[garygreen]

Gary, it has been pointed out to you on the numerous times we have had these conversations. All of these models are numeric solutions.

of course they're numerical integrations.  there is no general analytic solution, so it has to be a numerical method.  lol i didn't say that they aren't using a numerical method, you're just too confused to know the difference.  i'm saying that they're using a numerical method to simulate lots and lots of different initial conditions, and they're searching for initial conditions that lead to stable, periodic configurations.

tbh i don't even get what your argument is anymore.  you started with numerical simulations of the solar system are impossible, and you've now arrived at these are numerical simulations you ifiot!!! 

Again, we see that these are numerical methods, and not based on an analytical solution. This argument is clearly and fantastically wrong.

lol.  you don't have a clue what this is an image of, do you?  that's awesome.  please find more arenstorf orbits and post them.  once again, literally no one but you is saying that there is an analytic solution to n-body problems.  they're always solved with numerical methods.

Sandokan addressed Laskar here earlier this year: <pdfs>

unsurprisingly, sandy's author very selectively quotes Newton's Clock to make it seem like Ivars Peterson actually agrees with him.  he doesn't.  i'm also not surprised that you haven't bothered to read any of this material yourself.

[Tom Bishop]

Gary, it has been pointed out to you on the numerous times we have had these conversations. All of these models are numeric solutions.

of course they're numerical integrations.  there is no general analytic solution, so it has to be a numerical method.  lol i didn't say that they aren't using a numerical method, you're just too confused to know the difference.  i'm saying that they're using a numerical method to simulate lots and lots of different initial conditions, and they're searching for initial conditions that lead to stable, periodic configurations.

tbh i don't even get what your argument is anymore.  you started with numerical simulations of the solar system are impossible, and you've now arrived at these are numerical simulations you ifiot!!!

There are numerical simulations. They are the very sensitive ones that fall apart at the slightest touch, make odd orbits that look nothing like what is theorized in astronomy, and require at least two bodies of equal mass.

If you believe this to be something else entirely, then where are the three body simulations with bodies of different masses? Why do these simulations need to have at least two bodies of equal masses? You have explained nothing, and continuously ignore this question.

unsurprisingly, sandy's author very selectively quotes Newton's Clock to make it seem like Ivars Peterson actually agrees with him.  he doesn't.  i'm also not surprised that you haven't bothered to read any of this material yourself.

https://i.imgur.com/8HmRza0.png
https://i.imgur.com/W7k0ohY.png

Peterson was not misquoted. From Newton's Clock:

[edby]

Peterson was not misquoted.

Gary said Peterson was 'selectively quoted', not that he was misquoted.

[Tom Bishop]

Another find on Laskar's methods:

https://www.sciencedirect.com/science/article/pii/001910359290196E

Using a different approach based on perturbation techniques and
huge dedicated algebraic manipulations, Laskar (1985, 1988) managed to
transform the equations of motion of the eight main planets of the Solar
System in order to obtain a new system where only the slowly precessing
motions of the orbits where present, and not the orbital frequencies

From the Wikipedia article on perturbations:

This general procedure is a widely used mathematical tool in advanced sciences and engineering: start with a simplified problem and gradually add corrections that make the formula that the corrected problem becomes a closer and closer match to the original formula.

History

Perturbation theory was first devised to solve otherwise intractable problems in the calculation of the motions of planets in the solar system.

...Since astronomic data came to be known with much greater accuracy, it became necessary to consider how the motion of a planet around the Sun is affected by other planets. This was the origin of the three-body problem; thus, in studying the system Moon–Earth–Sun the mass ratio between the Moon and the Earth was chosen as the small parameter. Lagrange and Laplace were the first to advance the view that the constants which describe the motion of a planet around the Sun are "perturbed", as it were, by the motion of other planets and vary as a function of time; hence the name "perturbation theory"

[Rama Set]

I don’t understand how Tom can continually be presented with multiple different simulations of the solar system and the continue on to say there are no n-body problem solutions that have bodies of differing mass.

[Tom Bishop]

I don’t understand how Tom can continually be presented with multiple different simulations of the solar system and the continue on to say there are no n-body problem solutions that have bodies of differing mass.

I didn't write these sources that I am quoting. Lets see the three body simulations of three bodies with unequal masses. Feel free to provide evidence for your argument rather than submitting a content-less post.

[RonJ]

http://adsbit.harvard.edu//full/1991CeMDA..50...73W/0000073.000.html

Here's a good place to start.  Of course it may be completely fake as NASA is involved.  All you would have to do is prove all the equations are fake.

[Tom Bishop]

http://adsbit.harvard.edu//full/1991CeMDA..50...73W/0000073.000.html

Here's a good place to start.  Of course it may be completely fake as NASA is involved.  All you would have to do is prove all the equations are fake.

It's talking about a limited possibility for a generalized solution for the Three Body Problem. From the conclusion:



Essentially, it is not easy to model chaos:

Chaos and the Solar System
by Paul Trow

What exactly is chaos? We can give an example by a rigid pendulum, such as in a grandfather clock. If the pendulum swings freely, its motion will be perfectly regular and periodic, and if there were no friction, it would continue this way forever. The system is perfectly predictable – it is the opposite of chaos. But now suppose that we place an electric magnet at the base of the pendulum, and arrange for the magnet turn on momentarily at regular intervals – say once every second – at which time it exerts a magnetic force on the pendulum. This device is rather like a parent pushing a child on a swing, but unlike the parent who pushes in time with the swing, the magnet’s forces are out of phase with the pendulum. If the magnet exerts its force during the pendulum’s downward swing, it speeds the pendulum up – but if it does so during the upward swing, it slows the pendulum down. The question is simply this: what will happen to the pendulum? Will it swing regularly or irregularly? Can we predict its motion at all?

Since the device is such a simple deterministic system, and the magnet’s push occurs at regular intervals, we might guess that the pendulum’s motion would be periodic. In other words, after a while the motion would begin to repeat itself. Surprisingly, what actually happens is that the pendulum begins to swing irregularly, sometimes higher and sometimes lower, without any discernible pattern. We are no more able to predict how high the pendulum will go after a few swings than we are to predict the outcome of a roll of the dice. What this device shows is that a simple deterministic mechanism can generate what appears to be random motion – in other words, it is chaotic.

There is a historical irony in the fact that this simple device is chaotic. Galileo studied the motion of freely swinging pendulums, and discovered that their period is independent of the length of the pendulum. Indeed, this discovery, along with his famous analysis of falling bodies and projectiles, were some of the first quantitative descriptions of terrestrial motion. Galileo’s work was one of the two most significant influences on Newton’s thinking. The irony is that something so simple as a pendulum – the very symbol of the deterministic universe – can be altered so slightly as to produce chaos. And the historical question this raises is why it took almost three hundred for someone to recognize the possibility of chaotic motion. I think it is safe to say that because Galileo and the other great genius of the scientific revolution were searching for order in the universe, they were blind to the existence of chaos all around them.

The author goes on, describing that the motion of planetary systems has been an issue for a long time.

Describing the motion of any planetary system (including purely imaginary ones that exist only on paper) is the subject of a branch of mathematics called celestial mechanics. Its problems are extremely difficult and have eluded the greatest mathematicians in history.

The mathematician and theoretical physicist Henri Poincaré was instrumental in showcasing the challenges of Celestial Mechanics:

As other mathematicians had done before, Poincaré considered a special case in which there are just three planetary bodies (the so-called three-body problem). Poincaré, however, tried a novel approach to the problem: rather than trying to explicitly solve the equations of motion, as mathematicians had always done previously, he looked at the qualitative behavior of planetary orbits - for example, whether they were periodic or followed more irregular paths. This approach had a liberating effect, enabling him to see possibilities that others had overlooked. What he discovered was quite unexpected: the motion of a planet in a three-body system can be very wild and unpredictable indeed. Its orbit can follow an apparently random curve, winding back around itself over and over again, like a long and tangled string. As he described such curves:

When one tries to depict the figure formed by these two curves and their infinity of intersections, each of which corresponds to a doubly asymptotic solution, these intersections form a kind of net, web, or infinitely tight mesh; neither of the two curves can ever cross itself, but must fold back on itself in a very complex way … Nothing can give us a better idea of the complexity of the three-body problem.

The article continues:

Poincaré’s discovery was surprising because it contradicted age-old assumptions about the motion of the planets. Beginning with the early Greeks, who thought that the planets moved in circles, astronomers had long believed that planetary motion was built up from simple motion. The theories of Kepler and Newton reinforced this belief. Before Poincaré, no one had imagined that such complicated, unpredictable motion could occur in the solar system. It must have come as a shock to him to realize that the motion of a planet could appear to be as random as that in a pinball machine.

[Rama Set]

I don’t understand how Tom can continually be presented with multiple different simulations of the solar system and the continue on to say there are no n-body problem solutions that have bodies of differing mass.

I didn't write these sources that I am quoting. Lets see the three body simulations of three bodies with unequal masses. Feel free to provide evidence for your argument rather than submitting a content-less post.

I wasn't talking about your sources.Please try and understand what is written, and if you have questions ask.  Gary linked two simulations of the solar system.  You also decided that a member of NASA's eclipse prediction team doesn't understand how NASA predicts eclipses, but you do.  You really can't make this up.

Hopefully someone coming to the site will see exactly how out of touch your arguments are with the evidence at hand.

[Tom Bishop]

I don’t understand how Tom can continually be presented with multiple different simulations of the solar system and the continue on to say there are no n-body problem solutions that have bodies of differing mass.

I didn't write these sources that I am quoting. Lets see the three body simulations of three bodies with unequal masses. Feel free to provide evidence for your argument rather than submitting a content-less post.

I wasn't talking about your sources.Please try and understand what is written, and if you have questions ask.  Gary linked two simulations of the solar system.  You also decided that a member of NASA's eclipse prediction team doesn't understand how NASA predicts eclipses, but you do.  You really can't make this up.

Hopefully someone coming to the site will see exactly how out of touch your arguments are with the evidence at hand.

Do a search for the terms we have been talking about in this thread in those links. They are based on perturbation and pattern-based methods. No one can model chaos. Don't be ridiculous.

Read Frank's comment again. He agrees that NASA is using the Saros Cycle, but is pointing out that he is getting his data for the sun and the moon in his work from the JPL DE model, which he thinks is a n-body simulation of the solar system. In reality it uses predictions based on perturbations... just like everything else... and which we have been egregiously defining in this thread.

Will Saros-mister Frank come here and tell us that all authors, celestial mechanics professors, and articles are wrong about perturbation methods?

Will Frank come here and tell us that what we are reading amounts to a coincidental series of typos, that the three body problem is a trivial thing that was solved by mathematicians hundreds of years ago, or, perhaps that JPL has a secret n-body simulation of the solar system?

[RonJ]

https://arxiv.org/pdf/1508.02312.pdf

Here's another paper on the 3 body problem.  Just what kind of specification are you looking for in the 3 body problem?  What exactly would it prove to you if a solution was available?

[Bobby Shafto]

...he is getting his data for the sun and the moon in his work from the JPL DE model,
which he thinks is a n-body simulation of the solar system.

Where does he say he thinks that?

[Tom Bishop]

https://arxiv.org/pdf/1508.02312.pdf

Here's another paper on the 3 body problem.  Just what kind of specification are you looking for in the 3 body problem?  What exactly would it prove to you if a solution was available?

The solutions are limited Ron. Lets ask this mathematician at askamathematician.com:

https://www.askamathematician.com/2011/10/q-what-is-the-three-body-problem/

Q: What is the three body problem?

Physicist: The three body problem is to exactly solve for the motions of three (or more) bodies interacting through an inverse square force (which includes gravitational and electrical attraction).

The problem with the 3-body problem is that it can’t be done, except in a very small set of frankly goofy scenarios (like identical planets following identical orbits).

My point is that the Three Body Problem can't create a sun with a planet that has a moon, like Copernicus told us. Astronomy is in the Stone Age. Prediction in astronomy is through other means that involve pattern-finding of the observed movements of the planets.

[Rama Set]

I don’t understand how Tom can continually be presented with multiple different simulations of the solar system and the continue on to say there are no n-body problem solutions that have bodies of differing mass.

I didn't write these sources that I am quoting. Lets see the three body simulations of three bodies with unequal masses. Feel free to provide evidence for your argument rather than submitting a content-less post.

I wasn't talking about your sources.Please try and understand what is written, and if you have questions ask.  Gary linked two simulations of the solar system.  You also decided that a member of NASA's eclipse prediction team doesn't understand how NASA predicts eclipses, but you do.  You really can't make this up.

Hopefully someone coming to the site will see exactly how out of touch your arguments are with the evidence at hand.

Do a search for the terms we have been talking about in this thread in those links. They are based on perturbation and pattern-based methods. No one can model chaos. Don't be ridiculous.

Those are numerical solution driven models of the solar system. It’s exactly what you said was impossible.

Read Frank's comment again. He agrees that NASA is using the Saros Cycle, but is pointing out that he is getting his data for the sun and the moon in his work from the JPL DE model, which he thinks is a n-body simulation of the solar system. In reality it uses predictions based on perturbations... just like everything else... and which we have been egregiously defining in this thread.

Will Saros-mister Frank come here and tell us that all authors, celestial mechanics professors, and articles are wrong about perturbation methods?

Will Frank come here and tell us that what we are reading amounts to a coincidental series of typos, that the three body problem is a trivial thing that was solved by mathematicians hundreds of years ago, or, perhaps that JPL has a secret n-body simulation of the solar system?

Frank said explicitly that “Modern eclipse predictions do NOT use the Saros.” The opposite of what you are saying. Furthermore he says, “Rather, they are based on the orbital mechanics of the Earth, Moon, and Sun as laid out by Newton’s theory of gravitation.”

This is in exact opposition of what you are saying. It could not be clearer.

[Tom Bishop]

Ed -

In a word “rubbish!”

Modern eclipse predictions do NOT use the Saros.

Rather, they are based on the orbital mechanics of the Earth, Moon, and Sun as laid out by Newton’s theory of gravitation. [Fred thinks that there is an n-body solar system out there based on Newton's Laws ]

More specifically, I use the Jet Propulsion Laboratory Developmental Ephemeris 430 (i.e., JPL DE430) to calculate the positions of the Moon, and Sun with respect to Earth. [Fred gives JPL DE as his evidence, because he mentions using them on his website for computing the positions of the sun or moon over the earth. JPL DE admits to be based on perturbation theory] This is the raw material from which the Besselian elements used in eclipse predictions are derived from (https://en.wikipedia.org/wiki/Besselian_elements). [See below] It involves a lot of spherical geometry to calculate every conceivable aspect of any solar eclipse.

Using this method, I can calculate the time of the start and end of any solar eclipse to a fraction of a second for any location on Earth. I challenge any flat Earther to match that precision and accuracy using flat Earth geometry.

Best regards,

Fred Espenak

PS - By the way, the JPL DE is also used to help navigate all the interplanetary spacecraft into orbits or flybys of the planets (e.g., New Horizons and Pluto).

Basselian elements

http://www.math.nus.edu.sg/aslaksen/gem-projects/hm/0304-1-08-eclipse/predictions.htm

Intro:

Bessel developed the method used to calculate and describe precisely any eclipse, based on using a coordinate system oriented to the shadow’s axis. The basic steps are: elements are calculated in the Besselian system to describe geometrical quantities; the observer’s position is transformed to Bessel’s coordinate system; equations of condition are formed; circumstances are derived that describe the time and the place of observable events or conditions in the Besselian system; the circumstances are transformed back to topocentric or geocentric coordinates. Many people have actually used the Besselian elements in calculating the eclipses.

Article continues:

Whether an eclipse will occur depends mostly on the coming together of two periodical phenomena, in this case the reaching of the proper lunar phase and the passing through a node. For more generality, we'll investigate the coming together of two arbitrary phenomena A and B. We assume that phenomenon A has a period PA, that phenomenon B has period PB, and that the lengths of those periods are constant.

...

Approximation With a Ratio of Whole Numbers

To base predictions of Z on periods, we must approximate γ with a ratio a⁄b of positive whole numbers. If we can find such a and b, then we can say that a periods PB are almost equal to b periods PA, and that hence that much time after a previous Z another Z will occur.

...

The first couple of very good approximations that we find for eclipses are listed in the following table. The very good approximations are a⁄b. The corresponding period of prediction and great period (to be explained later) are y (in years) en c (in years). The number of successful predictions in a row to be expected is between n1 and n2. The fraction of successful predictions of further eclipses based on earlier eclipses and the prediction period is equal to P. Very good approximation number 12 has the unusably large prediction period of 12393.4 years.

...

The Great Period
Eventually we use some approximation

(Eq. 10) γ' = a⁄b

for γ with whole numbers a and b. These numbers do not have to be determined using the method described above, and don't even need to give a particularly good approximation to γ. We assume (without loss of generality) that a and b have no divisors in common.

This approximation corresponds to the assumption that b periods PA are equal to a periods PB and that that much time after a previous Z there will be a next Z. We'll refer to this period of time as the period of prediction and will indicate it as y.

Plenty of other references of "periods" as the article continues.

We are reminded of the following quote of T.G. Ferguson in the Earth Review for September 1894, as appears in our literature:

No Doubt some will say, 'Well, how do the astronomers foretell the eclipses so accurately.' This is done by cycles. The Chinese for thousands of years have been able to predict the various solar and lunar eclipses, and do so now in spite of their disbelief in the theories of Newton and Copernicus. Keith says 'The cycle of the moon is said to have been discovered by Meton, an Athenian in B.C. 433,' then, of course, the globular theory was not dreamt of.

[Tom Bishop]

From Fred's website on Besselian elements:

http://www.eclipsewise.com/solar/SEhelp/SEbeselm.html

The eight Besselian elements needed to characterize a solar eclipse can be summarized as follows:

x, y - Cartesian coordinates of the lunar shadow axis in the (in units or Earth's equatorial radius)
L1, L2 - Radii of the Moon's penumbral and umbral/antumbral shadows in the (in units or Earth's equatorial radius)
d - Declination of the Moon's shadow axis on the celestial sphere
µ - Hour angle of the Moon's shadow axis on the celestial sphere
f1, f2 - Angles of the penumbral and umbral/antumbral shadow cones with respect to the axis of the lunar shadow
The details for actual eclipse calculations using the Besselian elements can be found in the references listed below.

Hardly a round earth model. A Round Earth Solar System can't be simulated with this information. Where is the Round Earth Element? Is it the mention of the Earth's "equatorial radius"? A Round Earth is proven, and is entirely simulated, because an equation is using something called the earth's "equatorial radius"? Patently ridiculous. The Flat Earth Radius has an analogue to the Round Earth Radius. That something with that name is used shows nothing.

The fact that "celestial sphere" is mentioned makes it obvious. The celestial sphere is a regular astronomy term for the local celestial sphere to where we find bodies in the sky above us.

This does not look like a simulation of the Sun-Earth-Moon system at all.

[Rama Set]

Ed -

In a word “rubbish!”

Modern eclipse predictions do NOT use the Saros.

Rather, they are based on the orbital mechanics of the Earth, Moon, and Sun as laid out by Newton’s theory of gravitation. [Fred thinks that there is an n-body solar system out there based on Newton's Laws ]

More specifically, I use the Jet Propulsion Laboratory Developmental Ephemeris 430 (i.e., JPL DE430) to calculate the positions of the Moon, and Sun with respect to Earth. [Fred gives JPE DE as his evidence, because he mentions using them on his website for computing the positions of the sun or moon. JPE DE admits to be based on perturbation theory] This is the raw material from which the Besselian elements used in eclipse predictions are derived from (https://en.wikipedia.org/wiki/Besselian_elements). [See below] It involves a lot of spherical geometry to calculate every conceivable aspect of any solar eclipse.

Using this method, I can calculate the time of the start and end of any solar eclipse to a fraction of a second for any location on Earth. I challenge any flat Earther to match that precision and accuracy using flat Earth geometry.

Best regards,

Fred Espenak

PS - By the way, the JPL DE is also used to help navigate all the interplanetary spacecraft into orbits or flybys of the planets (e.g., New Horizons and Pluto).

Basselian elements

http://www.math.nus.edu.sg/aslaksen/gem-projects/hm/0304-1-08-eclipse/predictions.htm

Intro:

Bessel developed the method used to calculate and describe precisely any eclipse, based on using a coordinate system oriented to the shadow’s axis. The basic steps are: elements are calculated in the Besselian system to describe geometrical quantities; the observer’s position is transformed to Bessel’s coordinate system; equations of condition are formed; circumstances are derived that describe the time and the place of observable events or conditions in the Besselian system; the circumstances are transformed back to topocentric or geocentric coordinates. Many people have actually used the Besselian elements in calculating the eclipses.

Whether an eclipse will occur depends mostly on the coming together of two periodical phenomena, in this case the reaching of the proper lunar phase and the passing through a node. For more generality, we'll investigate the coming together of two arbitrary phenomena A and B. We assume that phenomenon A has a period PA, that phenomenon B has period PB, and that the lengths of those periods are constant.

...

Approximation With a Ratio of Whole Numbers

To base predictions of Z on periods, we must approximate γ with a ratio a⁄b of positive whole numbers. If we can find such a and b, then we can say that a periods PB are almost equal to b periods PA, and that hence that much time after a previous Z another Z will occur.

...

The first couple of very good approximations that we find for eclipses are listed in the following table. The very good approximations are a⁄b. The corresponding period of prediction and great period (to be explained later) are y (in years) en c (in years). The number of successful predictions in a row to be expected is between n1 and n2. The fraction of successful predictions of further eclipses based on earlier eclipses and the prediction period is equal to P. Very good approximation number 12 has the unusably large prediction period of 12393.4 years.

...

The Great Period
Eventually we use some approximation

(Eq. 10) γ' = a⁄b

for γ with whole numbers a and b. These numbers do not have to be determined using the method described above, and don't even need to give a particularly good approximation to γ. We assume (without loss of generality) that a and b have no divisors in common.

This approximation corresponds to the assumption that b periods PA are equal to a periods PB and that that much time after a previous Z there will be a next Z. We'll refer to this period of time as the period of prediction and will indicate it as y.

Etc.

We are reminded of the following quote of T.G. Ferguson in the Earth Review for September 1894, as appears in our literature:

No Doubt some will say, 'Well, how do the astronomers foretell the eclipses so accurately.' This is done by cycles. The Chinese for thousands of years have been able to predict the various solar and lunar eclipses, and do so now in spite of their disbelief in the theories of Newton and Copernicus. Keith says 'The cycle of the moon is said to have been discovered by Meton, an Athenian in B.C. 433,' then, of course, the globular theory was not dreamt of.

I am not sure why you keep highlighting the word period.  Is this supposed to be some sort of gotcha moment?

[Tom Bishop]

I am not sure why you keep highlighting the word period.  Is this supposed to be some sort of gotcha moment?

It's pattern-based prediction. The fact that "periods" and the ancient Saros Cycle is needed at all, and is plastered all over NASA's website, rather than a purely mathematical model of the earth-moon-sun system, says it all.

Astronomy is still in the Stone Age.

Astronomers must appeal to "perturbations" and "periods" rather than actual models of the solar system.

Flat Earth Civilizations came up with the idea to predict astronomical phenomena with patterns. If Fred wants an argument from a Flat Earther he need only look in the mirror.

[markjo]

Flat Earth Civilizations came up with the idea to predict astronomical phenomena with patterns.

Tom, what evidence do you have that Flat Earth civilizations were able to use just patterns like Saros cycles to accurately predict solar eclipses?

[Rama Set]

I am not sure why you keep highlighting the word period.  Is this supposed to be some sort of gotcha moment?

It's pattern-based prediction. The fact that "periods" and the ancient Saros Cycle is needed at all, and is plastered all over NASA's website, rather than a purely mathematical model of the earth-moon-sun system, says it all.

lol, you dont even know what the word period means in this context.   A period is simply an amount of time it takes to complete one cycle of a repeating event.  Of course orbits have a period in this context.

Astronomy is still in the Stone Age.

Incorrect.

Astronomers must appeal to "perturbations" and "periods" rather than actual models of the solar system.

Flat Earth Civilizations came up with the idea to predict astronomical phenomena with patterns. If Fred wants an argument from a Flat Earther he need only look in the mirror.

You dont know what a period means, something I learned in high school in probably grade 9 or 10.  The odds of you understanding any of this subject becomes even less likely.  To borrow your turn of phrase, you should feel ashamed and embarrassed to so badly misrepresent the topic you are disputing.