*

Offline BillO

  • *
  • Posts: 513
  • Huh?
    • View Profile
Re: What are the (flat Earth) stars?
« Reply #60 on: November 07, 2019, 03:55:45 PM »
I have things to do right now.  It's winter where I live and I have the mundane tasks of chopping and stacking firewood.  Allow me to get back to on this.  But as for Ginenthal being one of the top scholars in the world, that has to be a joke right?  As far as I can tell, all he's ever really done is write in defense of Velikovsky's physics quackery.  Velikovsky being a psychiatrist and all.   
Here a quack, there a quack, everywhere a quack quack.

*

Offline BillO

  • *
  • Posts: 513
  • Huh?
    • View Profile
Re: What are the (flat Earth) stars?
« Reply #61 on: November 07, 2019, 07:22:01 PM »
Back from my chores.

The book is written by Charles Ginenthal, one of the top scholars in the world.
Dealt with that above.



Basically, what Velikovsky proposed is that electrical and magnetic forces must be included in celestial mechanics.
I'm not going to read any more Velikovsky to try to determine if what your saying here is correct or not, but just as I would not take a hairdresser's advice on brain surgery, I would not take a psychiatrists advice on physics.  Especially one that published so much unfounded rambling and is the foremost example of pseudoscience.


And he was right.
Possibly, but under what conditions?  Certainly not those generally (or ever) found in universe.

Here is the exact formula for the BIEFELD-BROWN EFFECT:
LOL!  This is something Brown as a high school student and let it take his imagination away.  Despite numerous attempts by others this effect has never been demonstrated.  More quackery and pseudoscience.

This is the Weyl-Majumdar-Papapetrou-Ivanov solution.
Weyl, Majumdar, Papapetrou independently did some interesting academic calisthenics for sure.

However, these solutions were an attempt to use Einstein's and Maxwell's work to predict, or find a solution for the classical distribution of a system of point charges.  In Newtonian physics, this is simply done, however, even after the work of the above gentlemen a useful Einstein-Maxwell solution has not been found.  Their solution(s) require a system of super-highly charged masses on the order of black holes, and the solutions only work in a simplified static case (time independent).  Not something we've ever seen ... so ,yeah, just some interesting intellectual workouts.

Now, once you bring Ivanov into it you do the other an injustice.  Ivanov did some real physics in his life, but his work on this was soundly rejected, especially when he proposed a static solution could provide a means of propulsion!

Hermann Weyl, a physicists several ranks higher than Einstein
Weyl was a real physicist alright, but not exactly a household name.  Again, his work on this does not have teh application you are looking for and infact has no real application at all (so far).

If you do not like Velikovsky, then you are going to be enthralled by Kepler, who FAKED/FUDGED the entire set of data for the Nova Astronomia:
One writer's opinion piece.  Meh...

Here is an analysis of Jacques Laskar's numerical approach using only mainstream sources:
And what Laskar said was that while you could predict the motions of the planets for 10,000,000 years, you could probably not predict them for 100,000,000 years.  I can't see how bringing this up helps your point.  It's not like he's saying "This thing can't exist as it's going to blow apart at any second!"  I think you're desperately grasping at straws.

Chapter 3 from Newton, Einstein & Velikovsky includes the references on numerical methods, a sure sign you did not read it at all.
There is no math in that chapter.  There is a lot of unsubstantiated rhetoric, but no math.  Quite a typical approach in pseudoscience.

Also, right on the first page of that W. Hayes paper you linked to he states: "The Solar System is known to be ‘practically stable’, in the sense that none of the known planets is likely to suffer mutual collisions, or be ejected from the Solar System, over the next several billion years."   Citing the work of Laskar.  Again, I don't see how this helps your case.  You are talking such tiny, tiny chaotic effects that the researchers don't even know what is casing them but they suspect observational data is not accurate enough to feed the models.  Did you even read that paper?

Here is the introductory paragraph: "The existence of chaos among the jovian planets is a contested issue. There exists both apparently unassailable evidence that the outer Solar System is chaotic, and that it is not. The discrepancy is particularly disturbing given that computed chaos is sometimes due to numerical artefacts. Here, we discount the possibility of numerical artefacts and demonstrate that the discrepancy seen between various investigators is real. It is caused by observational uncertainty in the orbital positions of the jovian planets, which is currently a few parts in 10 million.  Within that observational uncertainty, there exist clearly chaotic trajectories with complex structure and Lyapunov times—the timescale for the onset of chaos—ranging from 2 million years to 230 million years, as well as trajectories that show no evidence of chaos over 1Gyr timescales. Determining the true Lyapunov time of the outer Solar System will require a more accurate observational determination of the orbits of the jovian planets. A full understanding of the nature and consequences of the chaos may require further theoretical development."
Here a quack, there a quack, everywhere a quack quack.

*

Offline Tim Alphabeaver

  • *
  • Posts: 170
  • That's no beaver
    • View Profile
Re: What are the (flat Earth) stars?
« Reply #62 on: November 07, 2019, 11:11:24 PM »
I don't understand. Who was talking about analytical solutions? Those are numerical solutions that I linked you to:

Quote
https://web.archive.org/save/https://academic.oup.com/pasj/article/70/4/64/4999993

Over a thousand new periodic orbits of a planar three-body system with unequal masses  -- “ Here, we report 1349 new families of planar periodic orbits of the triple system where two bodies have the same mass and the other has a different mass.

Further down, in the section "Numerical searching for periodic orbits" we verify that these are numerical simulations: -- “ As mentioned by Li and Liao (2017), many periodic orbits might be lost by means of traditional algorithms in double precision. Thus, we further integrate the equations of motion by means of a "clean numerical simulation"

Now, where can we find examples of numerical three body problem solutions with bodies of different masses?

Sandokhan, do you know where we can find them?

You could try looking up the thing I told you to look up, NASA's Horizons catalogue.
https://ssd.jpl.nasa.gov/?horizons_doc
Searching this document for "integrate":
"comets and asteroids numerically integrated by Horizons."
"Comets and asteroids are numerically integrated on demand over a maximum interval of A.D. 1600 to A.D. 2500"
"To construct an SPK file for a comet or asteroid, Horizons retrieves the latest orbit solution and numerically integrates the object's trajectory over a user-specified time span less than 200 years."
"and are then numerically integrated on-demand by Horizons to other times of interest"

Need I go on?

From your link:

Quote
Comet and asteroid ephemerides are integrated from initial conditions called "osculating elements". These describe the 3-dimensional position and velocity of the body at a specific time. The integrator starts with this state and takes small time steps, summing the perturbing forces at each step before taking another step. A variable order, variable step-size integrator is used to control error growth. In this way, the gravitational attraction of other major solar system bodies on the target body trajectory is taken into account.

Summing of perturbing forces?

This sounds like what Dr. Gopi Krishna Vijaya is explaining in his Replacing the Foundations of Astronomy paper:

https://reciprocalsystem.org/PDFa/Replacing%20the%20Foundations%20of%20Astronomy%20(Vijaya,%20Gopi%20Krishna).pdf

Quote
Epicycles Once More

Following the Newtonian era, in the 18th century there were a series of mathematicians – Bernoulli, Clairaut, Euler, D’Alembert, Lagrange, Laplace, Leverrier – who basically picked up where Newton left off and ran with it. There were no descendants to the wholistic viewpoints of Tycho and Kepler, but only those who made several improvements of a mathematical nature to Newtonian theory. Calculus became a powerful tool in calculating the effects of gravitation of all the planets upon each other, due to their assumed masses. The motion of the nearest neighbor – the Moon – was a surprisingly hard nut to crack even for Newton, and several new mathematical techniques had to be invented just to tackle that.

In the process, a new form of theory became popular: Perturbation theory. In this approach, a small approximate deviation from Newton's law is assumed, based on empirical data, and then a rigorous calculation of differential equation is used to nail down the actual value of the deviation. It does not take much to recognize that this was simply the approach taken before Kepler by Copernicus and others for over a thousand years – adding epicycles to make the observations fit. It is the same concept, but now dressed up in gravitational disguise:



In other words, the entire thought process took several steps backwards, to redo the same process as the Ptolemaic - Copernican epicycle theory, only with different variables. The more logical way of approach would have been to redirect the focus of the improved mathematical techniques to the assumptions in Newton’s theory, but instead the same equations were re-derived with calculus, without examining the assumptions. Hence any modern day textbook gives the same derivation for circular and elliptical motion that Newton first derived in his Principia. The equivalence of the epicycle theory and gravitational theory has not been realized, and any new discovery that fits in with the mathematical framework of Newtonian gravity is lauded as a “triumph of the theory of gravitation.” In reality, it is simply the triumph of fitting curves to the data or minor linear extrapolations – something that had already been done at least since 2nd century AD. Yet the situation is conceptually identical.

~

The Dead End

In the late 19th century, one of the French mathematicians – Henri Poincaré – had already discovered that many of the terms being used in the “perturbation” series by mathematicians like Laplace and Lagrange were becoming infinite for long periods of time, making the system unstable. In simple words, the solutions ‘blow up’ fairly quickly. He also showed that the general problem of 3 mutually gravitating bodies was insoluble through any mathematical analysis! Many physicists and mathematicians built up modern “Chaos theory” based on these ideas, to show simply that one cannot calculate the movements of the planets accurately. Thus began the field of non-linear dynamics.

In the middle of the 20th century, with computers entering the field, the mathematicians pretty much gave up on calculating the orbits by themselves and programmed the computer to do it, even though it was mathematically shown that these orbits were incalculable. They had to be satisfied with approximations or numerical methods (or “brute force” methods.) The result of it all was that after 300 years, Newtonian/Einsteinian thought lands in the same spot that Kepler ended: the orbits point to a living or chaotic system. Only now, there is the additional baggage of all the wrong concepts introduced with regard to “inverse-square law”, “gravitational attraction”, “gravitational mass” and “curved space-time” along with uncountable number of minor assumptions. In this process, an enormous amount of human effort was put to derive thousands of terms in equations over centuries. The entire enterprise has been a wild goose chase

Just because the reference that I gave you has the word "peturb" in doesn't mean it's not a numerical integration. That same paragraph also explicitly states they use numerical integration.
What exactly is your point here? I've given you the numerical solution to the n-body problem that you asked for, and you just dismissed it out of hand for seemingly no reason. If you don't want a discussion, don't bother replying.

Just re-read all of BillO's posts - he seems to know exactly what he's talking about.
« Last Edit: November 07, 2019, 11:14:29 PM by Tim Alphabeaver »
**I move away from the infinite flat plane to breathe in

*

Offline Tom Bishop

  • Zetetic Council Member
  • **
  • Posts: 6521
  • Flat Earth Believer
    • View Profile
Re: What are the (flat Earth) stars?
« Reply #63 on: November 07, 2019, 11:40:37 PM »
It appears to be based on perturbation theory.

https://en.wikipedia.org/wiki/JPL_Horizons_On-Line_Ephemeris_System

Quote
The real orbit (or the best approximation to such) considers perturbations [link takes us to the page on perturbation theory] by all planets, a few of the larger asteroids, a few other usually small physical forces, and requires numerical integration.

Numerical integration can be used with perturbations. Are you aware that Ptolmy's epicycles are numerical computations?

https://books.google.com/books?id=JVhTtVA2zr8C&pg=PA29&source=gbs_toc_r&cad=4#v=onepage&q&f=false



So the favorite word, "numerical", really means nothing regarding a dynamic n-body simulation or the acceptability of a mathematical procedure.
« Last Edit: November 08, 2019, 10:12:58 AM by Tom Bishop »

*

Offline BillO

  • *
  • Posts: 513
  • Huh?
    • View Profile
Re: What are the (flat Earth) stars?
« Reply #64 on: November 08, 2019, 03:04:13 AM »
It appears to be based on perturbation theory.
Oh, for goodness sake Tom, do you really have to drag 3600 year old 'mathematics' into this?  Is flat earth hypotheses that desperate that it needs to draw on arguing against ancient misconceptions to help it out?  You had to be laughing when you wrote that, right?
Here a quack, there a quack, everywhere a quack quack.

Re: What are the (flat Earth) stars?
« Reply #65 on: November 08, 2019, 06:49:10 AM »
It appears to be based on perturbation theory.
Oh, for goodness sake Tom, do you really have to drag 3600 year old 'mathematics' into this?  Is flat earth hypotheses that desperate that it needs to draw on arguing against ancient misconceptions to help it out?  You had to be laughing when you wrote that, right?
To be fair, he did start a previous post with “I don’t understand”. A rare moment of self-awareness. Tom has repeatedly shown he doesn’t understand this. And even if there were no solutions, analytical or numerical, to model a system, why is that significant?
As others have pointed out, the behaviour of a double pendulum is chaotic, there is no way of predicting its future state over long timespans.
Tom’s logic here would claim that this fact shows that the theory that double pendulums exist must not exist.
It’s a common FE tactic. “I don’t understand this model ergo the model is wrong”, or “This model is imperfect which demonstrates that the system it’s modelling can’t exist”.
Not only is that poor logic, it’s particularly disingenuous when you consider the gaping holes and inconsistencies in FE models.
If you are making your claim without evidence then we can discard it without evidence.

*

Offline Pete Svarrior

  • e
  • Planar Moderator
  • *****
  • Posts: 9933
  • (>^_^)> it's propaganda time (◕‿◕✿)
    • View Profile
    • The Flat Earth Society
Re: What are the (flat Earth) stars?
« Reply #66 on: November 08, 2019, 08:02:44 AM »
Oh, for goodness sake Tom, do you really have to drag 3600 year old 'mathematics' into this?  Is flat earth hypotheses that desperate that it needs to draw on arguing against ancient misconceptions to help it out?  You had to be laughing when you wrote that, right?
Okay, you clearly don't understand what "contributing to a discussion" means. We'll see you in a few weeks.
Read the FAQ before asking your question - chances are we've already addressed it.
Follow the Flat Earth Society on Twitter and Facebook!


*mic stays stationary and earth accelerates upwards towards it*

Re: What are the (flat Earth) stars?
« Reply #67 on: November 08, 2019, 02:47:38 PM »
Despite numerous attempts by others this effect has never been demonstrated.

But it has.

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2177463#msg2177463

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2178412#msg2178412

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2179065#msg2179065

Their solution(s) require a system of super-highly charged masses on the order of black holes, and the solutions only work in a simplified static case (time independent).  Not something we've ever seen ... so ,yeah, just some interesting intellectual workouts.

No black holes required at all.

All you need is a simple capacitor.

Ivanov did some real physics in his life, but his work on this was soundly rejected, especially when he proposed a static solution could provide a means of propulsion!

The Weyl-Ivanov solution cannot be rejected, it is a fact of science.

It represents the exact formula for the Biefeld-Brown effect: then you can use supercapacitors as a form of propulsion, the formula spells this out very clearly.





Weyl was a real physicist alright, but not exactly a household name.

Weyl was the best theoretical physicists in the world, 1917-1955.

“And now I want to ask you something more: They tell me that you and Einstein are the only two real sure-enough high-brows and the only ones who can really understand each other. I won’t ask you if this is straight stuff for I know you are too modest to admit it. But I want to know this -- Do you ever run across a fellow that even you can’t understand?”

“Yes,” says he.

“This will make a great reading for the boys down at the office,” says I. “Do you mind releasing to me who he is?”

“Weyl,” says he.

(an interview that Paul Dirac gave in America back in April, 1929)

One writer's opinion piece.

Dr. Donahue's paper was peer-reviewed and it includes the actual tables which do prove his point.

There is no math in that chapter.

But there is, the author references each and every conclusion with the very best works available today, which do include the calculations.











Now, let me address the numerical calculations for the n-body problem.

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.

*

Offline Tim Alphabeaver

  • *
  • Posts: 170
  • That's no beaver
    • View Profile
Re: What are the (flat Earth) stars?
« Reply #68 on: November 09, 2019, 03:44:23 AM »
[...]
Well after some to-and-froing it seems like we actually agree on this one!
**I move away from the infinite flat plane to breathe in

*

Offline Tim Alphabeaver

  • *
  • Posts: 170
  • That's no beaver
    • View Profile
Re: What are the (flat Earth) stars?
« Reply #69 on: November 14, 2019, 07:57:40 PM »
Within this 300 year time interval, we again have the huge problem of the sensitive dependence on initial conditions.
I think you've taken a very roundabout route to reach the same conclusion that I did in my first few posts in this thread: the universe is chaotic.
**I move away from the infinite flat plane to breathe in