This is altogether a terrible article. Here's a breakdown of everything it gets wrong:

which has its roots in the unsuccessful attempts to simulate a heliocentric Sun-Earth-Moon system.

The model isn't wrong—in fact, it actually simulates the Sun/Earth/Moon system quite well.

Due to the nature of Newtonian Gravity, a three body system inherently prefers to be a two body orbit and will attempt to kick out the smallest body from the system—often causing the system to be destroyed altogether.

The keyword there is

*attempt*—it's not guaranteed to break the system. The Earth and Moon have far more binding energy than can be supplied by tidal forces from the Sun.

There are a limited range of scenarios in which three body orbits may exist. It is seen that those configurations require at least two of the three bodies to be of the same mass, can only exist with specific magnitudes in specific and sensitive configurations, … The slightest imperfection, such as with bodies of different masses, or the effect of a gravitational influence external to the system, causes a chain reaction of random chaos which compels the entire system to fall apart

The differential equation has unstable equilibria. Shocker.

"Describing the motion of any planetary system (including purely imaginary ones that exist only on paper) is the subject of a branch of mathematics called celestial mechanics. Its problems are extremely difficult and have eluded the greatest mathematicians in history." — Paul Trow, Chaos and the Solar System (Archive)

Eluded the mathematicians, but not the physicists.

*Now add a third body, and everything falls apart. The problem goes from one that a smart undergraduate can tackle to one that has defied solution for 400 years.*

An unsolvable differential equation can still describe reality. Is there a point to the quote?

**Sections 2-3**The important thing to remember is that, for a long time—maybe a billion or two years—the solar system

*was* unstable. If a body had a close encounter with a much larger mass, it had 3 possible outcomes: colliding with the larger mass, deflection into a more eccentric orbit, and acceleration into a larger orbit. Eventually most bodies either hit a planet, get too much eccentricity and falls into the Sun, or get ejected into the Kuiper Belt, resulting in the modern set of planets in orbits too far apart for any close encounters.

Also, minor gravitational interactions between planets

*are* observed as slight orbital changes over decades or centuries. Even if a planet had enough energy to eject an adjacent planet (I haven't done the math yet but I doubt it), it would take hundreds of millions of years or more for perturbations to lead to encounters.

**The problem with the 3-body problem is that it can’t be done, except in a very small set of frankly goofy scenarios (like identical planets following identical orbits).**

Again conflating unsolvable equations with bad models.

This is precisely the issue of modeling the Heliocentric System, and why its fundamental system cannot exist.

This issue relies on the assumption that there are no setups that can last long periods of time without being the equal-mass solution that I've already dismissed as irrelevant.

Programming students participated in the New Mexico Supercomputing Challenge to simulate the solar system and found issues with creating basic orbits:

Simulation of Planetary Bodies in the Universe (N-Body) (Archive) (Source Code)

I recognize that algorithm, having used it myself. One thing I can say is: this algorithm leaves out a key invariant, and that can cause instability in close encounters between objects, or even just over time.

It has often been claimed that this simulation provides evidence that the Sun-Earth-Moon System and the Solar System are able to be simulated with Newtonian Gravity.

Universe Sandbox doesn't use Newtonian gravity. It uses general relativity.

Kidding. While it isn't technically using the Newtonian model, it's close enough at the scale of the solar system that it might as well be. Anyway, the quoted passage goes into how the simulation uses a set of 2-body problems between bodies and their main attractors. The bolded phrases seem to be cherrypicked to indicate that the simulation uses this alternative model because using the normal model would reveal the inherent instability of an incorrect system.

**This is entirely wrong, it's a problem of time complexity.**In conclusion:

**Every part of this article is either wrong or irrelevant, and it should be deleted.**