The Flat Earth Society
Flat Earth Discussion Boards => Flat Earth Theory => Topic started by: QED on May 04, 2019, 11:32:27 PM

Since my reply in the other thread carelessly left out the actual link for the code, I thought I’d present it fresh for those interested.
https://stjarnhimlen.se/comp/tutorial.html
It is written in BASIC, and you just need to execute it.
Happy orbiting.
Tom  run the code and stop complaining please.
Also Tom  everyone knows that the orbits in this solar system are quasistable, and are degrading. Hence, your request for stable orbits is poisoning the well. Stability is not present, is not needed, and is irrelevant to this conversation. For discussion of bound orbits, stability is offtopic.

That's not an nbody simulation. Newton's equations for gravity are expressed nowhere in that link.
That code is using the perturbation method of predicting the location of planets and celestial bodies, as described at Astronomical Prediction Based on Patterns  Perturbations (https://wiki.tfes.org/Astronomical_Prediction_Based_on_Patterns#Perturbations)
(https://i.imgur.com/0szvgKD.png)

That's not an nbody simulation. Newton's equations for gravity are expressed nowhere in that link.
That code is using the perturbation method of predicting the location of planets and celestial bodies, as described at Astronomical Prediction Based on Patterns  Perturbations (https://wiki.tfes.org/Astronomical_Prediction_Based_on_Patterns#Perturbations)
(https://i.imgur.com/0szvgKD.png)
You don’t want an nbody simulation, remember? You want the equations plotted. This will do that. Stop stalling. I predicted that you wouldn’t plot the equations and I was correct. Moreover, I predicted what diversion you would use, and was again correct.
I won’t respond to any more diversions you present regarding this topic. I have better things to do with my time.
This matter is closed until you decide to evaluate the evidence placed in front of you.
BTW, the longer you postpone doing so, the more foolish you will look. It is no problem for me to tolerate your refusal to plot them. At some later point which is advantageous to me, I will run the code, show you and everyone else the results, and use it to demonstrate that the evidence had been placed before you, and your intransigence against behaving zetetically cost time, resources, respect, and influence.

You don’t want an nbody simulation, remember?
I do want an nbody simulation. We were talking about the three body problem and the nbody problems and whether the heliocentric orbits work with Newtonian physics. This addresses none of that. This is not an nbody simulation. This is based on Perturbation Theory, and is totally invalid for demonstrating the possibility of the sunearthmoon system or 3+ body orbits.

You don’t want an nbody simulation, remember?
I do want an nbody simulation. We were talking about the three body problem and the nbody problems and whether the heliocentric orbits work with Newtonian physics. This addresses none of that. This is not an nbody simulation. This is based on Perturbation Theory, and is totally invalid for demonstrating the possibility of the sunearthmoon system or 3+ body orbits.
You are wrong, and do not understand what you are reading. Again. This plots the equations you wanted, which are solutions for the the orbits.
It also handles perturbations from those orbits, which is a bonus, but not really relevant for our purposes. In other words, it provides more than you need.
Accounting for perturbations is not the same as perturbation theory. You are using those words wrong because you do not understand them.

You think that these perturbations are different than the perturbation method of prediction described by the sources in the Wiki link? Interesting. However, and unfortunately, "I think that..." isn't very strong evidence. You should support your opinions. I encourage you to demonstrate yourself to be correct through references, sources or citations.
You also think that these predicted positions are the result of, or match with, an nbody simulation? Interesting again. If true, that is quite extraordinary. I can only encourage you once again to provide reference, source, or citation to strengthen your ideas and opinions.

You think that these perturbations are different than the perturbation method of prediction described by the sources in the Wiki link? Interesting. However, and unfortunately, "I think that..." isn't very strong evidence. You should support your opinions. I encourage you to demonstrate yourself to be correct through references, sources or citations.
You also think that these predicted positions are the result of, or match with, an nbody simulation? Interesting again. If true, that is quite extraordinary. I can only encourage you once again to provide reference, source, or citation to strengthen your ideas and opinions.
What purpose does it serve to provide references that you will not understand (intentionally or otherwise)?
Once again I have provided proof, and once again you claim it is not there. Interesting.
Do whatever you want, Tom. I shall continue:
1. Requesting that FET justify its claims
2. Requesting that FEers present a model
3. Refuting fraudulent criticisms of science with evidence.
What you do is rather irrelevant, because it involves no action.
Goodbye.

Sorry QED, the simulation uses Kepler's laws along with the periodic perturbations between the gas giants. It is, literally, the exact problem that Tom was talking about.
I might make my own simulation later.

You think that these perturbations are different than the perturbation method of prediction described by the sources in the Wiki link? Interesting. However, and unfortunately, "I think that..." isn't very strong evidence. You should support your opinions. I encourage you to demonstrate yourself to be correct through references, sources or citations.
You also think that these predicted positions are the result of, or match with, an nbody simulation? Interesting again. If true, that is quite extraordinary. I can only encourage you once again to provide reference, source, or citation to strengthen your ideas and opinions.
Why don't YOU provide us references, sources or citations to prove your ideas and opinions? I am craving for these for years now.

Sorry QED, the simulation uses Kepler's laws along with the periodic perturbations between the gas giants. It is, literally, the exact problem that Tom was talking about.
I might make my own simulation later.
The issue is that Perturbation Theory is used to gradually add corrections to make data fit the formula of choice:
https://en.wikipedia.org/wiki/Perturbation_theory
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 (https://en.wikipedia.org/wiki/Threebody_problem) in the calculation of the motions of planets in the solar system. For instance, Newton's law of universal gravitation explained the gravitation between two astronomical bodies, but when a third body is added, the problem was, "How does each body pull on each?" Newton's equation only allowed the mass of two bodies to be analyzed. The gradually increasing accuracy of astronomical observations led to incremental demands in the accuracy of solutions to Newton's gravitational equations, which led several notable 18th and 19th century mathematicians, such as Lagrange and Laplace, to extend and generalize the methods of perturbation theory. These welldeveloped perturbation methods were adopted and adapted to solve new problems arising during the development of quantum mechanics in 20th century atomic and subatomic physics. Paul Dirac developed perturbation theory in 1927 to evaluate when a particle would be emitted in radioactive elements.

Sorry QED, the simulation uses Kepler's laws along with the periodic perturbations between the gas giants. It is, literally, the exact problem that Tom was talking about.
I might make my own simulation later.
The issue is that Perturbation Theory is used to gradually add corrections to make data fit the formula of choice:
https://en.wikipedia.org/wiki/Perturbation_theory
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 (https://en.wikipedia.org/wiki/Threebody_problem) in the calculation of the motions of planets in the solar system. For instance, Newton's law of universal gravitation explained the gravitation between two astronomical bodies, but when a third body is added, the problem was, "How does each body pull on each?" Newton's equation only allowed the mass of two bodies to be analyzed. The gradually increasing accuracy of astronomical observations led to incremental demands in the accuracy of solutions to Newton's gravitational equations, which led several notable 18th and 19th century mathematicians, such as Lagrange and Laplace, to extend and generalize the methods of perturbation theory. These welldeveloped perturbation methods were adopted and adapted to solve new problems arising during the development of quantum mechanics in 20th century atomic and subatomic physics. Paul Dirac developed perturbation theory in 1927 to evaluate when a particle would be emitted in radioactive elements.
Why is that a problem?

Simply because it is adding a series of corrections to get to your ideal state, and is therefore not evidence for that ideal state. A series of corrections can get one to any state desired.

Simply because it is adding a series of corrections to get to your ideal state, and is therefore not evidence for that ideal state. A series of corrections can get one to any state desired.
The corrections are not added to get to an "ideal state". The corrections are added to get the model to better match observations. Isn't a model that accurately matches observations a good thing?

@Tom Bishop, the perturbations are derived from the theory and measurements of the planets and other objects. The perturbations do not correct the theory of orbital motions; they are provided by that theory. One begins the calculation of an object's orbit with a very rough approximation. Then one of several standard recipes is used to "correct" that rough approximation so that it better matches the ideal Newtonian theory of orbital motion.
I know of only one exception: Newtonian mechanics is not sufficient for highaccuracy prediction of the orbit of Mercury. In Mercury's case, General Relativity prescribes perturbations that should be applied to the Newtonian calculation of Mercury's orbit. (Of course one can also calculate Mercury's orbit directly from GR.)

The corrections are not added to get to an "ideal state". The corrections are added to get the model to better match observations. Isn't a model that accurately matches observations a good thing?
Adding corrections until the model matches observations makes the matter moot. Any model can be defined as the ideal state.
The perturbations do not correct the theory of orbital motions; they are provided by that theory.
Would this be backed up by your accompanying provided evidence of nothing at all?
That does not appear to be described anywhere. I encourage you to provide a direct citation for your statements.

The corrections are not added to get to an "ideal state". The corrections are added to get the model to better match observations. Isn't a model that accurately matches observations a good thing?
Adding corrections until the model matches observations makes the matter moot.
No. Adding corrections until the model matches observations is the whole point of making models. Understanding why the corrections to the model are necessary helps you to understand the workings of the system being modeled. Even the ancient geocentrists added corrections to their models (epicycles and deferents) to better match their observations.

Adding corrections until the model matches observations makes the matter moot. Any model can be defined as the ideal state.
This is a claim which requires evidence. Until you can present evidence which demonstrates that any model can be defined as the ideal state, your claim remains unfounded.
In fact, I can disprove your claim using a proof by contradiction. All I need to do is find a model which cannot be defined as the ideal state. That model exists. It is the FE model. It cannot explain the terminus.
It would be a wonderful demonstration of your position is you could define the FE model to describe a 24 hour cycle :)

The perturbations do not correct the theory of orbital motions; they are provided by that theory.
Would this be backed up by your accompanying provided evidence of nothing at all?
That does not appear to be described anywhere. I encourage you to provide a direct citation for your statements.
Considering the huge wealth of citations and software that others have provided in this and closely related threads recently, I don't think that I can add anything useful by providing more citations. The disagreement seems to be about how to interpret these many sources, and I only intended my comment to help explain them. I did notice one interesting quote in this thread here:
The issue is that Perturbation Theory is used to gradually add corrections to make data fit the formula of choice:
https://en.wikipedia.org/wiki/Perturbation_theory
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.
Note that the sentence that you quote from Wikipedia says that one uses the perturbations to obtain a "closer match to the original formula", not as you say to "make data fit the formula of choice". Wikipedia's sentence is describing a situation in which one simplifies a complicated problem and obtains a formula that is the exact solution to the simplified problem but only an approximate solution of the complicated problem. That formula is then corrected to more closely match the "original formula", which would be the exact solution of the complicated problem. The corrections are called "perturbations", and they are prescribed by the original complicated problem. You don't have to take my word for it. If you read further in the Wikipedia article, it describes an example in which one wants to model the motion of the Earth, Moon, and Sun. To simplify the problem, you start with the elliptical orbit of the Moon around the Earth. You then add a perturbation corresponding to the force of the Sun according to F=ma. If more accuracy is desired over a longer period, you can add more perturbations.

Give it another read. The F=ma example is the simplified state to which perturbations are applied; like the example of the simplified (traditional) model of the atom to which perturbations are applied because the simplified model does not represent reality.

So it appears to me that tom wants a solution to the 3 body problem in the form of :
for time = x ; solve for the position of body's a,b and c
This doesn't have a solution at present. (ie THIS is the unsolved 3 body problem)
What can be done is to step through from time = 0 until time = x , calculating positions of a,b and c at each time step (the smaller the steps the better the accuracy)
This is where toms argument that the heliocentric solar system is not possible falls apart. The universe does not jump to time = x it progresses from time = 0.

Give it another read. The F=ma example is the simplified state to which perturbations are applied; like the example of the simplified (traditional) model of the atom to which perturbations are applied because the simplified model does not represent reality.
No, you use the simplified models because they're simpler and easier to work with. You don't need to solve for every individual atom in a liter of water just to see if it can dissolve a given set of ions. You can instead just test for a table of measured K_{sp} values; if any of them fail, you get a precipitate forming.
Since that equation is technically Creative Commons. (https://xkcd.com/2034)

Give it another read. The F=ma example is the simplified state to which perturbations are applied; like the example of the simplified (traditional) model of the atom to which perturbations are applied because the simplified model does not represent reality.
Tom Bishop, that Wikipedia article says "Typically, the 'conditions' that represent reality are a formula (or several) that specifically express some physical law, like Newton's second law, the forceacceleration equation, F=ma.". In that sentence, I interpret "conditions that represent reality" to mean that F=ma can describe reality rather than only a simplification of it. Do you believe that Wikipedia is saying that F=ma can only be "the simplified state"? Can you explain in more detail why you interpret Wikipedia to be saying that? (I'm not sure what you mean when you refer to an equation as a "state". In physics literature that I have read the "state" is usually the information about the physical system: positions and velocities of the orbiting bodies in this example.)
Of course F=ma can describe a simplified model when some forces are not included in F. For example, in the full model describing the Moon's motion, F could include all gravitational forces from the Sun, Earth, Mars, Venus, asteroids, and all other objects acting on the Moon. In that case F=ma would represent reality, but the exact orbit would be difficult to calculate, so one might temporarily neglect smaller forces. An approximate orbital path can be calculated using only the force caused by the Earth acting on the Moon. Then a better approximation can be obtained by including effects of the forces that were neglected. That process of obtaining a better approximation is what we call "perturbation".