[edby]

[to Tom] tbh you obviously don't understand what your authors are even talking about.  they're looking for analytic solutions.  they're looking for sets of initial conditions that create periodic orbits.  these cases are special because if you know the initial conditions are t=0, then you have a single expression to tell you the positions of the objects at t=whenever.

but that doesn't have anything to do with numerical integration.  literally no one but you is claiming that anyone has an analytic model of the solar system.

Yup this seems merely like the distinction you find all over the place in engineering i.e. between closed form or analytic solutions, and numerical solutions. From Wikipedia:

A complete solution for a particular three-body problem would provide the positions for all three particles for all time, given three initial positions and initial velocities. In general, no closed-form solution for such a problem exists, and the time evolution of the system is believed to be chaotic. The use of computers, however, makes solutions of arbitrarily high accuracy over a finite time span possible using numerical methods for integration of the trajectories. https://en.wikipedia.org/wiki/Three-body_problem#Gravitational_systems 

[AATW]

Tell Fred that response is nonsense.

Tell him yourself.  I would love to read the correspondence between the two of you.

I did call it...

Interesting that Tom follows up his assertion that the response is nonsense with a link to a Wiki page which says:

Each ephemeris was produced by numerical integration of the equations of motion, starting from a set of initial conditions. Due to the precision of modern observational data, the analytical method of general perturbations could no longer be applied to a high enough accuracy to adequately reproduce the observations. The method of special perturbations was applied, using numerical integration to solve the n-body problem

There's more, but it's clear they're not just using patterns but using numerical solutions.
Tom's attempts to derail the thread and troll should be ignored.

[markjo]

I can't help but to wonder if Tom is under the impression that the various bodies our solar system are in stable orbits.  The moon is retreating from the earth at the rate of about 1 inch per year.  Gravitational perturbations cause asteroids and comets get kicked out the the oort cloud, asteroid and kuiper belts all the time.  It's even believed that the orbits of several planets have moved closer to or further away from the sun during the early development of the solar system.  Looking to the 3-body problem for stable periodic systems is purely academic because it just doesn't reflect the reality of the solar system that we live in.

[Tom Bishop]

tbh you obviously don't understand what your authors are even talking about.  they're looking for analytic solutions.  they're looking for sets of initial conditions that create periodic orbits.  these cases are special because if you know the initial conditions at t=0, then you have a single expression to tell you the positions of the objects at t=whenever.

but that doesn't have anything to do with numerical integration.  literally no one but you is claiming that anyone has an analytic model of the solar system.

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

From my last link about the supercomputer: https://academic.oup.com/pasj/article/70/4/64/4999993

Look at the sections:

1 Introduction
2 Numerical searching for periodic orbits
3 Results

Where do you see that they are searching for analytic solutions? It clearly says that they are numerically searching. This 'objection' is incorrect. It is widely accepted that there is no possible general purpose analytical solution, and it is rarely attempted. These numeric models are hoped to one day help create a general purpose analytic solution.

edby and Bobby, I see that you are making the same argument.

Recall this post:

https://twitter.com/poliastro_py/status/993418078036873216?lang=en

Look at this beautiful plot of several numerical methods for the restricted three body problem taken from Harier et al. "Solving Ordinary Differential Equations I". The use of high order Runge-Kutta methods is pervasive in Celestial Mechanics. Happy Monday!

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

[Tom Bishop]

Interesting that Tom follows up his assertion that the response is nonsense with a link to a Wiki page which says:

Each ephemeris was produced by numerical integration of the equations of motion, starting from a set of initial conditions. Due to the precision of modern observational data, the analytical method of general perturbations could no longer be applied to a high enough accuracy to adequately reproduce the observations. The method of special perturbations was applied, using numerical integration to solve the n-body problem

There's more, but it's clear they're not just using patterns but using numerical solutions.
Tom's attempts to derail the thread and troll should be ignored.

This was addressed with a definition and explanation of the perturbational methods provided earlier. That someone is claiming on Wikipedia that they provide "relitavistic corrections" or that they "account for the gravity of the many bodies of the solar system" or that they essentially "solved the n-body problem" does not matter. They did not solve the n-body problem, obviously.

Issac Newton, the authority who brought the laws of physics to the solar system, used the influence of God to explain why his solar system doesn't fall apart:

https://books.google.com/books?id=hy48DQAAQBAJ&lpg=PP1&pg=PA34#v=onepage&q&f=false

At the beginning of the 18th century, Newton famously wrote that the solar system needed occasional divine intervention (presumably a nudge here and there from the hand of God) in order to remain stable.¹¹ This was interpreted to mean that Newton believed his mathematical model of the solar system—the n body problem—did not have stable solutions. Thus was the gauntlet laid down, and a proof of the stability of the n body problem became one of the great mathematical challenges of the age.

¹¹Newton's remarks about divine intervention appear in Query 23 of the 1706 (Latin) edition of Opticks, which became Query 31 of the 1717 (2nd Edition) edition see Quote Q[New] in Appendix E). Similar 'theological' remarks are found in scholia of the 2nd and 3rd editions of Principia, and in at least one of Newton's letters. In a 1715 letter to Caroline, Princess of Wales, Leibniz observed sarcastically that Newton had not only cast the Creator as a clock-maker, and a faulty one, but now as a clock-repairman (see [Klo73], Part XXXIV, pp. 54-55).

Please tell us, if you are a true believer, who solved the n-body issues and got the solar system to work? Surely, there must be a name for this famous figure.

Tell us the name of this person to put this issue to bed.

[RonJ]

I am thinking that the whole universe is just an example of Brownian motion on a galactic scale.  The earth is just a minute part of that universe and we are all just moving thru time tying to make sense out of the limited observations we can make.  It has been observed that certain laws of motion do apply and can predict where an object will go if all the variables can be measured in advance and don’t change along the way.  I would agree that there probably isn’t an explicit equation of motion for the entire known solar system.  If there was that equation would have to have an infinite number of terms to fully describe every little thing.  I don’t think that you need to know everything about everything to calculate something useful.   Newtonian equations of motion can calculate the positions of the known bodies in the solar system with enough accuracy to be useful.  There will always be some previously unknown factor that can change things, but then the equation can be adjusted.  Brownian motion only accounts for the statistical, not the absolute.  I can fully agree that the solar system must contend with a certain amount of chaos.  That chaos so far only requires small changes in the overall scheme of things.  It’s like driving to work in the morning.  You know exactly where you will end up, but there may be some small delays or detours along the way that you didn’t know about when you left the house.  Eventually the sun will supernova, it has been said, and the earth, flat or round, will be consumed.  When that happens, it will just be another example of the chaotic nature of the galaxy and ashes to ashes and dust to dust for us all.

[Tom Bishop]

I can't help but to wonder if Tom is under the impression that the various bodies our solar system are in stable orbits.  The moon is retreating from the earth at the rate of about 1 inch per year.  Gravitational perturbations cause asteroids and comets get kicked out the the oort cloud, asteroid and kuiper belts all the time.  It's even believed that the orbits of several planets have moved closer to or further away from the sun during the early development of the solar system.  Looking to the 3-body problem for stable periodic systems is purely academic because it just doesn't reflect the reality of the solar system that we live in.

This is illogical, markjo. A supercomputer tested millions and millions of combinations and could only find solutions where at least two of the masses were exactly the same. If the masses were not exactly the same, or if the velocities or positions of the bodies of the system were slightly changed from their perfect configuration, the system quickly fell apart, as was studied by Poincare, and as was demonstrated in the demo provided to you earlier. These are highly sensitive configurations.

Mainstream Astronomy generally states that it is possible for a star to have a planet, and for that planet to have a moon. Why don't we see that in any of these orbits?

Making a slight adjustment to the masses of the bodies in the demo we saw earlier did not create a different "chaotic" system that somehow stayed together. It always created a chaotic system that tore itself apart. Such is the basis of Chaos Theory. One small chaotic element creates a very large chaotic result.

I request and demand that you demonstrate your argument.

[RonJ]

http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172009000100003#tab1

Well, there's been another loop in the discussion.  The OP Bobby was hypothesizing that you would need more than just pattern based descriptions to accurately predict eclipses.  My link points to a researcher that has all the equations using strictly Newtonian mechanics that accomplishes that objective.  Is this an infinite loop?  Where is the exit?

[RonJ]

Reply #63 was interesting.  The curves showed how an Arenstorf Orbit goes awry after a limited number of iterations.  What was interesting was the use of the work of Arenstorf to illustrate a point.  The Apollo program used the Arenstorf Orbits to successfully get men to the moon.   Of course, if you do a little research the orbits needed depended upon the recognized figures for the earths and moons gravity.  Also, the recognized distances were used.  In FET the earth’s gravity is greatly reduced and the Arenstorf Orbit wouldn’t even be possible in the given circumstances.  It is totally illogical to use an example based upon something that is unrecognized by FET.  It would a better idea to show why the 3-body problem won’t work using an example based upon the Flat Earth paradigm with a ‘greatly diminished’ force of gravity postulated by FET.   

[markjo]

I can't help but to wonder if Tom is under the impression that the various bodies our solar system are in stable orbits.  The moon is retreating from the earth at the rate of about 1 inch per year.  Gravitational perturbations cause asteroids and comets get kicked out the the oort cloud, asteroid and kuiper belts all the time.  It's even believed that the orbits of several planets have moved closer to or further away from the sun during the early development of the solar system.  Looking to the 3-body problem for stable periodic systems is purely academic because it just doesn't reflect the reality of the solar system that we live in.

This is illogical, markjo. A supercomputer tested millions and millions of combinations and could only find solutions where at least two of the masses were exactly the same. If the masses were not exactly the same, or if the velocities or positions of the bodies of the system were slightly changed from their perfect configuration, the system quickly fell apart, as was studied by Poincare, and as was demonstrated in the demo provided to you earlier. These are highly sensitive configurations.

Mainstream Astronomy generally states that it is possible for a star to have a planet, and for that planet to have a moon. Why don't we see that in any of these orbits?

Making a slight adjustment to the masses of the bodies in the demo we saw earlier did not create a different "chaotic" system that somehow stayed together. It always created a chaotic system that tore itself apart. Such is the basis of Chaos Theory. One small chaotic element creates a very large chaotic result.

I request and demand that you demonstrate your argument.

I'm not completely sure that I understand what you want.  Do you want me to demonstrate that the solar system is not stable? 

I think that this article may help clarify some misconceptions about 3-body systems that you seem to be operating under.  Yes, it's written for financial investors, but it has some good information that is relevant.
https://medium.com/@mikeharrisNY/misconceptions-about-the-three-body-problem-and-its-relation-to-forecasting-c0c0a2bf44cc

[Bobby Shafto]

I think that this article may help clarify some misconceptions about 3-body systems that you seem to be operating under.  Yes, it's written for financial investors, but it has some good information that is relevant.
https://medium.com/@mikeharrisNY/misconceptions-about-the-three-body-problem-and-its-relation-to-forecasting-c0c0a2bf44cc

Nice!

Learned a new term: Lyapunov Time

Which led to a Wikipedia article I didn't know existed: Stability of the Solar System

This is why I love this board.

[edby]

I think that this article may help clarify some misconceptions about 3-body systems that you seem to be operating under.  Yes, it's written for financial investors, but it has some good information that is relevant.
https://medium.com/@mikeharrisNY/misconceptions-about-the-three-body-problem-and-its-relation-to-forecasting-c0c0a2bf44cc

Nice!

Learned a new term: Lyapunov Time

Which led to a Wikipedia article I didn't know existed: Stability of the Solar System

This is why I love this board.

If you Google 'stability of the solar system' you will find a lot more

I am puzzled as to what Tom's argument is. I think it's something like:

1. If classical mechanics is true, then the solar system is highly unstable
2. The solar system is not highly unstable
3. Ergo classical mechanics is not true

The argument is valid (premises imply conclusion), the question is whether the premises are true. Also, whether that is what Tom is arguing. A lot of sidewinds in this discussion.

[Tom Bishop]

Do a search for "Laskar" in that Stability of The Solar System link. You will find that the analysis and derivatives are based on his work.

Sandokan addressed Laskar here earlier this year:

This explains it well.

It does not, on the contrary.

Scott Tremaine's arguments rest totally on Jacques Laskar's numerical simulations.

In summary:

Rama, look at the quotes Sandokan gave in response to edby about the millions of years stability stuff.



Where did he get his data on "eccentricity" and "orbital shape," one may ask? From the place all astronomers get it from under in their fantasy conjecture: The sky!

Smooth out over "long term trends." This clearly indicates a statistical analysis.

Newtons laws and equations are not used. It is based on something else entirely.

[Rama Set]

Yes continue to ignore modern eclipse predictors directly refuting you and the recent models of the solar system that are presented and cherry pick text from a while ago. It’s incredibly convincing.

[edby]

Oh I remember this is the Velikovsky stuff. We discussed that before.

[Tom Bishop]

Oh I remember this is the Velikovsky stuff. We discussed that before.

What is the rebuttal? I fail to see where one was provided.

I see that the sources are cited in the text:

[edby]

Charles Ginenthal is the author of Carl Sagan and Immanuel Velikovsky and co-author of Stephen J. Gould and Immanuel Velikovsky. He has published papers in the journals Aeon, Meta Research, and The Velikovskian (of which he is Publisher).

Aeon is a ‘digital magazine of ideas’
Meta Research does not seem to be a physics journal

What is the rebuttal? I fail to see where one was provided.

Velikovsky

[Tom Bishop]

The sources cited are not Velikovsky.

I see that the sources are cited in the text:

[RonJ]

Some of the arguments are interesting.  I see that sources like Jacques Laskar are used to make a point that the solar system is in chaos.  Actually, my research seemed to yield that Laskar did claim that stability was possible up to around 10 million years.  After that things may get shaky. What little I saw of a book of his certainly had an illustration of the solar system with the sun at the center and all the traditional planets orbiting them.  Maybe Laskar was making all the wrong assumptions in the first place and should have had the Sun orbiting above the flat Earth.  I see that the scientists so far that have worked on the 3-body problem have all been working under the assumption that the earth is a sphere and the center of the solar system is the sun.  I want to see some authoritarian works (with lots of equations of motion) showing that the 3-body problem can’t be solved using the FET paradigm.  That way, at least, I can get a handle on what the masses, orbits, and diameters of all the bodies happen to be.  You can’t seem to get any of that from the Wiki on this site.     

[markjo]

Tom. I don't think that anyone is saying that Saros isn't important for understanding why and more or less when eclipses happen.  Astronomers wouldn't keep bringing it up if it wasn't. 

However, Saros simply isn't as useful for predicting exactly where and when eclipses occur (especially total solar eclipses) as you might want to us think.  That is unless you can show us the procedure for using Saros alone to predict exactly when the next total solar eclipse will be visible in any given location.