Hello,

Sorry for the long text, it's necessary, I hope I don't break any forum rule.

If I would post my question straight it wouldn't be possible for you to answer it properly.

Anyway after the third paragraph of the "The Facts" section,

you may skip directly to the conclusion if you wish.

Also, I'll give some reference to who I am,

just in the attempt to explain that I have a background about the matter I'll discuss,

although I prefer to remain anonymous, as I'm still working,

and I have seen how people think the worse if you discuss certain topics nowadays,

anyway I do so, also because you are invited to test what I declare,

if you feel the need to test myself too.

- Introduction

English is my third language and I'm not using it daily since a while,

therefore I apologies in advance for any mistake.

I'm new, I'm not a flat earther in the sense that I do not sustain/share all the current ideas/theories,

although my recent research made me question the nature of gravity.

I'm not here to discuss the shape of the earth directly, although indirectly,

my work may point to argue against the necessity of a round earth, amongst the other things.

I'm a retired computer scientist (still active as entrepreneur),

I've practiced for almost twenty years, mostly as engineer in the field of AI and simulations,

with a couple of peer-reviewed publications, I've worked for a few Fortune500 companies,

I've focused mostly on technologies like neural networks, AI architectures (gpu side),

simulations, videogames, VR and a few other sectors.

I want also to clarify that I'm not religious, although I'm not either atheist,

I have respect for spirituality and for the knowledge in general,

I'm not here to discuss these ideas anyway, but I feel that is better to clarify it,

because in my opinion, there is much of a political/religious affair behind these topics,

which can turn rational people into not-so-rational version of themselves,

especially between religious extremists and atheists.

- The Facts

During my many experiments with world simulations, I stumbled upon an interesting case:

The statistical insignificance behind the formation of the solar system for how we know it

and the inconsistency with the Newtonian description of gravity.

Initially, I wanted to see if it was possible to reproduce the solar system formation,

under random circumstances in a real-time simulation, specifically,

obtaining some stable orbit first in a two-bodies system and then in a three-bodies system.

Short answer:

No, it's not possible up to my experiments and there is no proof of any other successful experiment.

If you can accept this answer you can skip to the bottom where you find my question and my hypothesis.

Otherwise, just keep reading.

I've started looking around for existing source code and/or approaches,

to avoid wasting time reinventing the wheel and to inform myself (in terms of APIs).

A real-time simulation, must compute the current state of the "world" for each rendered frame,

just like it happens in a videogame.

I didn't find a single working example that wasn't cheating in some way (in which way is explained below).

I found also a college professor that even released some completely non-functional source code along with a video lesson,

I guess no one of the student/viewers has even checked the validity of the program.

Then I've examined scientific material, some physics simulation, from university professors or students.

Of the four reliable (with source code) that I found online,

all of them were forcing the orbit through the equations,

that obviously produce an elliptic orbit, but only because is forced,

in the same way that you play an animation of a 3D avatar in a videogame,

each point is calculated to be at the same exact spot expected for that elliptic,

like moving on a rail, the only difference in this analogy,

is that the orbit equations compute that spot in real-time (at each iteration),

rather than pre-computing the whole thing (like for common animation techniques).

Therefore, I've decided to give it a try myself,

starting from the simulations I found initially.

Those were cheating in the sense that they had forced the parameters

to be "ideal" in order to make the orbit occur, for a two-bodies problem.

On top of that, as it's known by any physicist or mathematician interested to the topic,

the three-bodies, is even harder as a case, there is now a method to solve it computationally,

but again, it falls in the case of an equation pre-inscribing the paths.

If that's not enough, the simulations I found cheated even more,

in order to add the sun at the center, literally overwriting gravity,

with a naive constrained rotation of the earth around the sun's center of mass,

rather than computing it.

Anyway, I've removed everything that I've considered "irregular"

for a proper physics simulation in real-time.

Then I've uncovered more theoretical problems, especially regarding the mathematical precision,

almost all graphic engines nowadays only support "float" precision,

numbers cannot be too small and/or very precise,

but I've plugged-in a third-party library to gain "double" precision (more than enough),

and I wrote the physics implementation I needed from scratch anyway.

Another problem with most of these simulations you find online is the interpolation method they use.

There are several ways to represent movement through interpolation mathematically,

theoretically one is good as much as the others, practically though, while programming a computer,

especially for how things work in a rendering pipeline, that's not exactly true.

I had fixed this oversight, with a better Euler interpolation first,

accounting for order of operations correctly and using Runge-Kutta methods of 4th order as well,

which is a much better approximation.

Later on, I found that Runge-Kutta was not even necessary in my specific case,

but it was good to learn more in depth some of this,

and is important to specify what was tried out and accounted for.

With this two variations of the same simulation, also cheating myself a bit,

positioning the celestial bodies, earth, moon and sun, in a "semi-ideal" starting location,

therefore not considering that according to some theory,

the moon may have been part of the earth originally, or other bodies impacts, etc;

which would had made it more complicated and wasn't necessary for what I wanted to observe,

which anyway I didn't.

I wasn't able to obtain any stable orbit for more than a few revolutions,

inevitably the masses collapsed or repelled each other because the speed overcoming the gravity,

or viceversa, plus the impacts, the random initial acceleration (which later I fixed, cheating even more), etc.

Of course, to make this consistent, I've run the simulations tens or hundreds of million of times,

in batches with different configurations, with an automation to stop and report in case a stable orbit was found,

set to be equal or greater than ten full revolutions, for simplicity;

which happened only once, but unfortunately the moon was lost in space,

the earth managed to keep a consistent number of orbits (a few tens),

anyway even in that case the earth finally collapsed into the sun in a slow concentric spiral,

that took a considerable long time respect to the other simulations, not even completing ten orbits in most cases.

After several weeks of simulations on two different machines, that was my best success.

I've stared to think that there was something odd, therefore I've asked myself,

if I should reduce the problem to something much simpler,

like the orbit of a smaller satellite around the earth,

and after one month of new experiments, I was again deluded,

because doesn't matter what mass or other parameter I decided for the bodies, it wasn't working.

The only way to make it work was to do exactly like for the other simulations,

which consist in "cheating" even more,

specifying the parameters and limits that are ideal for the orbits to happen and persist.

This is the best example (most accessible) I found online, that is available to anyone,

without the need to be registered with any private scientific institution:

There is the source code linked into the description, it's made with Unity.

This guy did a very good job at creating a decent simulation,

apart some improvement needed for the precision, which he's not considering,

but because its target was a videogame-like simulation,

he cheated in two ways:

1) Finding the optimal parameters by trial and error and then fixing the numbers appropriately.

2) Making the earth revolve around the sun thanks to an instruction that forces the earth to move in circle,

as explained above for the other examples I found as well.

Notice that to find the correct parameters during a simulation by changing them randomly at each restart,

is exponentially less probable than doing it sequentially or just according to your own data or tests.

- The argument

I've decided to involve people I knew and I trusted for some opinion, one engineer with a PhD in physics,

which also helped me pointing out about the Runge-Kutta method as alternative for the interpolation problem,

even taking my results for good, remained skeptical,

for reasons that at some point became apparently personal and not objective,

unable to formulate a better hypothesis he concluded that there is some computational limitation,

this is not acceptable as an argument, and he even admitted it in the end, but then he lost interest,

and I didn't want to insist more, as we were already in an argument for other personal things,

from which I've deduced he wasn't objective anymore (still I may be wrong about it),

He suggested to figure out a model myself to prove it, or call for some expert to help me out.

Where my point is that is actually provable by anyone able to simulate it,

therefore someone should prove that such an assertion is wrong instead.

I've then asked a software engineer specialized in videogame development,

his approach was even more lazy, not being expert in mathematics like the previous peer,

he analyzed the experiment and admitting that the software may be right,

this may have been just a problem of physics he couldn't know or understand,

so that was a part he couldn't validate, therefore it didn't prove anything to him

and just like my first friend, he also suggested to figure out a model myself to prove it.

He still talks to me about it at least, instead than dismissing it entirely.

I've asked one more reliable friend, who happens to be a mathematician and professor,

which only came to the point of agreeing with me that maybe a Newtonian physics approach

may not entirely explain for orbits formations, but anyway other modern physics approaches,

from relativity to quantum physics may give the answer, which for me was at least a more positive perspective,

as at least it recognizes the problem.

Still, not understanding enough about computer programming,

he didn't want to speculate more on the topic. Reasonable.

Running out of experts I know personally, and knowing that people don't like this topic,

especially because the arguments generated around FE and other conspiracy theories,

I've decided to come here for...

- The question

With this story and the almost full explanation of what I've tried,

I'm here with the hope to find any person with the necessary skills in mathematics and/or

on physics simulation systems, to help me understand how to achieve a working simulation,

or on the other hand that can instead help with the research of a mathematical model

that may explain the computational results, as myself I'm not a mathematician,

surely not of the level that is needed to undertake this research.

If someone is sincerely interested,

and will be able to share privately with me some reference that attests its curriculum,

after some private chat and sharing the necessary personal data (no trolls, don't waste time),

I will disclose my data and my material, from there we could start collaborating privately.

- The hypothesis

For now, it appears to me, that is not realistic to think,

that our solar system formed as a result of a random macroscopic series of events.

It's not a matter of how many stars there are, or how much time has passed,

it's just doesn't result possible to simulate it according to the current description of gravity,

independently of how many hundreds of million of simulations are performed.

Keep in mind that nowadays we can simulate much more complex systems, like fluids for instance.

Under these apparent conditions, such equilibrium, even if found,

shouldn't necessarily being considered a "miracle"?

That's not what I sustain though, my hypothesis instead is that we got the math wrong,

or our solar system is somehow artificial?

Which sounds absurd but has more chances than happening randomly,

to think that we were so lucky to be on one star system out of billions to have worked out,

is intellectually offensive at the best, as we can see other stars and their planets,

which is even more counter-intuitive, as it should be pretty rare, according to my own analysis.

I'm not here for a debate, you can verify what I said by yourself, it's fully reproducible,

I'm here to find someone interested to research into this,

therefore avoid any comment with the purpose of debating in general,

if you want more details or have some technical question, anyway,

you are more than welcome.