# Thread: Is the Solar System's Barycenter Inside or Outside the Sun?

1. Originally Posted by Hornblower
In the Wiki article to which Robert Tulip linked in response to my most recent questions, the author said the Fourier transform treatment has a lot of use in electrical engineering, and made a vague reference to cosmology. Nothing about application to orbital mechanics. I cannot tell whether or not it is anything more than a mathematical curiosity as presented in this thread.
Fourier Transform is of use for signal processing. The wave function of the sun against the barycenter can be treated as a signal. When this signal is processed, it shows strong peaks at the predicted points, decomposing the solar radius measure into its component planetary functions. See https://en.wikipedia.org/wiki/Signal_processing and https://en.wikipedia.org/wiki/Functi...nal_processing for more information to validate this method.

When I asked NASA how they produced their barycenter data, they explained the incremental computation process, by shifting all the planets by a set time period and recalculating. This method produces a wave function which can be decomposed to illustrate its planetary drivers.

My interest now is that most of the component signals match to the expected planetary drivers (eg the Jupiter Saturn cycle produces more than 40% of the power of the barycenter wave function) but some of the component signals do not match to any planetary factor known to me.

As linked earlier in this thread, I raised this at BAUT in 2012 and received extremely helpful replies from Shaula and Tusenfem.

2. Now I can see applying this analysis in a thought exercise. An alien astronomer with the spectrograph of our dreams detects the Sun's looping motion from its Doppler shift. Perhaps he could tease out the periodic components from what at a glance looks like an irregular jumble and infer the masses and orbital elements of the four giant planets.

3. Originally Posted by Hornblower
Now I can see applying this analysis in a thought exercise. An alien astronomer with the spectrograph of our dreams detects the Sun's looping motion from its Doppler shift. Perhaps he could tease out the periodic components from what at a glance looks like an irregular jumble and infer the masses and orbital elements of the four giant planets.
Isn't that exactly what exoplanet hunters do?

4. Originally Posted by grapes
Isn't that exactly what exoplanet hunters do?
I am pretty sure that is what they are doing when they encounter multiple orbital periods. I don't know whether or not they have found a Doppler signal for something as far out and slow as Neptune and its corresponding term in the Sun's motion.

5. Originally Posted by Robert Tulip
When I asked NASA how they produced their barycenter data, they explained the incremental computation process, by shifting all the planets by a set time period and recalculating. This method produces a wave function which can be decomposed to illustrate its planetary drivers.
Is there a name for that method? I use the term iterations, but perhaps there is a better name for it; there should be. I'm fairly sure this is required for all but 2-body models.

Apparently, only recently has there been effective mathematical work regarding chaos in orbital mechanics. Resonance in precession ratios has also come into play, though these are long period factors.

6. Originally Posted by Hornblower
Now I can see applying this analysis in a thought exercise. An alien astronomer with the spectrograph of our dreams detects the Sun's looping motion from its Doppler shift. Perhaps he could tease out the periodic components from what at a glance looks like an irregular jumble and infer the masses and orbital elements of the four giant planets.
Yes, and the great thing about having so much planetary data already in the solar system is that NASA has used it to produce a 6000 year system barycenter calculation. To get a similar thing for other stars we might need to keep watching to the year 8000 AD, inferring the planetary orbits from Doppler Shift?

7. Originally Posted by George
Is there a name for that method? I use the term iterations, but perhaps there is a better name for it; there should be. I'm fairly sure this is required for all but 2-body models.

Apparently, only recently has there been effective mathematical work regarding chaos in orbital mechanics. Resonance in precession ratios has also come into play, though these are long period factors.
https://forum.cosmoquest.org/showthr...66#post2059466
Originally Posted by Robert Tulip
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.

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 after-the-fact to the numerically integrated planetary ephemerides so, in a sense, they deliberately "put in" periodicities as necessary to approximate the actual result."

8. "Numerical integration" (or "numerically integrated ephemeris") seems like a lousy term. What other kind of integration is there, alphabetical integration? What other things can have integration applied to them? Essentially, everything that moves, or is 2 or more dimensional, or....

"Ephemeral integration"
"Ephemeral analysis"
"Ephemeral iterations"
"Orbital elemental iterations"
"Orbital integrations"

??? [Ok, don't take me too serious. ]
Last edited by George; 2017-Mar-30 at 07:57 PM.

9. Originally Posted by George
Resonance in precession ratios has also come into play, though these are long period factors.
George, resonance in precession ratios is a speculative area which I hope will prove fruitful. What examples are you aware of?

A possible example that I have raised previously is that the Solar System Barycenter wave period of 178.9 years driven by the gas giants is 1/144th of the earth's precession period of 25771 years. That means both stand in a one to twelve ratio to the zodiac age period of 2148 years, the time it takes the equinox points to precess by 30 degrees of arc along the ecliptic.

I like to imagine earth's precession as like a gyroscope bouncing on a spinning torus. The analogy is just a weak pictorial model to place the sun and planets, with the earth's spin wobble as the gyroscope enframed by the overall solar system structure of time driven by the gas giants as the torus.

That would mean the earth-moon distance is somehow connected by resonance to the whole solar system orbital structure, that the dynamics of lunisolar torque are regulated by the gas giant orbital periods. It is like when Neptune reached its stable orbit, the earth was part of the whole gravitational net, connected by a precession resonance.

An additional related fact is that each successive conjunction of Jupiter, Saturn and Neptune every 178.9 years is 30 degrees of arc along the ecliptic from the last one, so there are twelve conjunctions in each JSN cycle during a zodiac age.

I am not advocating those resonance ideas as I lack ability to test them, but would be interested in any reasoning to consider them or not.

10. Originally Posted by George
"Numerical integration" (or "numerically integrated ephemeris") seems like a lousy term. What other kind of integration is there, alphabetical integration? What other things can have integration applied to them? Essentially, everything that moves, or is 2 or more dimensional, or....

"Ephemeral integration"
"Ephemeral analysis"
"Ephemeral iterations"
"Orbital elemental iterations"
"Orbital integrations"

??? [Ok, don't take me too serious. ]
Analytic integration is the other kind, which is used whenever possible. It depends on having an exact equation of motion that in a thought exercise will give exact results for whatever numbers we plug in. That is the sort of calculus that luminaries such as Newton and Leibniz developed. With a two body problem we can get an exact expression for position as a function of time if we know the initial positions, velocities and forces at a particular point in time, along with a formula for gravitational force as a function of separation. For three or more bodies, mathematicians have proved that no such exact formula is possible, so we fall back on rough and dirty step by step vector sums which are inherently less accurate. Accuracy is improved by shortening the step size, and it becomes a contest between improved accuracy and available computer time and memory.

11. Originally Posted by Robert Tulip
George, resonance in precession ratios is a speculative area which I hope will prove fruitful. What examples are you aware of?

A possible example that I have raised previously is that the Solar System Barycenter wave period of 178.9 years driven by the gas giants is 1/144th of the earth's precession period of 25771 years. That means both stand in a one to twelve ratio to the zodiac age period of 2148 years, the time it takes the equinox points to precess by 30 degrees of arc along the ecliptic.

I like to imagine earth's precession as like a gyroscope bouncing on a spinning torus. The analogy is just a weak pictorial model to place the sun and planets, with the earth's spin wobble as the gyroscope enframed by the overall solar system structure of time driven by the gas giants as the torus.

That would mean the earth-moon distance is somehow connected by resonance to the whole solar system orbital structure, that the dynamics of lunisolar torque are regulated by the gas giant orbital periods. It is like when Neptune reached its stable orbit, the earth was part of the whole gravitational net, connected by a precession resonance.

An additional related fact is that each successive conjunction of Jupiter, Saturn and Neptune every 178.9 years is 30 degrees of arc along the ecliptic from the last one, so there are twelve conjunctions in each JSN cycle during a zodiac age.

I am not advocating those resonance ideas as I lack ability to test them, but would be interested in any reasoning to consider them or not.
My hunch is that if there were any such true resonances, the orbital dynamics people would have reported them by now. After all, they have done computer simulations that show that a slower precession rate of Earth's spin axis in the absence of the Moon could mean troublesome resonances with the planets.

Alignments of the giant planets which give us the maximum excursion of the Sun from the overall barycenter are not the only ones that would give peaks in their gravitational perturbation analogous to the familiar spring tides. Various combinations of these planets on opposite sides of the Sun could create combined perturbations of the Earth/Moon system that are just as strong, while leaving the Sun nearly at the barycenter.

12. Originally Posted by George
"Numerical integration" (or "numerically integrated ephemeris") seems like a lousy term. What other kind of integration is there, alphabetical integration? What other things can have integration applied to them? Essentially, everything that moves, or is 2 or more dimensional, or....

"Ephemeral integration"
"Ephemeral analysis"
"Ephemeral iterations"
"Orbital elemental iterations"
"Orbital integrations"

??? [Ok, don't take me too serious. ]
Blame David Gibb, apparently
https://en.m.wikipedia.org/wiki/Davi...mathematician)

Your "alphabetic" isn't too far off--usually it's symbolic integration, or, as Hornblower says, analytic integration.

https://en.m.wikipedia.org/wiki/Symbolic_integration

13. Originally Posted by Robert Tulip
I am not advocating those resonance ideas as I lack ability to test them, but would be interested in any reasoning to consider them or not.
I did the math, and using your value 25771, the astrological multiplication did come out very close, but when I looked it up (just googled it I mean), I found values that differed from the ones that you are using. I'm not sure of what the current uncertainty is. If it's not actually that close, would that be a reason to not consider them?

14. Originally Posted by Robert Tulip
George, resonance in precession ratios is a speculative area which I hope will prove fruitful. What examples are you aware of?
They use the term "secular resonance" for this and Google reveals a number of sites, of course. I have begun to do a ceramic read of Morbidelli's, "Modern Celestial Mechanics" (2011). How much good I will do here with it is certainly in doubt, but perhaps it will still be fun.

A possible example that I have raised previously is that the Solar System Barycenter wave period of 178.9 years driven by the gas giants is 1/144th of the earth's precession period of 25771 years. That means both stand in a one to twelve ratio to the zodiac age period of 2148 years, the time it takes the equinox points to precess by 30 degrees of arc along the ecliptic....

An additional related fact is that each successive conjunction of Jupiter, Saturn and Neptune every 178.9 years is 30 degrees of arc along the ecliptic from the last one, so there are twelve conjunctions in each JSN cycle during a zodiac age.
That's interesting, and 12 is almost that of Jupiter's period and closer perhaps if we add its secular precession.

Here (at bottom) is a table and chart of the precession rates. Saturn is about 1 degree per 179 years.

15. Originally Posted by Hornblower
Analytic integration is the other kind, which is used whenever possible.
Ah, of course. My error. Analog computers are especially helpful in many fields. [I recall using them for a vibrations course.] But, playing the "average Joe" roll, "numerical integration" just seems too generic, though adding "ephemerides" changes it, I suppose.

Accuracy is improved by shortening the step size, and it becomes a contest between improved accuracy and available computer time and memory.
I am still a little unclear whether calling this an iteration calculation is correct, but it is, right? I like using this term but don't want to misuse it.

16. Originally Posted by grapes
Blame David Gibb, apparently
https://en.m.wikipedia.org/wiki/Davi...mathematician)

Your "alphabetic" isn't too far off--usually it's symbolic integration, or, as Hornblower says, analytic integration.

https://en.m.wikipedia.org/wiki/Symbolic_integration
You are thinking like a physicist and not like me at all. Alphabetic integration gives you:

Attachment 22233

17. Ha, I wonder how long they spent making sure there was nothing in that soup...

18. Originally Posted by grapes
I did the math, and using your value 25771, the astrological multiplication did come out very close, but when I looked it up (just googled it I mean), I found values that differed from the ones that you are using. I'm not sure of what the current uncertainty is. If it's not actually that close, would that be a reason to not consider them?
It is not my value - https://en.wikipedia.org/wiki/Axial_precession#Values says modern analysis places the range between 25,771.4 and 25,771.575 years for earth's precession period, a difference of about two months.
The constant term of this speed (5,028.796195 arcseconds per century in above equation) corresponds to one full precession circle in 25,771.57534 years (one full circle of 360 degrees divided with 5,028.796195 arcseconds per century)[24] although some other sources put the value at 25771.4 years, leaving a small uncertainty.
The "Great Year" calculation of earth's precession period was traditionally estimated at 25920 years, often rounded to either 26000 or 25800 years. 25920 = 6x6x6x6x4x5 = 144x180. Some people used to like these whole number factors.

Looking at the ratio between the SSB period and earth's spin wobble, 178.9 x 144 = 25761.6. This is ten years short of the calculated precession period of 25771.4 years. The variance from a 144 multiple is given by 25771.4/25761.6 - 1 = 0.038%, close enough to make investigation of a possible relationship a question at least worth asking.

The average wave period 178.9 combines three conjunction periods of Jupiter, Saturn and Neptune. My calculations give these as JS 178.67, JN 178.92, SN 179.36

The orbital dynamics people mentioned by Hornblower might be able to say if this could be a real resonance. But of course the speculative linking of earth's slow orbital wobble to the whole temporal structure of the solar system integrated in the SSB might be too obscure or difficult to investigate properly, and the 1/144 ratio may just be a coincidence.

I only mentioned this here because George raised the topic of precession resonance, and I found this ratio intriguing.

19. It appears to me that the Earth's spin axis orientation stability is marginal at best when compared with a laboratory disk gyroscope that is precessing in response to the constant downward gravitational action of the Earth. After all the Earth is only slightly oblate, in addition to being lumpy and partially fluid, and the gravitational perturbations that make it precess are all over the place and in the long run are chaotic. The celestial mechanics experts have concluded that even very feeble perturbations from the planets can cause the obliquity to drift a large amount over millions of years if the precession period ever gets into any sort of resonance with a particular planet, or perhaps with a combination of planets in conjunction to give the analogy of a spring tide. The precession period varies with the obliquity, so I can entertain the possibility that periodic variations in the overall strength of perturbations from the planets could tweak the precession cycle into some sort of synchronization. Of course I do not have the mathematical tools to test it in principle.

Once again, the strength of the gravitational gradient torque imposed on the Earth by the giant planets has little to do with the Sun's displacement from the overall barycenter. If we put Jupiter on one side and the other giants on the other side, all in a straight line, the Sun's barycentric displacement will be minimal, but the torque on the Earth will be just as strong as with all the planets on the same side. Jupiter contributes about 95% of this torque, Saturn nearly 5%, Uranus and Neptune a total of about 0.1%. My inclination would be to ignore Uranus and Neptune for this purpose. That is a far cry from what my alien astronomers would do if they could observe the Sun's barycentric motion for a thousand years or so and do Fourier transform analysis of it.

20. rj1
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Hi, new to site. This thread looks like it could help answer something I've been pondering for a couple months.

So the solar system barycenter is on position 0,0,0 on an XYZ Cartesian coordinate system, never moving from that point. Everything else around it moves, including the Sun to a small extent compared to planets, moons, asteroids, comets, etc.

Motion of the planets occurs in 3 dimensions that are independent of one another (exception being Earth because the Sun-Earth ecliptic is defined as z=0 I think reading up on it).

I've been thinking about this in terms of the n-body problem from a classical mechanics basis. You could use the precise ephemerides developed by JPL to get planetary positions hundreds to thousands of years apart. The X, Y, and Z positions will independently repeat so many times. If you chose two of say Jupiter on the imaginary Y plane being in the same dimension Y after 1 (or 0.9999 or 1.0001) revolution around the barycenter, everything else in the solar system would have revolved as well but would be in different positions. So in theory the mass of Jupiter could be removed comparing System A to System B in one dimension since the rest of the systems would be equal in that dimension . There would need to be gravitational forces that Jupiter exerts as well that would need to be discounted, but couldn't this be used as a simplification method for n-body systems?

21. Originally Posted by rj1
Hi, new to site. This thread looks like it could help answer something I've been pondering for a couple months.

So the solar system barycenter is on position 0,0,0 on an XYZ Cartesian coordinate system, never moving from that point. Everything else around it moves, including the Sun to a small extent compared to planets, moons, asteroids, comets, etc.

Motion of the planets occurs in 3 dimensions that are independent of one another (exception being Earth because the Sun-Earth ecliptic is defined as z=0 I think reading up on it).

I've been thinking about this in terms of the n-body problem from a classical mechanics basis. You could use the precise ephemerides developed by JPL to get planetary positions hundreds to thousands of years apart. The X, Y, and Z positions will independently repeat so many times. If you chose two of say Jupiter on the imaginary Y plane being in the same dimension Y after 1 (or 0.9999 or 1.0001) revolution around the barycenter, everything else in the solar system would have revolved as well but would be in different positions. So in theory the mass of Jupiter could be removed comparing System A to System B in one dimension since the rest of the systems would be equal in that dimension . There would need to be gravitational forces that Jupiter exerts as well that would need to be discounted, but couldn't this be used as a simplification method for n-body systems?
I cannot make any mathematical sense out of what you are trying to say here. It appears that you have a line of thought that is difficult to express verbally.

22. Order of Kilopi
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Originally Posted by rj1
So the solar system barycenter is on position 0,0,0 on an XYZ Cartesian coordinate system, never moving from that point.
The barycenter between the Sun and all of the other planets ("solar system barycenter") is ]constantly moving because the planets are constantly moving in elliptical orbits with different eccentricities. But we can use the barycenter as the origin of a system of coordinates and define that it is at 0, 0, 0. This has no physical effects and is nothing to do with the n-body problem.

The rest of the unclear post is irrelevant to the thread. However, we cannot merely "discount" a major body in the n-body problem.

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