, but what are these models for exactly? Navigation? Observation?

[01101001]

Robert, excuse my ignorance, but what are these models for exactly? Navigation? Observation?

Robert Tulip's first BAUT topic: Science and Astrology. Coincidence?

[PraedSt]

Lol!

Off topic: How do you keep coming up with these past threads? Encyclopaedic memory?

[01101001]

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]

Suddenly, I have this irresistible urge to play with my Slinky.

[orionjim]

Hmmm,
His link looks like our solar systems "current sheet" to me.

See this NASA link:
http://ulysses.jpl.nasa.gov/science/...01JA000299.pdf

Jim

[Robert Tulip]

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]

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]

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]

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.

[Robert Tulip]

.. 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.

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. The notes on this composition are built from the positions of Jupiter, Saturn and Neptune over 179 years with every fourth note a Jupiter-Saturn conjunction/unison. These notes can be mapped as vectors between the planetary helixes.

[tusenfem]

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 Z-axis, which means that there is also a periodic motion "up-and-down" along the Z-axis. So even more deviation from a nice spiral.

Also, the location of the barycentre of the solar system moves at the most 2 R_sun 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 R_sun = 14 10⁸ m / 6 10¹² m = 2 10^-4

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]

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]

the planet's orbits are inclined with respect to the Z-axis, which means that there is also a periodic motion "up-and-down" along the Z-axis. 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 R_sun 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 R_sun = 14 10⁸ m / 6 10¹² m = 2 10^-4This 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 and here. A sine wave model of the contribution of Jupiter, Saturn and Neptune to this path is here.

[Robert Tulip]

Attached 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 2-D representational of a 3-D cylinder. The 5-2 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 puts bars connecting equivalent points on the cylinder. The Jupiter-Saturn 5-2 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]

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]

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]

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 Jupiter-Saturn 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 non-astronomical 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 multi-helix 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]

Robert, are you referring to Kepler’s Third Law which states that the cubes of the planets’ orbital semi-major axes are proportional to the squares of their orbital periods? Are you seeking something like the flawed Titius-Bode Law of orbital sizes? http://en.wikipedia.org/wiki/Titius%E2%80%93Bode_law

[PraedSt]

Attached 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:

A number of near-integer-ratio 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 near-resonances 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 time-scales, 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 time-scales 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). 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]

Continuing my research, please see attached 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 1882-2061. 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 1896-1903 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]

Robert, are you referring to Kepler’s Third Law which states that the cubes of the planets’ orbital semi-major axes are proportional to the squares of their orbital periods? Are you seeking something like the flawed Titius-Bode Law of orbital sizes? http://en.wikipedia.org/wiki/Titius%E2%80%93Bode_law

Hi 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]

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]

The attached diagram 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]

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]

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 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.