[JSS]

[...]It's a limited simulation.[...]

I've realised that this discussion is actually a non-discussion. So reality isn't analytically solvable: so what? This doesn't provide an argument for or against either the globe or the flat earth as both are equally not analytically solvable.

It's a chance for all of us (myself included) to show how much we know about numeric solvers but that's about it in terms of actual content.

It's no longer arguing for a flat or globe earth no. Most discussions tend to go down some rabbit hole like this. Can't imagine why. 

It's an argument against people who think that any solution that isn't analytically solvable means the solution is somehow invalid and can't represent reality.

It's like trying to argue with someone who claims because we don't know ALL the digits of pi, the shape of a circle is actually a triangle.

It's good debating practice at the very least.

[Tom Bishop]

That is an incorrect understanding. It is not understood that the existing special solutions of the Three Body Problem requiring symmetry and bodies of equal masses are the numerical solutions.

https://wiki.tfes.org/Three_Body_Problem#Analytical_Vs._Numerical

Analytical Vs. Numerical

Q. I think those quotes are talking about analytical solutions. There are working numerical solutions...

A. This is a misconception which stems from some sources which state that there are no analytical solutions, only numerical solutions. This might cause a casual reader to assume that there must be solutions in which the conventional systems of astronomy work. While it is true that the analytical approach of creating an equation to predict future positions based on initial conditions is much more difficult, the working 'numerical solutions' are the special cases described above -- the figure eight and other highly symmetric configurations.

The "numerical solutions" are symmetrical and require at least two of the three bodies to be of the same mass.

Over a Thousand New Solutions - New Scientist

From the New Scientist article Infamous three-body problem has over a thousand new solutions we read:

  “ Perhaps the most important application of the three-body problem is in astronomy, for helping researchers figure out how three stars, a star with a planet that has a moon, or any other set of three celestial objects can maintain a stable orbit.
But these new orbits rely on conditions that are somewhere between unlikely and impossible for a real system to satisfy. In all of them, for example, two of the three bodies have exactly the same mass and they all remain in the same plane. ”

Clicking on the arxiv.org source at the bottom of the that article takes us to the paper The 1223 new periodic orbits of planar three-body problem with unequal mass and zero angular momentum, where we see at the bottom of p.1:

  “ Therefore, without loss of generality, we consider m1 = m2 = 1 and m3 is varied. ”

Elsewhere in the paper it describes:

  “ Thus, we further integrate the motion equations by means of “Clean Numerical Simulation” (CNS) [17–20] with negligible numerical noises in a long enough interval of time ”

Over 600 New Orbits

Similarly, the phys.org article Scientists discover more than 600 new periodic orbits of the famous three-body problem describes the discovery of other symmetrical orbits:



  “ These 695 periodic orbits include the well-known figure-eight family found by Moore in 1993, the 11 families found by Suvakov and Dmitrasinovic in 2013, and more than 600 new families reported for the first time. The two scientists used the so-called clean numerical simulation (CNS), a new numerical strategy for reliable simulations of chaotic dynamic systems proposed by the second author in 2009, which is based on a high order of Taylor series and multiple precision data, plus a convergence/reliability check. ”

Figure Eight

The famous symmetrical Figure Eight problem was discovered numerically:

http://numericaltank.sjtu.edu.cn/three-body/three-body.htm

  “ The famous figure-eight family was numerically discovered by Moore [10] in 1993 and rediscovered by Chenciner and Montgomery [11] in 2000. ”

1349 New Families

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 same paper, 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" ”

We see that these special solutions are the numerical solutions. Just where are the solutions with different masses? Opponents are unable to show that there are solutions with different masses, that there are non-symmetrical configurations, or that the Sun-Earth-Moon system can be simulated by the Three Body Problem.

[Tom Bishop]

A simulation of the outer Solar System; Euler Forward Method vs. Euler Symplectic:



Description: " On the left the solar system is evolved forward in time using the Forward Euler method while on the right the Symplectic Euler method is used.  Both schemes may be evaluated explicitly; however, it should be noted that the Symplectic Euler method is defined implicitly and is only made explicit due to the form of the Hamiltonian being separable into functions of purely the positions and momenta.  The Forward Euler scheme does not preserve any properties of the system and is only 1st order accurate.  The Symplectic Euler scheme is also only 1st order accurate, but it preserves the structure of the elliptical orbits and Hamiltonian providing the time step is reasonably small.  Both methods used the same time step of 200 days with the rest of the parameters being drawn from Hairer, Lubich, and Wanner's text on geometric integration as in my previous video https://www.youtube.com/watch?v=b3J3lDYQRAs "

With the regular Eular method Jupiter flies out of the Solar System after a single orbit. When the simulation starts Jupiter immediately jumps out of its orbit, to beyond Pluto, as does Saturn.

Wikipedia states that the 'Forward Euler method' is also known as the 'Euler method':

  “ In mathematics and computational science, the Euler method (also called forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. ”

Euler Forward is the normal Euler method.

Descriptions from Science Direct abstracts state:

  “ Forward Euler is the simplest numerical integrator. ”

The Solar System immediately starts flying apart with the normal methods? Why is that?

Another paper states the same when only the Sun-Jupiter-Saturn system is simulated:

  “ Following [8, 7], let us consider the Sun-Jupiter-Saturn system, where for simplicity we neglect the other bodies and influences in the solar system. Surprisingly, applying a standard numerical method yields a dramatically wrong solution, where one of the planets is ejected from its orbit. In contrast, a well chosen symplectic integrator with the same initial data yields the correct behavior. ”

Standard methods cause it to fall apart. Symplectic integration is needed. Symplectic integrators are the geometry preserving methods discussed in the New Scientist article at the end of https://wiki.tfes.org/Symplectic_Integrators

A quote from rosettacode:

https://rosettacode.org/wiki/N-body_problem

  “ The slightest perturbation from symmetry causes the system to become unstable. ”

Funny. Neither the Sun Earth Moon system or the Solar System are symmetrical systems. Lets see some demonstration that these systems actually work. And please don't claim that it's stable for x timespan with only yourself as the source. We can see experimental demonstration in the video above that it's not stable, and that it immediately degrades.

[JSS]

That is an incorrect understanding. It is not understood that the only existing special solutions of the Three Body Problem requiring symmetry and bodies of equal masses are the numerical solutions, not the analytical solutions.

https://wiki.tfes.org/Three_Body_Problem#Analytical_Vs._Numerical

This entire copy of the Wiki page which is mostly a copy of a New Scientist article is simply talking about various three-body orbits that have been discovered and mathematically proven to be stable.

It says nothing about the ability to use iterative numerical solutions to predict orbits, which work fine, see Voyager I and Voyager II.

Once again, we have sent ROBOTS TO OTHER PLANETS using n-body simulators.  They work fine.  How does the above article disprove the pictures we got back from Neptune?

  “ The slightest perturbation from symmetry causes the system to become unstable. ”

Funny. Neither the Sun Earth Moon system or the Solar System are symmetrical systems. Lets see some demonstration that these systems actually work. And please don't say that it's stable and quote yourself as a source like others here have.

Funny, neither the Sun Earth Moon system or the Solar System are stable in the long term.  Eventually the moon will escape the Earth, eventually the Earth will be swallowed by the sun or be ejected from the Solar System, given enough time.

No orbit is stable in the real world, given enough time. Even those proven in the earlier post about New Scientist wouldn't' be stable forever.

Please try and remember the difference between pure math and the actual world. The real world is a messy place. You can have stable orbits in math, you can't have them in reality.

You asked "Lets see some demonstration that these systems actually work."

Voyager 1 and 2 (Grand tours of the solar system)
Viking 1 and 2 (Mars landers)
Pathfinder (Another Mars lander)
Opportunity (Yet more Mars)
Cassani (Orbited Saturn and visited lots of moons)
Moon Landings (People walked around)
DSCOVR (Parked at the L1 point, predicted by Newtons laws)

Hundreds of others. https://en.wikipedia.org/wiki/List_of_Solar_System_probes

Here, this lets you look up missions and see the plotted courses and all the math.  https://trajbrowser.arc.nasa.gov/traj_browser.php

How did they get there? Scientists used n-body simulators and a lot of math. If we couldn't simulate the orbits of planets and moons we could never get stuff to them.

[Tom Bishop]

Funny, neither the Sun Earth Moon system or the Solar System are stable in the long term.

Is your definition of "long term" more than a few of orbits?

I ran the discussed Sun-Earth-Moon model in Scilab and got the same results:



The Moon was quickly ejected from the system.

Doesn't look like this works, sorry.

NASA

The inherent instability of these problems is more evidence against those claims. The space probes would need to be constantly and endlessly correcting, whereas NASA is claiming to simply put them into stable orbits with only brief and minor corrections.

[JSS]

Funny, neither the Sun Earth Moon system or the Solar System are stable in the long term.

Is your definition of "long term" more than a few of orbits?

I ran the discussed Sun-Earth-Moon model in Scilab and got the same results:



The Moon was quickly ejected from the system.

Doesn't look like this works, sorry.

NASA

The instability of these problems is more evidence against those claims. The space probes would need to be constantly and endlessly correcting, whereas NASA is claiming to simply put them into stable orbits with only brief and minor corrections.

So your failure to correctly understand a math paper proves that all the space probes we launched aren't real?

Just because you don't understand something doesn't mean it's impossible.

You need to understand the paper you got that simulation from.

They are discussing various ways of using Newtons methods to simulate the solar system, and are showing one method works better than another method.

Did you miss this part of that papers summary?

"In contrast, a well chosen algorithm with the
same initial data yields the correct behavior.
We explain the main ideas of how the evolution of
the solar system can be computed over long times"

They are saying VERY clearly that they can simulate the system correctly over long times.

So you are basically copy-pasting a method which is known to have problems, and ignoring the solution in THE  SAME PAPER that solves it.

Also, you say NASA is "claiming" to put them into stable orbits. Can we clarify this? Are you saying NASA is lying about the hundreds of probes and people that have been put into space?

[Tom Bishop]

Did you miss this part of that papers summary?

"In contrast, a well chosen algorithm with the
same initial data yields the correct behavior.
We explain the main ideas of how the evolution of
the solar system can be computed over long times"

They are saying VERY clearly that they can simulate the system correctly over long times.

Right, only if they use a geometry-preserving method with a symplectic integrator. It's an admission that it doesn't come about naturally and that they have to use work-arounds.

[JSS]

Did you miss this part of that papers summary?

"In contrast, a well chosen algorithm with the
same initial data yields the correct behavior.
We explain the main ideas of how the evolution of
the solar system can be computed over long times"

They are saying VERY clearly that they can simulate the system correctly over long times.

Right, only if they use a geometry-preserving method with a symplectic integrator. It's an admission that it doesn't come about naturally and that they have to use work-arounds.

It's called math. Sometimes it's complex.

Wait, are you saying only 'natural math' is valid? As opposed to unnatural math?  Is that like homeopathic math?

Regardless, right there in the paper you are quoting it says that yes, they can simulate solar system dynamics accurately and over the long term. That is very clear.

So they can simulate the solar system correctly, but it doesn't count because they use methods you disapprove of?

What math in particular do you object to, and what is your proof for finding it invalid? What is is about symplectic integrators that you can prove are incorrect? Please explain.

[Code-Beta]

I asked before, and I didn't get answer. Moon moves few centimeters by year form Earth. Is that predicted by Heliocentric model. I have feeling it shoud be bigger?

[JSS]

I asked before, and I didn't get answer. Moon moves few centimeters by year form Earth. Is that predicted by Heliocentric model. I have feeling it shoud be bigger?

It's predicted by current physics, yes. It will continue to get further away, but slower and slower until it will reach it's maximum distance in about 50 billion years.

If we use nothing but Newton's laws, the orbit would not change. But tidal forces between the Moon and the Earth are also at work here, it's what caused the Moon to become tidally locked so one side always faces us. Currently the Moons gravity is slowing down the Earth, but energy must be conserved so that gravitational exchange adds energy to the Moons orbital speed and pushes it outward.

Read up on 'tidal locking' for some interesting science. I find it fascinating how all these effects balance out in ways that seem strange at first but then make perfect sense when you follow the flow of energy.

[Groit]

I asked before, and I didn't get answer. Moon moves few centimeters by year form Earth. Is that predicted by Heliocentric model. I have feeling it shoud be bigger?

It's predicted by current physics, yes. It will continue to get further away, but slower and slower until it will reach it's maximum distance in about 50 billion years.

The Sun will put a stop to it. In about 5 billion years when it swells to a red giant and swallows the Earth and moon.

[JSS]

The Sun will put a stop to it. In about 5 billion years when it swells to a red giant and swallows the Earth and moon.

Not if we move the Earth first. Sure, it might be easier to just move the people but humans are stubborn. I'm confident moving a planet will be easier than moving grandpa who lived in the same house for the past billion year and STILL calls level 7 AI intelligences "those damn square heads" every Thanksgiving at dinner and embarrasses everyone.

Of course the Andromeda galaxy will 'hit' ours in 4.5 billion years so we might get super unlucky and have a close encounter with another star first and not need to worry about what happens to our sun as we are ejected into empty space. 

[Groit]

Not if we move the Earth first. Sure, it might be easier to just move the people but humans are stubborn. I'm confident moving a planet will be easier than moving grandpa who lived in the same house for the past billion year and STILL calls level 7 AI intelligences "those damn square heads" every Thanksgiving at dinner and embarrasses everyone.

Well, since the Earth is accelerating at 9.81 m/s^2, then it shouldn't take us to long to find a suitable star system.  (sorry couldn't help it)

I take it you meant move the Earth farther out as the Sun swells, and keeping us in the 'Goldilocks zone'.

[JSS]

Well, since the Earth is accelerating at 9.81 m/s^2, then it shouldn't take us to long to find a suitable star system.  (sorry couldn't help it)

I take it you meant move the Earth farther out as the Sun swells, and keeping us in the 'Goldilocks zone'.

Yes, it would be quite the engineering problem.  Of course, if we survive as a species that long then I'd consider that even MORE impressive. Even more impressive than accelerating the earth at 9.81 m/s^2.

[Code-Beta]

What about Jupiter's Moons. Orbital rezonances? Why don't they throw each other out of stable orbit?

[BRrollin]

Well, since the Earth is accelerating at 9.81 m/s^2, then it shouldn't take us to long to find a suitable star system.  (sorry couldn't help it)

I take it you meant move the Earth farther out as the Sun swells, and keeping us in the 'Goldilocks zone'.

Yes, it would be quite the engineering problem.  Of course, if we survive as a species that long then I'd consider that even MORE impressive. Even more impressive than accelerating the earth at 9.81 m/s^2.

Interesting idea. Is there a corresponding Goldilocks zone for red giants? The surface temperature actually goes DOWN in this phase, giving the red spectrum. I worry that the Goldilocks zone would be inside the envelope!

[J-Man]

Hello. I am persionaly Globe Earther, but I found one odd thing. Modern Astronomy claims that Earth and other planeds were created form asteroids colliding. More specificly, asteroids came form gases form Nebula, and then they collided and made planets. But, if you hit something in motion, it will lose some of its speed.A Planet needs a constant/near constant speed to otbit somenting. But according to modern astronomy, earh was made by millions of asteroids hitting. So why didn't original Earth slow up just lose its orbit?

And did we mananged to get rebbutal to N-body problem?

Are there any personal accounts of this happening? Shouldn't I be able to look up and see planets formed today? With billions of these things must happen repeatedly, thousands of times a day.

[ChrisTP]

Hello. I am persionaly Globe Earther, but I found one odd thing. Modern Astronomy claims that Earth and other planeds were created form asteroids colliding. More specificly, asteroids came form gases form Nebula, and then they collided and made planets. But, if you hit something in motion, it will lose some of its speed.A Planet needs a constant/near constant speed to otbit somenting. But according to modern astronomy, earh was made by millions of asteroids hitting. So why didn't original Earth slow up just lose its orbit?

And did we mananged to get rebbutal to N-body problem?

Are there any personal accounts of this happening? Shouldn't I be able to look up and see planets formed today? With billions of these things must happen repeatedly, thousands of times a day.

I don't know what you're expecting to see in a process that takes millions of years...

[greenolive]

Code-Beta,

     The word planets comes from the Greek "planetes asteres", that literally means wandering stars. All stars were created by God around 6,000 years ago (from Genesis 1:16).

This world is flat, with Antarctica slightly rising toward the four corners of the earth from it's circular coast (from Ecclesiastes 1:7). The word universe is not in the King James Bible, as there is no universe, and the word planets is only in there once, in 2 Kings 23:5. That verse means that the idolatrous priests burnt incense to wandering stars, along with other things, that were correctly known to be the lights of heavenly bodies.

Code-Beta, stars are the size of figs (Revelation 1:16,20, 2:1, 6:13, 12:1, Isaiah 34:4). And they are lights, inside of what would be the rib cage of heavenly bodies (Job 38:7, Genesis 37:9 (Genesis 15:5), Judges 5:20, Revelation 1:20, 9:1, Daniel 8:10).

The sun and the moon are both around 6 feet wide (Genesis 37:9,10, Revelation 12:1), a few inches thick (Isaiah 3:18, Revelation 12:1), and are equal in size as they are both "great lights" (from Genesis 1:16).

Jerusalem is the center of the world (Ezekiel 5:5, Revelation 20:9), and the stars, along with the sun and the moon rise in the firmament (from Genesis 1:17), where God placed them at the creation of the world, as they pass over the world - being the highest they will ever be, due south of the geographic North Pole, on the longitude line of Jerusalem. From there they go down in the west (except for a few stars that do not rise or go down), being the lowest they will ever be as they pass over the north (Ecclesiastes 1:5, Joshua 10:12,13, Judges 5:20).

Glory to God.

[ChrisTP]

Code-Beta,

     The word planets comes from the Greek "planetes asteres", that literally means wandering stars. All stars were created by God around 6,000 years ago (from Genesis 1:16).

This world is flat, with Antarctica slightly rising toward the four corners of the earth from it's circular coast (from Ecclesiastes 1:7). The word universe is not in the King James Bible, as there is no universe, and the word planets is only in there once, in 2 Kings 23:5. That verse means that the idolatrous priests burnt incense to wandering stars, along with other things, that were correctly known to be the lights of heavenly bodies.

Code-Beta, stars are the size of figs (Revelation 1:16,20, 2:1, 6:13, 12:1, Isaiah 34:4). And they are lights, inside of what would be the rib cage of heavenly bodies (Job 38:7, Genesis 37:9 (Genesis 15:5), Judges 5:20, Revelation 1:20, 9:1, Daniel 8:10).

The sun and the moon are both around 6 feet wide (Genesis 37:9,10, Revelation 12:1), a few inches thick (Isaiah 3:18, Revelation 12:1), and are equal in size as they are both "great lights" (from Genesis 1:16).

Jerusalem is the center of the world (Ezekiel 5:5, Revelation 20:9), and the stars, along with the sun and the moon rise in the firmament (from Genesis 1:17), where God placed them at the creation of the world, as they pass over the world - being the highest they will ever be, due south of the geographic North Pole, on the longitude line of Jerusalem. From there they go down in the west (except for a few stars that do not rise or go down), being the lowest they will ever be as they pass over the north (Ecclesiastes 1:5, Joshua 10:12,13, Judges 5:20).

Glory to God.

It's a good thing this thread has nothing to do with religion otherwise this might have been solid evidence for your point.