'Numerical' is a generic term and does not refer to the Three Body Problem. Ptolmy uses 'numerical computation' in the Almagest. Was he solving Newton's Laws and Three Body Problems?

https://books.google.com/books?id=JVhTtVA2zr8C&pg=PA29&source=gbs_toc_r&cad=4#v=onepage&q&f=false---

Dr. Gopi Krishna Vijaya says that Newtonian astronomers use perturbations/epicycles with a gravitational disguise.

https://reciprocalsystem.org/PDFa/Replacing%20the%20Foundations%20of%20Astronomy%20(Vijaya,%20Gopi%20Krishna).pdfEpicycles Once More

“ Following the Newtonian era, in the 18th century there were a series of mathematicians – Bernoulli, Clairaut, Euler, D’Alembert, Lagrange, Laplace, Leverrier – who basically picked up where Newton left off and ran with it. There were no descendants to the wholistic viewpoints of Tycho and Kepler, but only those who made several improvements of a mathematical nature to Newtonian theory. Calculus became a powerful tool in calculating the effects of gravitation of all the planets upon each other, due to their assumed masses. The motion of the nearest neighbor – the Moon – was a surprisingly hard nut to crack even for Newton, and several new mathematical techniques had to be invented just to tackle that.

In the process, a new form of theory became popular: Perturbation theory. In this approach, a small approximate deviation from Newton's law is assumed, based on empirical data, and then a rigorous calculation of differential equation is used to nail down the actual value of the deviation. It does not take much to recognize that this was simply the approach taken before Kepler by Copernicus and others for over a thousand years – adding epicycles to make the observations fit. It is the same concept, but now dressed up in gravitational disguise: ”

“ In other words, the entire thought process took several steps backwards, to redo the same process as the Ptolemaic - Copernican epicycle theory, only with different variables. The more logical way of approach would have been to redirect the focus of the improved mathematical techniques to the assumptions in Newton’s theory, but instead the same equations were re-derived with calculus, without examining the assumptions. Hence any modern day textbook gives the same derivation for circular and elliptical motion that Newton first derived in his Principia. The equivalence of the epicycle theory and gravitational theory has not been realized, and any new discovery that fits in with the mathematical framework of Newtonian gravity is lauded as a “triumph of the theory of gravitation.” In reality, it is simply the triumph of fitting curves to the data or minor linear extrapolations – something that had already been done at least since 2nd century AD. Yet the situation is conceptually identical. ”

From the VSOP talk page, the solar system model which is linked at the bottom of the page you provided:

“ Modelling VSOP on a ubiquitous PC computer program, starting with only one element for each of the three parameters (L, B R) and then slowly incrementing the number of elements, gives a sense of irony that it is in fact nothing more than a more complex development of the ancient deferent / epicycle system used by Ptolemy. A system that despite being totally dismissed out of hand for being intellectually "wrong", was able to provide a prediction service accurate enough to match the observational resolution available (naked eye, with no reliable mechanical timekeeping). A system that, astoundingly to this author, was able to detect and measure, accurately, the lunar evection, one of the still-used perturbations of the Earth-Moon system. Summing powers of sines and cosines is certainly tantamount to circles upon (or perhaps within) circles; recursing, or perhaps simply nesting, almost endlessly. Whilst of course this is totally irrelevant to the mathematics, it perhaps behoves Wikipedia's wider terms of reference to include this as a philosophical point. ”

All of this tells me that it's not truly a simulation of gravity.

Dr. Vijaya says:

" The Dead End

In the late 19th century, one of the French mathematicians – Henri Poincaré – had already discovered that many of the terms being used in the “perturbation” series by mathematicians like Laplace and Lagrange were becoming infinite for long periods of time, making the system unstable. In simple words, the solutions ‘blow up’ fairly quickly. He also showed that the general problem of 3 mutually gravitating bodies was insoluble through any mathematical analysis! Many physicists and mathematicians built up modern “Chaos theory” based on these ideas, to show simply that one cannot calculate the movements of the planets accurately. Thus began the field of non-linear

dynamics.

In the middle of the 20th century, with computers entering the field, the mathematicians pretty much gave up on calculating the orbits by themselves and programmed the computer to do it, even though it was mathematically shown that these orbits were incalculable. They had to be satisfied with approximations or numerical methods (or “brute force” methods.) The result of it all was that after 300 years, Newtonian/Einsteinian thought lands in the same spot that Kepler ended: the orbits point to a living or chaotic system. Only now, there is the additional baggage of all the wrong concepts introduced with regard to “inverse-square law”, “gravitational attraction”, “gravitational mass” and “curved space-time” along with uncountable number of minor assumptions. In this process, an enormous amount of human effort was put to derive thousands of terms in equations over centuries. The entire enterprise has been a wild goose chase "