[Tom Bishop]

http://www.scholarpedia.org/article/Three_body_problem

https://wiki.tfes.org/Celestial_Mechanics_Cannot_Predict_The_Solar_System#The_Best_of_the_Best

Do these look like Heliocentric Orbits to you?

Neither of these are attempts at numerical solutions/simulations.  They are both the result of trying to find an analytic solution and run the solution on a computer to test it.  The two approaches use computers but are entirely different.  There is no analytic solution (yet), but numerical solutions exist and are deadly accurate.  You've been told this by many people in this thread.  You're mixing things up because you don't understand what your dealing with.

Incorrect

These are numerical solutions. The Runge-Kutta method is demonstrated in the second image. The Rung-Kutta method is a numerical method.

https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods

In numerical analysis, the Runge–Kutta methods are a family of implicit and explicit iterative methods, which include the well-known routine called the Euler Method, used in temporal discretization for the approximate solutions of ordinary differential equations

https://www.intmath.com/differential-equations/12-runge-kutta-rk4-des.php

Runge-Kutta is a common method for solving differential equations numerically. It's used by computer algebra systems.

My butt simple numerical solution is there for you or anyone else to try.  I'll give you all the help you need to get it going and to understand it.

I seriously doubt that your magazine-provided solar system sim does what you think it does. I will have a look when I get a chance.

[markjo]

The n-body situations with more than two bodies need bodies of the same mass (or some of the bodies mass-less) because that is the only way to bring equilibrium to the system.

What makes you think that our solar system is in equilibrium?

Otherwise, with unequal masses, the system attempts to kick out the smallest body, and the system often falls apart entirely.

First of all, small bodies are booted out of our solar system fairly regularly.  Secondly, collisions among bodes happen quite often too (especially in the early part of the solar system's history).

Progress can only be made if we assume such wacky scenarios.

Progress? 

[totallackey]

All it uses is Newton's law of universal gravitation.  When I saw this thread I remembered it but was sure it had been lost forever, however yesterday I found a few old floppy disks and sure enough my program was there and readable.  Now, this is a dreadfully simple program with no fancy GR or corrections for coarse step-wise calculation approximations, and is further limited by the dismal Applesoft floating point precision yet it will faithfully run a simulation of the Sun, Mercury, Venus and Earth for the equivalent of hundreds of years - without the orbits getting chaotic and looking like knots...

So, it is totally useless and crapola, uh..?

needless and mindless words snipped for brevity becasue this does not even have a moving sun included and actually demonstrates ZERO use of Newton's formulas.

Yep, absolute and verifiable bs...

[BillO]

Incorrect

These are numerical solutions. The Runge-Kutta method is demonstrated in the second image. The Rung-Kutta method is a numerical method.

https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods

In numerical analysis, the Runge–Kutta methods are a family of implicit and explicit iterative methods, which include the well-known routine called the Euler Method, used in temporal discretization for the approximate solutions of ordinary differential equations

https://www.intmath.com/differential-equations/12-runge-kutta-rk4-des.php

Runge-Kutta is a common method for solving differential equations numerically. It's used by computer algebra systems.

Yeah, I know the Runge-Kutta methods and what they are for - you apparently don't.

Going back to the:http://www.scholarpedia.org/article/Three_body_problem#Equations  the entire preamble is using mathematical analysis to derive the Hamiltonians which they then use to create a system of differential equations which then need to be integrated - in their case by computer.

You do know what is meant by mathematical analysis, don't you?  Calculus is one of the main processes of mathematical analysis.  If a solution is arrived by trough doing calculus (especial integration) it is an analytic solution, whether or not that integration was done by a machine or not.  Your references are attempting to compute an analytic solution.  Whether or not they use Runge-Kutta methids or not to do the integration.

I seriously doubt that your magazine-provided solar system sim does what you think it does. I will have a look when I get a chance.

Well, this should be interesting and a test of you intellectual honesty.

Yes the magazine provided the algorithm, but it is simple to understand and I really don't need you to 'splain it to me.  For each object defined: use Newton's law of universal gravitation to determine the net force on it due to each of the other other bodies.  Use Newtons 2nd law of motion to calculate the change in velocity.  Move the object one step.  Repeat.

[BillO]

All it uses is Newton's law of universal gravitation.  When I saw this thread I remembered it but was sure it had been lost forever, however yesterday I found a few old floppy disks and sure enough my program was there and readable.  Now, this is a dreadfully simple program with no fancy GR or corrections for coarse step-wise calculation approximations, and is further limited by the dismal Applesoft floating point precision yet it will faithfully run a simulation of the Sun, Mercury, Venus and Earth for the equivalent of hundreds of years - without the orbits getting chaotic and looking like knots...

So, it is totally useless and crapola, uh..?

This is really not worth replying to ... but  I never said it was going to be anything but a demonstration that purely numerical methods can produce stable systems of multiple bodies.  It does.  q.e.d.

needless and mindless words snipped for brevity becasue this does not even have a moving sun included and actually demonstrates ZERO use of Newton's formulas.

Ahhh, that's odd as there at least 2 of them in there.  My guess is you don't have much in the way of math or computer skills.  A bit of blustering then?  Would you care to demonstrate how the sun's motion would be significant to the orbital dynamics of the solar system?


Yep, absolute and verifiable blustering...

[Tom Bishop]

Regarding the Pop-Science Magazine Solar System Sim written in Applesoft BASIC

I took a look at this one. It appears to merely be creating 2-body orbits around a static sun. It does not appear to be a three-body or n-body problem simulator.

I placed the code from the last page into an online Applesoft BASIC Emulator here: http://www.calormen.com/jsbasic/

Using the settings Bill gave, I made two Earths, rotating in opposite directions, in the same orbit.



Full settings:

Code: [Select]

Sun-Earth1-Earth2 (3 Objects)

Sun
M1 = 1.9885E30
X1 = 0
Y1 = 0
VX1 = 0
VY1 = 0

Earth 1
M2 = 5.9724E24
X2 = 1.5210E11
Y2 = 0
VX2 = 0
VY2 = 29290

Earth 2
M3 = 5.9724E24
X3 = 0
Y3 = 1.5210E11
VX3 = 29290
VY3 = 0

Scale = 2E11
Time Step = 50000
Here were the results:

[Tom Bishop]

Yeah, I know the Runge-Kutta methods and what they are for - you apparently don't.

Going back to the:http://www.scholarpedia.org/article/Three_body_problem#Equations  the entire preamble is using mathematical analysis to derive the Hamiltonians which they then use to create a system of differential equations which then need to be integrated - in their case by computer.

You do know what is meant by mathematical analysis, don't you?  Calculus is one of the main processes of mathematical analysis.  If a solution is arrived by trough doing calculus (especial integration) it is an analytic solution, whether or not that integration was done by a machine or not.  Your references are attempting to compute an analytic solution.  Whether or not they use Runge-Kutta methids or not to do the integration.

Poliastro says that the image represents numerical methods for the Restricted Three Body Problem. Are you to assert that you know better than an astrodynamics software developer?

https://twitter.com/poliastro_py/status/993418078036873216

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!

https://pbs.twimg.com/media/DclUYMPXcAEOCUF.jpg

Progress can only be made if we assume such wacky scenarios.

Progress? 

Yes, progress towards creating the basic orbits seen in the heliocentric system with the ideas of Newton, Kepler, and Copernicus. Because so far, over hundreds of years and the efforts of the greatest minds on earth, it has not been done.

[markjo]

Yes, progress towards creating the basic orbits seen in the heliocentric system with the ideas of Newton, Kepler, and Copernicus. Because so far, over hundreds of years and the efforts of the greatest minds on earth, it has not been done.

Of course it's been done.  How do you think that deep space probes are able to use gravity assists tool around the solar system?

BTW, what kind of progress have the greatest minds of the FE community made in modeling the FE solar system?

[Tom Bishop]

Yes, progress towards creating the basic orbits seen in the heliocentric system with the ideas of Newton, Kepler, and Copernicus. Because so far, over hundreds of years and the efforts of the greatest minds on earth, it has not been done.

Of course it's been done.  How do you think that deep space probes are able to use gravity assists tool around the solar system?

BTW, what kind of progress have the greatest minds of the FE community made in modeling the FE solar system?

Now you are appealing to NASA and trying to move the conversation to look at something else? Have you gave up already, Markjo?

It is apparent that you are implicitly agreeing that your position is incredibly weak, are backed into a corner, and trying to do anything possible to avoid facing reality.

The Heliocentric System Cannot Be Predicted

The Heliocentric System Cannot Be Created

The Heliocentric System Cannot Even Exist

[BillO]

Regarding the Pop-Science Magazine Solar System Sim written in Applesoft BASIC

Pop-Science?  Maybe, but I never had a subscription to them.  Just the ones I mentioned.

I took a look at this one. It appears to merely be creating 2-body orbits around a static sun. It does not appear to be a three-body or n-body problem simulator.

Bang, there it goes.  Either you are being intentionally intellectually dishonest or you don't know how to read this code.  Maybe get someone else to have a look at it if you have trouble with simple linearized math.  Look at the subroutine beginning at 440 and returning at 590.  You can see how every object entered into the system is taken into account and the force between each is calculated using Newton's law of Universal gravity.  Every single one.  I get the feeling that you think none of your FE followers will be able or inclined to read the code or do the simple math so that you can say whatever you wish.

I placed the code from the last page into an online Applesoft BASIC Emulator here: http://www.calormen.com/jsbasic/

Using the settings Bill gave, I made two Earths, rotating in opposite directions, in the same orbit.

Why?  Why did you not do the 4 body situation?

Here were the results:

Okay, so that's exactly what I would expect.    How long did you let it run?.  I wrote no collision routine, so bodies will just pass right through each other when in precisely the same orbit. They are basically dimensionless.  This situation may not create an instability for quite a while, if ever.  If you want to do that put one 'earth' on a slightly different orbit - for instance use the average distance and the average speed.  That way the small offset of gravitation will create an instability.  It should begin to visibly blow up in about 4 or 5 orbits.

Try this:

Code: [Select]

Sun-Earth1-Earth2 (3 Objects)

Sun
M1 = 1.9885E30
X1 = 0
Y1 = 0
VX1 = 0
VY1 = 0

Earth 1
M2 = 5.9724E24
X2 = 1.5210E11
Y2 = 0
VX2 = 0
VY2 = 29290

Earth 2
M3 = 5.9724E24
X3 = -1.496E11
Y3 = 0
VX3 = 0
VY3 = 29780

Scale = 2E11
Time Step = 50000

[BillO]

Poliastro says that the image represents numerical methods for the Restricted Three Body Problem. Are you to assert that you know better than an astrodynamics software developer?

No, I certainly would not do that.  However, I can't see the whole thing here.  I have no idea of the work he is talking about and what the goals were.  Do you have a link handy to the original work?

[markjo]

Yes, progress towards creating the basic orbits seen in the heliocentric system with the ideas of Newton, Kepler, and Copernicus. Because so far, over hundreds of years and the efforts of the greatest minds on earth, it has not been done.

Of course it's been done.  How do you think that deep space probes are able to use gravity assists tool around the solar system?

BTW, what kind of progress have the greatest minds of the FE community made in modeling the FE solar system?

Now you are appealing to NASA and trying to move the conversation to look at something else? Have you gave up already, Markjo?

It is apparent that you are implicitly agreeing that your position is incredibly weak, are backed into a corner, and trying to do anything possible to avoid facing reality.

No, I'm just agreeing that you are incredibly stubborn about accepting any evidence that proves that you're wrong.

The Heliocentric System Cannot Be Predicted

The Heliocentric System Cannot Be Created

The Heliocentric System Cannot Even Exist

Do you think that space probes could use gravitational assists to tool around the solar system if the relevant space agencies didn't have a very accurate models of the solar system so that they could predict where the relevant celestial bodies would be at a given time?

I'm sorry, how well did you say that your FE solar system model is coming along?

[totallackey]

This is really not worth replying to ... but  I never said it was going to be anything but a demonstration that purely numerical methods can produce stable systems of multiple bodies.  It does.  q.e.d.

If your goal is producing utter fiction, then congratulations!

Quite a high bar you set for yourself!

needless and mindless words snipped for brevity becasue this does not even have a moving sun included and actually demonstrates ZERO use of Newton's formulas.

Ahhh, that's odd as there at least 2 of them in there.  My guess is you don't have much in the way of math or computer skills.  A bit of blustering then?  Would you care to demonstrate how the sun's motion would be significant to the orbital dynamics of the solar system?


Yep, absolute and verifiable blustering...
[/quote]
LMMFAO!!!

"Would you care to demonstrate how the sun's motion would be significant to the orbital dynamics of the solar system?"

You actually asked that question as if it was legitimate?

If you need that explained to you...omg...

[BillO]

LMMFAO!!!

"Would you care to demonstrate how the sun's motion would be significant to the orbital dynamics of the solar system?"

You actually asked that question as if it was legitimate?

If you need that explained to you...omg...

Oh, yes.  I just remembered the problems you FE'ers have with understanding uniform motion, inertial frames of reference and Newton's first law of motion.  Pity.

So my guess is you won't demonstrate how the sun's motion would be significant to the orbital dynamics of the solar system, right?  Good choice as you can't, but I doubt you will ever understand why it is of no significance.

[AATW]

The Heliocentric System Cannot Even Exist

That's an interesting claim. Care to back that up?

[Tom Bishop]

The Heliocentric System Cannot Even Exist

That's an interesting claim. Care to back that up?

Look at the failure of the Three Body Problem efforts of astronomers and mathematicians to simulate the Sun-Earth-Moon system. The available solutions do not look like heliocentric systems at all. They are unable to create anything that looks like a Sun-Earth-Moon system. They just can't create it.

Others have pointed out the impossibility of Heliocentric motions in other ways:

https://malagabay.wordpress.com/2012/11/03/inventions-and-deceptions-hill-sphere/

The impossibility of the Moon’s orbit [according to Newtonian Gravity] was highlighted back in 1979 by Walter C Wright in his book “Gravity is a Push”:

“My conclusion is that the sun and the earth have no pull factor on the moon”



Ralph Rene similarly concluded that Newtonian Gravity was “impossible” in his 1998 book “The Last Skeptic of Science”:







Miles Mathis reviewed the work of Ralph Rene and concluded: “Mr. René is correct”.

    I think we must see that he is correct. We have a real problem here, and the standard-model answer is just one more pathetic dodge.
    … … … …
    Mr. René is correct. Even if the Moon and Earth could theoretically inhabit the same orbit, the Moon would have to be pulled lower at New Moon by the Sun. If it were, it could not re-establish its original distance. Once its distance from the Earth had been increased, its pull from the Earth would be lessened, due to the same equation. It would escape very quickly.

    Another Hole in Celestial Mechanics
    Miles Mathis
    http://milesmathis.com/cm2.html

It is apparent why, in the Restricted Three Body Problem simulations discussed earlier, the moon needs to be of zero mass in those models.

[Curious Squirrel]

{snipped for brevity}

I would point out that at best all this shows is that Newtonian gravitation doesn't work to explain celestial motion. It does NOT however prove that "The Heliocentric System Cannot Even Exist" as you so boldly claim. Can you please present your evidence supporting the statement that a heliocentric solar system cannot exist, and not simply fringe sources proclaiming Newtonian mechanics are incorrect?

[Rama Set]

Further to that, numerical solutions of the three-body problem are used regularly, and the heliocentric solar system can be modeled very accurately as an aggregate of two-body systems.  But Tom never acknowledges this.

[Tom Bishop]

{snipped for brevity}

I would point out that at best all this shows is that Newtonian gravitation doesn't work to explain celestial motion.

I am glad to see agreement that the Heliocentric System cannot be created or exist under current theory. Celestial Mechanics is in the stone age, without even a working theory.

What else do you have besides Newton? The Solar System is based on Newtonian physics. Einstein's General Relativity isn't any different, and only makes very slight adjustments to Newton's gravity.

From http://milesmathis.com/cm2.html

Unfortunately, it is known by everyone, including them, that Einstein never claimed to have overthrown Newton. Einstein only claimed to have extended Newton's equations by importing time (and therefore mass) differentials into his field. That is, GR is Newton plus SR. And this means that modern physicists have nowhere to hide. Their new field equations do not solve this problem, since motions are still determined by mass interactions. No amount of new math can hide the fact that the Moon is out of balance at New Moon and Full Moon in the three-body problem, no matter whether you try to solve it with Newton's math, Laplace's math, or Einstein's math.

Einstein's gravity predicts essentially the same thing as Newton's gravity. I don't see where you are going with your assertion.

It does NOT however prove that "The Heliocentric System Cannot Even Exist" as you so boldly claim. Can you please present your evidence supporting the statement that a heliocentric solar system cannot exist, and not simply fringe sources proclaiming Newtonian mechanics are incorrect?

Ralph Rene's example with the moon is pretty clear. It's using Newton's own equation.

His reputation as a "crank" is because he says that Newton was wrong. Since you are apparently agreeing with that assessment, that makes you the "crank" as well.

If no one can answer these challenges, then we must conclude that under the current model the Heliocentric System cannot exist.

[BillO]

I would point out that at best all this shows is that Newtonian gravitation doesn't work to explain celestial motion.

No it certainly does not, not in it's or René's wildest dreams.

Others have pointed out the impossibility of Heliocentric motions in other ways:

Ralph René is a well known nutbag, moon mission denier, conspiracy theorist and school drop-out.  https://en.wikipedia.org/wiki/Ralph_Ren%C3%A9

And for some reason you take his word over folks like Newton, Einstein, Neil Degrasse Tyson.  Of course you do!

Yeah, I also agree with René’s calculation of the forces on the moon from the earth and the sun.  He got that grade school math right, however his interpretation was hilarious.  What he forgets/misses/bumbles, and apparently you missed it too a, is that the moon is also orbiting the sun as it orbits the earth which completely satisfies the force on it from the sun.

Tom, you’re reading the wrong stuff, putting your lot in with the wrong people and you don’t have the math and/or physics skills to see how they are leading you astray, and you are also doing it willfully.  Why?

You made a claim about the simulator I provided:

I took a look at this one. It appears to merely be creating 2-body orbits around a static sun. It does not appear to be a three-body or n-body problem simulator.

I respectfully request that either you justify this baseless claim by reference to my code, or that you retract it here.