[Tom Bishop]

You are providing zero evidence, Rama Set. Go and ask a mathematician about the three body problems you say simulate the Sun-Earth-Moon system. Can't be done.

Astronomy cannot simulate the Sun-Earth-Moon system.

We are witnessing the continued failure of Team Ball to defend their position that the solar system can be simulated, which is repeatedly professed to be true. Year after year, this conversation repeats itself. The fantasy cannot exist under Newton's laws. The Three Body Problem shows that. It is not an merely academic exercise. It was Newton's own personal failing to model his theory, and which required an appeal to divine intervention to solve. Farcical failure.

[Rama Set]

I don’t understand where your failure to understand comes from. You have been provided multiple simulations of the solar system in this thread. All this is ignoring, of course, that we have successfully navigated proves in to the orbits of other planets, which is sportingly not brought up. But really, the denial is pathological, and the misunderstandings are disastrous. Literally a member of the NASA eclipse team directly refuting your position is in this thread and you deny it. So whatever argument you believe you are making is utterly unconvincing.

[Tom Bishop]

There is zero evidence that the n-body issues have been solved. Provide evidence that the n-body problems have been solved and that the solar system, or the sun-earth-moon system, can be simulated.

Why do the existing solutions and simulations of the three body problem require at least two bodies of the exact same mass? This has yet to be addressed.

I thought we were told that it was possible for a sun to have a planet, and for that planet to have a moon? That's not possible in astronomy? Then none of it is possible. It is a farce.

It is difficult for you guys to show that it is possible because you are wrong.

[markjo]

You are providing zero evidence, Rama Set. Go and ask a mathematician about the three body problems you say simulate the Sun-Earth-Moon system. Can't be done.

Astronomy cannot simulate the Sun-Earth-Moon system.

Perhaps not, but it can provide an accurate approximation.

[Bobby Shafto]

...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 ]

That is not what Fred can be said to think based on the statement her wrote. This is the crux of the divergence from my opening post. Espenak is not saying that there is an N-Body solution. It's irrelevant to what Fred is saying.

You're conflating issues. I don't think it's intentional. I think you are just mistaken and you've erected a false dichotomy based on the N-body issue.

[RonJ]

https://engineering.purdue.edu/people/kathleen.howell.1/Publications/Dissertations/1998_Wilson.pdf

Here is a 3 body problem plus spacecraft.  The 3 main bodies are Earth, Moon, and Sun.  All the motions and gravitational field vectors are calculated so the spacecraft can successfully navigate it's mission.  The spacecraft did complete the mission and verified all the calculations of the 3 body problem.  Now you have a calculation and an actual verification of the accuracy.  The problem is no longer theory, it's fact.

[Tom Bishop]

As far as I am aware, it is not possible to even approximate the Sun-Earth-Moon system. The video you posted implies masses of different sizes; when this is not the case with the Three Body Problem.

Take a look at the Three Body Problem family gallery: http://three-body.ipb.ac.rs/

Here is an N-Body Orbit Gallery, which showcases the limited orbits that can be made, and which must assume that bodies are of equal mass or mass-less: http://rectangleworld.com/demos/nBody/

The ones that look like a heliocentric system don't exist. I am unable to find that family anywhere in the list of families.

https://engineering.purdue.edu/people/kathleen.howell.1/Publications/Dissertations/1998_Wilson.pdf

Here is a 3 body problem plus spacecraft.  The 3 main bodies are Earth, Moon, and Sun.  All the motions and gravitational field vectors are calculated so the spacecraft can successfully navigate it's mission.  The spacecraft did complete the mission and verified all the calculations of the 3 body problem.  Now you have a calculation and an actual verification of the accuracy.  The problem is no longer theory, it's fact.

That's a student's dissertation about navigating around a hypothetical system with existing three body problem solutions. The name of the chapters tell that it is using the restricted three body problem, where two of the masses are massive and one is of a negligible mass.

[RonJ]

That is completely true, however the model outlined in the dissertation was actually employed to send the GENESIS satellite to collect solar wind samples and return it to the earth.  That project was completed.  You have to do more research to realize that fact. 

Do more research on what 'restricted' means.  Your definition is incorrect.  A 3 body restricted mission was completed a long time ago.  What that means is Earth, Moon, spacecraft.  The restricted part means that one of the bodies doesn't affect the other two.  Anytime you have gravitational force between two bodies each body will affect the other.  The earth rotates around the sun, but it could also be said that the sun rotates around the earth.  The sun is a lot more massive so the orbit is quite small in relation to the orbit of the earth.  The same goes for the Earth Moon relationship.  If you send a spacecraft into the gravitational field of the earth, moon, or sun those bodies will also move, but it's like pissing in the ocean, you won't be able to measure it.  The effect on the spacecraft is completely different because of the ratio of the masses. The masses of any of the objects involved don't have to be the same.  Each can be different. 

In the case of the GENESIS mission the problem solved and demonstrated to work was the restricted 4 body problem.  Earth, Moon, Sun, and spacecraft.  Each with a completely different mass.  Example shown and demonstrated to work.  I don't think a caveman could have completed the project.

[garygreen]

Peterson was not misquoted. From Newton's Clock:

do you really not understand what quote mining is?  it's dishonest to selectively quote a text to make it seem as if the author is making a different point than he or she is actually making.  yes, the author makes that remark about laskar's work in 1983.  but then immediately after that he explains that other simulations absolutely did model the solar system directly and confirmed laskar's results.  he describes the nature and results of some of those simulations.

the source that you presented as a credible authority explicitly disagrees with everything you are claiming, and he says so directly.  read the quotes i posted.  he's quite clear.

Lets see the three body simulations of three bodies with unequal masses.

i already provided you with a nine-body simulation.  this is literally a simulation of the solar system carried out by directly calculating newton's laws and letting the system evolve. 
A three million year integration of the earth's orbit

[JCM]

Sounds like 3 million year predictions is not accurate enough for Mr. Bishop.  Is the bar for RE math a billion years? Infinity with zero inaccuracy?  As for patterns, those Saros cycles are from 2000 up to 12000 year patterns...  How is any human being without today’s computing power supposed to make predictions on a cycle that takes thousands of years and they can’t see most of them in any one region of the planet.  This is assuming there aren’t clouds covering up a partial eclipse.  It is impossible for anyone on the planet to make accurate solar eclipse predictions without modern calculations.  We are still waiting how the ancients could predict the exact locations on the planet where solar eclipses will be visible.  Not when somewhere on the planet, but where,  width, distance, direction of those solar eclipses?  Lunar eclipses are easy compared to pinpointing the shadow of the moon onto the Earth exactly.

[George Jetson]

Peterson was not misquoted. From Newton's Clock:

do you really not understand what quote mining is?  it's dishonest to selectively quote a text to make it seem as if the author is making a different point than he or she is actually making.  yes, the author makes that remark about laskar's work in 1983.  but then immediately after that he explains that other simulations absolutely did model the solar system directly and confirmed laskar's results.  he describes the nature and results of some of those simulations.

the source that you presented as a credible authority explicitly disagrees with everything you are claiming, and he says so directly.  read the quotes i posted.  he's quite clear.

Lets see the three body simulations of three bodies with unequal masses.

i already provided you with a nine-body simulation.  this is literally a simulation of the solar system carried out by directly calculating newton's laws and letting the system evolve. 
A three million year integration of the earth's orbit

From the abstract of that Harvard paper:  " The initial conditions are taken from the JPL DE 102 ephemeris." 

Wikipedia says about the JPL DE 102 ephemeris:  "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, in effect putting the entire Solar System into motion in the computer's memory, accounting for all relevant physical laws. "

Tom's point stands.

[George Jetson]

Sounds like 3 million year predictions is not accurate enough for Mr. Bishop. 

A quotation from gary's paper:  "'Accurate' can only be loosely defined in this context." 

[Rama Set]

Peterson was not misquoted. From Newton's Clock:

do you really not understand what quote mining is?  it's dishonest to selectively quote a text to make it seem as if the author is making a different point than he or she is actually making.  yes, the author makes that remark about laskar's work in 1983.  but then immediately after that he explains that other simulations absolutely did model the solar system directly and confirmed laskar's results.  he describes the nature and results of some of those simulations.

the source that you presented as a credible authority explicitly disagrees with everything you are claiming, and he says so directly.  read the quotes i posted.  he's quite clear.

Lets see the three body simulations of three bodies with unequal masses.

i already provided you with a nine-body simulation.  this is literally a simulation of the solar system carried out by directly calculating newton's laws and letting the system evolve. 
A three million year integration of the earth's orbit

From the abstract of that Harvard paper:  " The initial conditions are taken from the JPL DE 102 ephemeris." 

Wikipedia says about the JPL DE 102 ephemeris:  "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, in effect putting the entire Solar System into motion in the computer's memory, accounting for all relevant physical laws. "

Tom's point stands.

No it doesn’t. It is a simulation of multiple objects of varying mass. Tom claimed this was impossible.

[JCM]

Did you read the paper?  You are suggesting that 1 radian of error to Earths location after 3 million years of calculations proves Toms point?  1 radian!  It’s not 100% perfect over millions of years so the Earh is flat, that’s what you are saying. 

Tom's point stands.

Your bar for RE math is impossible to meet, yet FE requires magic to make the most critical parts of it work (even with magic, it still doesn’t work).  Not just magic like UA, but selective magic UA, a cartwheeling universe around the accelerating Earth, accelerating and decelerating magically held aloft Sun and Moon without visibly changing in speed, magic bendy light in specific ways up down curving whichever way is needed at that moment in time, ice wall no one has ever seen...  I can go on for a while here I haven’t even listed the most obvious issues...

   Literally, nothing in FEH matches reality and that’s ok.

[Tom Bishop]

i already provided you with a nine-body simulation.  this is literally a simulation of the solar system carried out by directly calculating newton's laws and letting the system evolve. 
A three million year integration of the earth's orbit

https://i.imgur.com/AY2HS7B.png

Read the first two sentences of that abstract:

Abstract

We have integrated the equations of motion of the nine planets and the Earth's spin axis for 3.05 million years into the past. The equations include the dominant relativistic corrections and the corrections for the quadropole movement of the Earth-Moon system

Why would we need "relativistic corrections" if this is, as you assert, a full simulation of gravity?

The Wikipedia article on Perturbation Theory says:

  “ 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. ”

If your formula doesn't work, just keep adding corrections until it does. Science!

[Rama Set]

It’s a simulation, not an implementation of the scientific method. The question of why you would add relativistic corrections to a model using GR seems pretty self-evident.

[George Jetson]

Did you read the paper?  You are suggesting that 1 radian of error to Earths location after 3 million years of calculations proves Toms point?  1 radian!  It’s not 100% perfect over millions of years so the Earh is flat, that’s what you are saying. 

Actually the paper says "At the end of integration, the fractional error in the earth's position is shown to be less than 0.03 radian, and larger errors of up to several radians are shown for other planets."    This is only theoretical however because you cannot verify the positions of the planets 3 million years ago.  To quote the paper:  "We believe that the physical model, the initial conditions and the integration procedure are accurate enough that the fractional error in Earth's position is less than 0.03 radian."

The off topic grandstanding rhetorical stuff in your post will ignored.

[RonJ]

Please shut off your trolling motor, drop anchor, and put out a hook and a line for some facts that you can keep.

If your formula doesn't work, just keep adding corrections until it does. Science!

Newtonian equations work fine.  You can get any desired level of accuracy you want.  When you need more accuracy all you do is provide the necessary accuracy to the variables in the formula.  Of course that's the crux of the problem.  There are always measurement errors.  In some cases there are variables out there that are unknown.  Anytime you have a measurement error it usually tells you something.  Sometimes small errors are completely expected and have a known cause.  Other times you can have an error that's unexpected and you can use that information for further investigation.  Everything is probabilistic.  If I make a measurement 10000 times and all the numbers are within say 1 in a million and I then get a number that is way out of that range, what would be the expected result?  Probably I wouldn't expect that the formula is defective.  I would look for an obvious problem with the equipment or some anomalous event nearby that had an unwanted effect on your measurement.  In most cases you will end up finding out why there was a problem with the reading.  If you made another 10000 readings that were completely different and weren't expected by your equations, only then, would I suspect my equations.

[Bobby Shafto]

This has gone way off the rails.

The N-body problem is a red herring.

The issue I raised in the opening post of this topic is the TFES Wiki's (Tom's) claim that eclipse predictions are based on patterns. That's wrong, and whether or not the N-Body problem eludes solution doesn't matter. Cycles are time-based. There is nothing about a Saros cycle that can provide the parameters needed to calculate Besselian elements of a solar eclipse.

You can't get this from a cycle:


You can't produce this based on a mere cycle:


This is the predicted solar eclipse for July 2, 2019. It's part of Saros cycle 127. But that's not the basis for predicting the detailed characteristics of the eclipse: the where, the how much, the duration, etc. For that, you need the Besselian elements, which are based on the relative position and motion of the earth/moon/sun and spherical geometry of the earth. It doesn't matter if the ephemeris providing  earth/moon/sun location and motion are divinely granted or calculated based on a perfect solution to the 3-body problem of these 3 bodies, with or without perturbation by other solar system or galactic bodies. It doesn't matter. That's a distraction. Either intentional or misguided.

The ability to calculate where on earth the eclipse will be seen, the degree of totality, the coverage of the umbra and penumbra, precisely when it will begin and end, etc. doesn't hinge on solving the n-body problem.  There is no flat earth model analog for how Fred Espenak performs his calculations by using an ephemeris of a rotating globe earth, orbited by a globe moon, orbiting a spherical sun. It's based on spherical geometry and absolutely requires input of position and motion of the 3-bodies. It's not "patterns" at all.

Tom has managed to derail this and get everyone debating aspects how the ephemerides are produced, under the illogical reasoning that if a million-year stable n-body solution can't be calculated using Newtonian mechanics, that the entire edifice collapses and all that remains is "patterns."

When eclipse #58 in Saros Cycle 127 begins, it will occur and have the characteristics predicted. That prediction won't be just a table look up of a pattern. It will be calculated based on the shape of the earth, the shape of the moon's shadow on the convex surface of the globe earth, based on position and motion of the 3-body earth-moon-sun system taken from an ephemeris, the utility or accuracy of which doesn't require a solution to the n-body problem.

[Curiosity File]

This has gone way off the rails.

The N-body problem is a red herring.

The issue I raised in the opening post of this topic is the TFES Wiki's (Tom's) claim that eclipse predictions are based on patterns. That's wrong, and whether or not the N-Body problem eludes solution doesn't matter. Cycles are time-based. There is nothing about a Saros cycle that can provide the parameters needed to calculate Besselian elements of a solar eclipse.

You can't get this from a cycle:


You can't produce this based on a mere cycle:


This is the predicted solar eclipse for July 2, 2019. It's part of Saros cycle 127. But that's not the basis for predicting the detailed characteristics of the eclipse: the where, the how much, the duration, etc. For that, you need the Besselian elements, which are based on the relative position and motion of the earth/moon/sun and spherical geometry of the earth. It doesn't matter if the ephemeris providing  earth/moon/sun location and motion are divinely granted or calculated based on a perfect solution to the 3-body problem of these 3 bodies, with or without perturbation by other solar system or galactic bodies. It doesn't matter. That's a distraction. Either intentional or misguided.

The ability to calculate where on earth the eclipse will be seen, the degree of totality, the coverage of the umbra and penumbra, precisely when it will begin and end, etc. doesn't hinge on solving the n-body problem.  There is no flat earth model analog for how Fred Espenak performs his calculations by using an ephemeris of a rotating globe earth, orbited by a globe moon, orbiting a spherical sun. It's based on spherical geometry and absolutely requires input of position and motion of the 3-bodies. It's not "patterns" at all.

Tom has managed to derail this and get everyone debating aspects how the ephemerides are produced, under the illogical reasoning that if a million-year stable n-body solution can't be calculated using Newtonian mechanics, that the entire edifice collapses and all that remains is "patterns."

When eclipse #58 in Saros Cycle 127 begins, it will occur and have the characteristics predicted. That prediction won't be just a table look up of a pattern. It will be calculated based on the shape of the earth, the shape of the moon's shadow on the convex surface of the globe earth, based on position and motion of the 3-body earth-moon-sun system taken from an ephemeris, the utility or accuracy of which doesn't require a solution to the n-body problem.

Another interesting aspect of these modern computations is they show detailed models of the exact size and shape of the moon and compensate for the eart's terrain as the shadow passes over it. You can actually see in the shadow structures such as crater rims etc on the moon. I'll see if I can find the article I read that had a motion model that showed this. Quite fascinating.