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Re: Update: Earth-Moon-Sun Trajectory equations
« Reply #20 on: April 27, 2019, 06:14:34 PM »
KAM theory consequence: the motions are quasi-periodic. This is absolutely fine and fits well with how we understand the solar system.

But it can't be fine.

All Hamiltonian systems which are not integrable are chaotic.

Since the solar system is not integrable, and experiences unpredictable small perturbations, it cannot lie permanently on a KAM torus, and is thus chaotic.

KAM theory is valid for "sufficiently" small perturbations.

In reality, the perturbations in the solar system are far too large to apply KAM theory.

So, the mathematicians have to rely on computing Lyapunov exponents, in order to try to predict any region of instability/chaos.

Jack Wisdom (MIT): It is not possible to exclude the possibility that the orbit of the Earth will suddenly exhibit similar wild excursions in eccentricity.

Even measuring initial conditions of the system to an arbitrarily high, but finite accuracy, we will not be able to describe the system dynamics "at any time in the past or future". To predict the future of a chaotic system for arbitrarily long times, one would need to know the initial conditions with infinite accuracy, and this is by no means possible.

Lyapunov exponents and symplectic integration.

Let d(t) be the distance between two solutions, with d(0) being their initial separation. Then d(t) increases approximately as d(0)eλt in a chaotic system, where λ is the Lyapunov exponent. The inverse of the Lyapunov exponent, 1/λ, is called the Lyapunov time, and measures how long it takes two nearby solutions to diverge by a factor of e.

Sussman and Wisdom's 1992 integration of the entire solar system displayed a disturbing dependence on the timestep of the integration (measurement of the Lyapunov time).

Thus, different researchers who draw their initial conditions from the same ephemeris at different times can find vastly different Lyapunov timescales.

Wayne Hayes, UC Irvine

To show the importance and the dependence on the sensitivity of the initial conditions of the set of differential equations, an error as small as 15 meters in measuring the position of the Earth today would make it impossible to predict where the Earth would be in its orbit in just over 100 million years' time.

“The word ‘chaotic’ summarizes many fundamental concepts characterizing
a dynamical system such as complex predictability and stability. But above
all, it acts as a warming of the difficulties which are likely to arise when trying to
obtain a reliable picture of its past and future evolution. As an example, a
commonly accepted definition states that a system is ‘unstable’ if the trajectories of
two points that initially are arbitrarily close . . . diverge quickly in time. This has
strong implications, as small uncertainties in initial conditions . . . might [also] be
consistent with completely different future trajectories: The conclusion is that we
can exactly reproduce the motion of a chaotic system only if WE KNOW, WITH
ABSOLUTE PRECISION, THE INITIAL CONDITIONS – A STATEMENT
THAT, IN PRACTICE, CAN NEVER BE TRUE."

Alessandra Celletti, Ettore Perozzi, Celestial Mechanics: The Waltz of the Planets

Let us take a closer look the chaotic dynamics of planetary formation; thus, a clear indication that the initial conditions cannot be predicted with accuracy (as we have seen, a mere 15 meters difference in the data will have catastrophic consequences upon the calculations).

OFFICIAL SCIENCE INFORMATION

Four stages of planetary formation

Initial stage: condensation and growth of grains in the hot nebular disk

Early stage: growth of grains to kilometer-sized planetesimals

Middle stage: agglomeration of planetesimals

Late stage: protoplanets


For the crucial stages, the initial and early stages, prediction becomes practically impossible.

As if this wasn't enough, we have absolute proof that in the age of modern man planet Earth underwent sudden pole shifts (heliocentrical version), thus making null and void any integration of the solar system/Lyapunov exponents calculations which do not take into account such variations of the system's parameters:

http://www.theflatearthsociety.org/forum/index.php?topic=30499.msg1635693#msg1635693

http://www.theflatearthsociety.org/forum/index.php?topic=30499.msg1546053#msg1546053

Let me show you what sensitive dependence on initial conditions means, using one of the most famous examples: the Lorenz attractor butterfly effect.

In 1961, Lorenz was running a numerical computer model to redo a weather prediction from the middle of the previous run as a shortcut. He entered the initial condition 0.506 from the printout instead of entering the full precision 0.506127 value. The result was a completely different weather scenario.

Here is the set of Lorenz equations:



Now, the set of differential equations which describe the planetary orbits is much more complicated than this.




NOTHING can be said about the RE heliocentrical system beyond a time scale of 300 YEARS.

Dr. Robert W. Bass

Ph.D. (Mathematics) Johns Hopkins University, 1955 [Wintner, Hartman]
A. Wintner, world's leading authority on celestial mechanics
Post-Doctoral Fellow Princeton University, 1955-56 [under S. Lefschetz]
Rhodes Scholar
Professor, Physics & Astronomy, Brigham Young University

"In a resonant, orbitally unstable or "wild" motion, the eccentricities of one or more of the terrestrial planets can increase in a century or two until a near collision occurs. Subsequently the Principle of Least Interaction Action predicts that the planets will rapidly "relax" into a configuration very near to a (presumably orbitally stable) resonant, Bode's-Law type of configuration. Near such a configuration, small, non-gravitational effects such as tidal friction can in a few centuries accumulate effectively to a discontinuous "jump" from the actual phase-space path to a nearby, truly orbitally stable, path. Subsequently, observations and theory would agree that the solar system is in a quasi-periodic motion stable in the sense of Laplace and orbitally stable. Also, numerical integrations backward in time would show that no near collision had ever occurred. Yet in actual fact this deduction would be false."

"I arrived independently at the preceding scenario before learning that dynamical astronomer, E. W. Brown, president of the American Astronomical Society, had already outlined the same possibility in 1931."

Dr. Robert Bass, Stability of the Solar System:

https://web.archive.org/web/20120916174745/http://www.innoventek.com:80/Bass1974PenseeAllegedProofsOfStabilityOfSolarSystemR.pdf

Dr. E.W. Brown

Fellowship, Royal Society
President of the American Mathematical Society
Professor of Mathematics, Yale University
President of the American Astronomical Society

What this means is that the interval of assured reliability for Newton's equations of gravitational motion is at most three hundred years.

Dr. W.M. Smart

Regius Professor of Astronomy at Glasgow University
President of the Royal Astronomical Society from 1949 to 1951







Within this 300 year time interval, we again have the huge problem of the sensitive dependence on initial conditions.

You have a wonderful talent for collecting information on a topic. So appropriate respect must be given to you for that.

What I’ve noticed about your synthesis of it, however, is that you extend the conclusions beyond what you can reliably deduce given your expertise.

You see, there are many systems that are chaotic. Heck, the double pendulum is a chaotic system, yet our graduate students solve this problem in their freshman year. So you are conflating “chaotic” with “unknowable,” which leads me to think you may not understand chaos enough to apply it to the solar system.

I will concede one of your points, namely that since we do not have the initial conditions of the solar system, we cannot model it’s entire evolution from those conditions.

But you see, and this is really a basic point which surprises me that you miss, we know the conditions NOW, and so we can use them to model it going forward.

How else do you think we got those pictures of Pluto?

Now, to be fair and honest, it is true that small uncertainties in our knowledge NOW may lead to large deviations in our predictions later. That is the price you pay when you play with chaos :).

In the future, if this actually ever happens, then you’ll get to say to me “I told you so.” Until then, every day that goes by, we use our equations to make accurate predictions, everything from manned missions to the dozens of satellites we collect data from.

So I’ve racked up a few thousand “I told you so”s. Maybe one day you’ll get one too!
« Last Edit: April 27, 2019, 06:17:08 PM by QED »
The fact.that it's an old equation without good.demonstration of the underlying mechamism behind it makes.it more invalid, not more valid!

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Re: Update: Earth-Moon-Sun Trajectory equations
« Reply #21 on: April 27, 2019, 06:37:35 PM »
we know the conditions NOW, and so we can use them to model it going forward.

You cannot assume anything beyond a time period of 300 years (past and future).

How can you assume NOW that the conditions belong to a heliocentrical planetary system, when the best mathematicians find themselves helpless in deriving the initial conditions, a fact which precludes you from stating that the heliocentrical system is true.

You cannot model anything since even the events of some 2000 years ago (official chronology of history) have been proven astronomically (using  the Gauss Easter formula) to have never existed in the first place:

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg758652#msg758652

Could the three body problem paradox stem from the fact that the Newtonian equations of orbital motion might be incorrect?
« Last Edit: April 27, 2019, 06:42:35 PM by sandokhan »

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Re: Update: Earth-Moon-Sun Trajectory equations
« Reply #22 on: April 28, 2019, 02:52:34 AM »
we know the conditions NOW, and so we can use them to model it going forward.

You cannot assume anything beyond a time period of 300 years (past and future).

How can you assume NOW that the conditions belong to a heliocentrical planetary system, when the best mathematicians find themselves helpless in deriving the initial conditions, a fact which precludes you from stating that the heliocentrical system is true.

You cannot model anything since even the events of some 2000 years ago (official chronology of history) have been proven astronomically (using  the Gauss Easter formula) to have never existed in the first place:

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg758652#msg758652

Could the three body problem paradox stem from the fact that the Newtonian equations of orbital motion might be incorrect?

Running the trajectories beyond a 300 year period is not a problem.

We know the conditions now because we measure them. We know the locations of the planets and their satellites. How do you think we send probes there?

“The best mathematical minds cannot derive them”

Sandokhan, we do not derive initial conditions. They are inputs. The manner in which you formulate your own sentences about these matters betrays your lack of expertise. It may be convincing to the uninitiated, but to a trained physicist it becomes immediately obvious that you are not really understanding what you write.

It appears that your confidence in our inability to do this rests on your assurance that the heliocentric model is a hoax or fabrication. This really does not carry much weight with me.

We have n-body simulations for solar system and GALAXY formation. A colleague down the hall from me publishes this. I bet if you ran a search you’d come across her name in the first ten minutes and not know it.

Not only can we eclipse this random 300 year barrier you have, but we use the equations to model how entire galaxies likely form. We can simulate how elliptical galaxies form from collisions between spiral galaxies. We have simulations which depict the collision between the Milky Way and the Andromeda galaxy.

In light of this, I am impressed at your stubbornness to continue arguing that we don’t even know the EMS trajectories. But also in light of this, it also seems quite absurd that you do.
« Last Edit: April 28, 2019, 02:54:42 AM by QED »
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Re: Update: Earth-Moon-Sun Trajectory equations
« Reply #23 on: April 28, 2019, 05:20:21 AM »
QED, your words are not evidence. You have made reference to literally nothing which says or suggests that the three body sun-earth-moon problem can exist as a stable system.
« Last Edit: April 28, 2019, 05:24:19 AM by Tom Bishop »

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Re: Update: Earth-Moon-Sun Trajectory equations
« Reply #24 on: April 28, 2019, 05:45:12 AM »
QED, your words are not evidence. You have made reference to literally nothing which says or suggests that the three body sun-earth-moon problem can exist as a stable system.

Your reply strikes me as a low content post, and is a direct lie. I began this thread with reference to the exact equations. It appears as though your last ditch effort, once finally faced with the direct evidence you adamantly demanded in the previous thread, is to simply deny the existence of the link at the top of this one. And you are doing this in front of everyone who’s since followed the link and knows the equations are right there.

I am embarrassed for you right now.

If you have somehow become capable of denying the existence of something directly in front of you which everyone else can see, then how can we trust you to accurately and honestly evaluate information for the FES?

That raises a great deal of red flags. In fact, I haven’t seen so many red flags since the Beijing Olympics.
« Last Edit: April 28, 2019, 05:57:43 AM by QED »
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Re: Update: Earth-Moon-Sun Trajectory equations
« Reply #25 on: April 28, 2019, 05:47:53 AM »
QED, your words are not evidence. You have made reference to literally nothing which says or suggests that the three body sun-earth-moon problem can exist as a stable system.

Your reply strikes me as a low content post, and is a direct lie. I began this thread with reference to the exact equations. It appears as though your last ditch effort, once finally faced with the direct evidence you adamantly demanded on the previous thread, is to simply deny the existence of the link at the top of this thread. And you are doing this in front of everyone who’s since followed the link and knows the equations are true.

The section you linked to doesn't say that those equations result in a stable system. There are several examples in that book of three body equations for systems that results in unpredictable behavior and falls apart. Kindly provide something that supports your positon.
« Last Edit: April 28, 2019, 06:02:55 AM by Tom Bishop »

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Re: Update: Earth-Moon-Sun Trajectory equations
« Reply #26 on: April 28, 2019, 05:56:29 AM »
QED, your words are not evidence. You have made reference to literally nothing which says or suggests that the three body sun-earth-moon problem can exist as a stable system.

Your reply strikes me as a low content post, and is a direct lie. I began this thread with reference to the exact equations. It appears as though your last ditch effort, once finally faced with the direct evidence you adamantly demanded on the previous thread, is to simply deny the existence of the link at the top of this thread. And you are doing this in front of everyone who’s since followed the link and knows the equations are true.

The section you linked to doesn't say that those equations result in a stable system. There are plenty of examples in that book of three body equations that result in chaotic systems that fall apart. Provide something that supports your positon.

Let me ask you a question, Tom.

What is your operative definition for:

- stable system
- chaotic system
- a system that falls apart.

This is important. Because it occurs to me from your reply that you think unless the solar system is stable, non-chaotic, or eternal, that somehow this means we cannot have equations for it.

This is simply a bizarre discussion, I must say. Respectfully, I must express that I am afraid you may be using terms which you do not understand - at least not according to their physical import.

The reason why is because I have never ever ever heard a physicist say that equations cannot exist unless those three conditions are met.

I know this is not true, but your rebuttals read like someone who is just making everything up and throwing it all at the wall hoping something will stick.

I really wish you’d take me up on my offer to help you. I offer it again respectfully, professionally, and in friendship.

If you can provide your operative definitions for those terms, I can probably help you understand what is going on here. Until then, I am left guessing what on Earth you are talking about - because it really doesn’t make any sense to me. And it really SHOULD, because I’ve been doing this stuff professionally for several years and I have a terminal degree in it.
« Last Edit: April 28, 2019, 06:02:18 AM by QED »
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Re: Update: Earth-Moon-Sun Trajectory equations
« Reply #27 on: April 28, 2019, 06:04:54 AM »
The source you gave says neither that the system will be a "stable system," a "chaotic system," or that it will be a "system that falls apart". There is zero information on that subject and therefore you have provided zero evidence.

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Re: Update: Earth-Moon-Sun Trajectory equations
« Reply #28 on: April 28, 2019, 06:38:26 AM »
The source you gave says neither that the system will be a "stable system," a "chaotic system," or that it will be a "system that falls apart". There is zero information on that subject and therefore you have provided zero evidence.

It's painfully clear QED didn't present any evidence in his last post, he simply asked a question of you. You said:

The section you linked to doesn't say that those equations result in a stable system. There are several examples in that book of three body equations for systems that results in unpredictable behavior and falls apart. Kindly provide something that supports your positon.

He asked:

Let me ask you a question, Tom.

What is your operative definition for:

- stable system
- chaotic system
- a system that falls apart.

Seemingly, answering the questions, may help level the language for the discussion. So why not just answer the questions?

Not much is known about the celestial bodies and their distances.

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Re: Update: Earth-Moon-Sun Trajectory equations
« Reply #29 on: April 28, 2019, 09:33:57 AM »
The source you gave says neither that the system will be a "stable system," a "chaotic system," or that it will be a "system that falls apart". There is zero information on that subject and therefore you have provided zero evidence.

I do believe that claim is a non-sequitur. An absence of evidence is not evidence for the opposite. Given the faux pas this far, it is a reasonable conclusion that you are not able to diagnose the operative conditions in the references I have provided.

It will assist our progress if you offer those definitions so that I can help you. Our efforts are only frustrated by ignoring my request, since it is quite unclear what knowledge (and/or mis-knowledge) you are bringing to the table.

To wit: there IS information on those subjects contained in the references I provided.
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Re: Update: Earth-Moon-Sun Trajectory equations
« Reply #30 on: April 28, 2019, 09:40:06 AM »
QED, your words are not evidence. You have made reference to literally nothing which says or suggests that the three body sun-earth-moon problem can exist as a stable system.

Whether he says it here or not, we know it is a stable system from observation, and from travels between Earth, Moon and Sun.

If they were not stable, the lunar craft sent to the Moon by USA, Russia, India, Japan, China and Saudi Arabia would have missed their marks.

No?


We also know the stability of the other planets from travels to and between them.

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Re: Update: Earth-Moon-Sun Trajectory equations
« Reply #31 on: April 28, 2019, 09:42:49 AM »
QED, your words are not evidence.

Only his? Or does this apply to everybody's words?

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Re: Update: Earth-Moon-Sun Trajectory equations
« Reply #32 on: April 28, 2019, 12:19:25 PM »
QED, your words are not evidence. You have made reference to literally nothing which says or suggests that the three body sun-earth-moon problem can exist as a stable system.

Whether he says it here or not, we know it is a stable system from observation, and from travels between Earth, Moon and Sun.

If they were not stable, the lunar craft sent to the Moon by USA, Russia, India, Japan, China and Saudi Arabia would have missed their marks.

No?


We also know the stability of the other planets from travels to and between them.

The orbits are stable on human time scales. Since the multi-body interaction is chaotic, predictions of trajectories may not be reliable beyond a few 100 million years. Of course, that is a running number. With reasonable assumptions, the predictions can be extended further.

What Tom doesn’t understand is that although the solar system is technically a chaotic system, the gravitational force is very weak, and so this permits us to compute predictions with relative ease.

How else could we launch a probe that would meet Pluto exactly in its orbit 9 years later?

Tom strikes me as someone who is very eager to find anything to justify his position. So when he discovers that the solar system is chaotic, he probably goes:

Aha! It’s chaotic! I knew Newton was bullshit! I knew it was a conspiracy!

Then he probably tracks down some technical details of this chaos description to use as debate fodder, and subsequently feels remarkably safe with his position on the issue.

But it doesn’t seem like he ever bothered to ask the question most people would in that situation:

What does the solar system being chaotic MEAN?

And that’s his problem! He just assumes what it means. And he’s wrong.

But if you try to reason with him, I think he interprets it as a trick. Or perhaps he thinks that because he found technical details (which he cannot assess) the matter is proven.

Im not entirely sure, but for whatever reason, he has placed himself into an entrenched position where he is not able to adjust his view even if it is based on a basic mistake that is shown to him.

It’s like you thinking there are 5 apples on the table, and then I go: “no there’s 6, look.” And instead of just looking and realising you miscounted, you weave a network of half-relevant and misinterpreted information, including the history of apples and cultivation methods in various cultures, and different products made from apples — all to hold on to the position that there just absolutely NEEDS to be 5 apples on that table.
The fact.that it's an old equation without good.demonstration of the underlying mechamism behind it makes.it more invalid, not more valid!

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Re: Update: Earth-Moon-Sun Trajectory equations
« Reply #33 on: April 28, 2019, 03:50:40 PM »
You have yet to show that the moon can make even a single orbit around the earth without crashing into the sun, being pulled to orbit around the Sun, or being thrown out into space, per what often happens with the three body interactions from the sources we have read. Please provide reference to a source which suggests or shows that the heliocentric Sun-Earth-Moon system works at all.
« Last Edit: April 28, 2019, 03:53:16 PM by Tom Bishop »

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Re: Update: Earth-Moon-Sun Trajectory equations
« Reply #34 on: April 28, 2019, 04:36:25 PM »
You have yet to show that the moon can make even a single orbit around the earth without crashing into the sun, being pulled to orbit around the Sun, or being thrown out into space, per what often happens with the three body interactions from the sources we have read. Please provide reference to a source which suggests or shows that the heliocentric Sun-Earth-Moon system works at all.
Tom, you don't need 3-body equations to figure out that the moon hasn't reached or exceeded the earth's escape velocity.
Abandon hope all ye who press enter here.

Science is what happens when preconception meets verification.

If you can't demonstrate it, then you shouldn't believe it.

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Re: Update: Earth-Moon-Sun Trajectory equations
« Reply #35 on: April 28, 2019, 04:43:29 PM »
per what often happens with the three body interactions from the sources we have read.

When, where, and to which bodies has this "often" happened?

Please provide reference to a source which suggests or shows that the heliocentric Sun-Earth-Moon system works at all.

Go outside on a moonlit night, and look up at the Moon. Repeat at intervals over your lifetime.

Do the same with the sun during the day.

Let us know as soon as you see either exhibiting chaotic behaviour
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Re: Update: Earth-Moon-Sun Trajectory equations
« Reply #36 on: April 28, 2019, 05:20:50 PM »
You have yet to show that the moon can make even a single orbit around the earth without crashing into the sun, being pulled to orbit around the Sun, or being thrown out into space, per what often happens with the three body interactions from the sources we have read. Please provide reference to a source which suggests or shows that the heliocentric Sun-Earth-Moon system works at all.

That is another lie. I have provided the equations which show the moon makes tons of orbits. You just flatly (see what I did there - that was for you Tom) deny that the equations exist. But everyone can see them there.

Further comments denying what is clearly written ABOVE them seems to be low content posting to me. If you are not willing to discuss the equations like a gentleman, and just continue repeating this blanket denial, then I’m going to have to report you. Others may want to engage in a fruitful conversation about it, and you are derailing this thread now. Please don’t do that.
« Last Edit: May 01, 2019, 02:33:33 PM by QED »
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Re: Update: Earth-Moon-Sun Trajectory equations
« Reply #37 on: May 01, 2019, 12:02:46 PM »
This update is in regards to a prior thread about the 3 body problem.

Summary
Prior discussion ended with a call for direct evidence of solutions to the 3 body problem, specifically to describe the motions of the Sun-Earth-Moon system under the central force model. Multiple references were provided, but a request was made for a synopsis which contained distilled results easily identified - rather than committing to several hundred pages of technical manuscript.

This Offering
I have procured a link to a concise summary that is intended for an upper division undergraduate physics student audience. The benefit of this approach is that it presents the nominal equations without additional theoretical applications often found in publications or research. Hence, it is my hope that this resource will prove useful for FEers who seek direct evidence that the 3 body trajectories are not only known, but reasonably simple and accessible to a scientific but not necessarily professional physicist audience.

As always, it is my pleasure to offer my time in fielding any questions you may have about this resource.

http://farside.ph.utexas.edu/teaching/celestial/Celestialhtml/node100.html

There is a general misconception surrounding mathematical equations. Just because it's not possible to write a function down explicitly as "f(x)=something", that does not mean that the function doesn't exist.

We can define a function via its analytic attributes without writing it down. We can for example define a function via it being the solution to a differential equation or to an integral equation. The function exists, even though we haven't written it down as "f(x)=something".

Consider for example Riemann's zeta-function. For x>1 it's possible to write it down explicitly as f(x). For x<1 it's not possible to write this function down as f(x). For x<1, the function is defined via a functional equation. (A functional is essentially a mathematical object/tool that assigns an attribute to a function.)



Just because it's not possible to write down the trajectories for a three-body-system as explicit functions, that doesn't mean that they don't exist.

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Re: Update: Earth-Moon-Sun Trajectory equations
« Reply #38 on: May 04, 2019, 01:33:29 AM »
You have yet to show that the moon can make even a single orbit around the earth without crashing into the sun, being pulled to orbit around the Sun, or being thrown out into space, per what often happens with the three body interactions from the sources we have read. Please provide reference to a source which suggests or shows that the heliocentric Sun-Earth-Moon system works at all.

That is another lie. I have provided the equations which show the moon makes tons of orbits. You just flatly (see what I did there - that was for you Tom) deny that the equations exist. But everyone can see them there.

Further comments denying what is clearly written ABOVE them seems to be low content posting to me. If you are not willing to discuss the equations like a gentleman, and just continue repeating this blanket denial, then I’m going to have to report you. Others may want to engage in a fruitful conversation about it, and you are derailing this thread now. Please don’t do that.

Equations from a random source you found is not a guarantee that they will result in a working system. Please quote where those equations have made a working heliocentric system.

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Offline QED

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Re: Update: Earth-Moon-Sun Trajectory equations
« Reply #39 on: May 04, 2019, 02:42:12 AM »
You have yet to show that the moon can make even a single orbit around the earth without crashing into the sun, being pulled to orbit around the Sun, or being thrown out into space, per what often happens with the three body interactions from the sources we have read. Please provide reference to a source which suggests or shows that the heliocentric Sun-Earth-Moon system works at all.

That is another lie. I have provided the equations which show the moon makes tons of orbits. You just flatly (see what I did there - that was for you Tom) deny that the equations exist. But everyone can see them there.

Further comments denying what is clearly written ABOVE them seems to be low content posting to me. If you are not willing to discuss the equations like a gentleman, and just continue repeating this blanket denial, then I’m going to have to report you. Others may want to engage in a fruitful conversation about it, and you are derailing this thread now. Please don’t do that.

Equations from a random source you found is not a guarantee that they will result in a working system. Please quote where those equations have made a working heliocentric system.

A random source? Perhaps random for you, but not for us. The derivations and discussions contained therein are canonical. You can find them in just about every physics course and every textbook. The fact that they strike you as random underlines your naivety in this area, I suppose. The equations make a working heliocentric model in every appearance they make. That is their function.

So I don’t understand what it is you want. Do you want me to PLOT them for you? You want someone else to take them and show you the orbits they describe FOR YOU?

No. As I said before, you can do your own homework. Besides, even if I showed you the plots, you would just deny it anyway. I’m learning how you operate, you see, and that is your pattern.

No indeed! Plot them yourself. And see FOR YOURSELF, in true zetetic fashion, that they work.

I predict that you will not do so, because I believe that you know deep down that you have been caught. Hence, the only way to retain your fragile hold on your FE claim is to avoid discovering direct evidence at any cost. Hence, you will never, ever come within a mile of actually attempting to plot those equations. The victory you would earn by demonstrating them false is infinitely shadowed by your fear of proving them correct by mistake.

A shame really. If you actually applied yourself, then you might just learn something of value.

Plus, you never know, I could be mistaken.
The fact.that it's an old equation without good.demonstration of the underlying mechamism behind it makes.it more invalid, not more valid!

- Tom Bishop

We try to represent FET in a model-agnostic way

- Pete Svarrior