The author does not call it a proof of the stability for the n-body problems and I see no reason to assume that it is. There is a body of science for the n-body problems and this isn't it. I would suggest citing that science in the future.
I still haven't seen any quotes of published papers that state that we can't use n-body calculations to predict comets and land spacecraft on other worlds
There are dozens of physcists who say that the three body problems are insoluable. They cite Poincare's paper as proving that it is insoluble and inherently chaotic. We post those quotes all the time.
This is the response to that, to post random found simulations which do not state that they are solving the stability issues of the n-body problems. We must "infer" that this is the purpose or feature of the simulation.
I agree that the author does not claim to address chaotic systems. It looks like precise initial conditions are inputted - so there would be no chaotic dynamics to analyze.
I agree and have also read about the inability to find analytical solutions to the differential equations. But I’m confused why this is being raised - this isn’t the topic of the post.
The topic is numerical solutions using a known mathematical process. They show the orbits that follow from the equations when solved using this method. Do you dispute any of the mathematics on the webpage?
It is convincing to me that the numerical method used is accurately applied. So I take this as computational evidence that Newton’s gravity can depict orbits.
However, this doesn’t mean I think you are wrong in your replies. The chaotic dynamics and variations using initial conditions are interesting, and arise when perturbation analytical methods are used to try to find closed form solutions for the differential equations.
I would enjoy discussing that in a new thread, but that is not what THIS thread is about.
Lastly, I respectfully object to statement that this post was a response to Poincare’s work and the chaotic dynamics. It was not, and I never said this. I fear it would “poison the well” to hold this numerical solution to an analytical standard. They are different things.