Three Body Problem

The Three Body Problem is a four hundred year old problem of mathematics which has its roots in the unsuccessful attempts to simulate a heliocentric Sun-Earth-Moon system.

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. 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, and exhibit odd loopy orbits that look quite different than the systems of astronomy proposed by Copernicus. 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.

— Paul Trow, Chaos and the Solar System (Archive)

400 Years of Defiance
In The Physics Problem that Isaac Newton Couldn't Solve (Archive) physics and astronomy professor Robert Scherrer informs us:

Newton's Solution
Mathematician and astronomer Issac Newton is credited to have "brought the laws of physics to the solar system."1 To solve the multi-body problems of his system Newton famously invoked divine intervention (Archive):

1The University of California San Diego credits Newton with providing the laws of physics for the Solar System (Archive):

Henri Poincaré
http://n.ethz.ch/~stiegerc/HS09/Mechanik/Unterlagen/Lecture13.pdf (Archive)

Ask A Mathematician
https://www.askamathematician.com/2011/10/q-what-is-the-three-body-problem/ (Archive)

A Thousand New Solutions
From a New Scientist article titled Infamous three-body problem has over a thousand new solutions (Archive):

As suggested, the field of Celestial Mechanics is still on step zero—the stone age. The found orbits are nothing like heliocentric astronomy and there will be an attempt to use them as a skeleton to "build the whole system up from."

Two Bodies of Equal Mass
The research group with the super computer published another study titled: Over a thousand new periodic orbits of a planar three-body system with unequal masses (Archive)

Poliastro
Poliastro, an astrodynamics software developer, shares several numerical methods for the restricted three body problem:

https://twitter.com/poliastro_py/status/993418078036873216?lang=en (Archive)



Arenstorf orbits are the knotted closed trajectories which are the result of Restricted Three Body Problem solutions.

Chaos Theory: A Demo
The available solutions to the Three Body Problem, beyond being unlike anything seen in Heliocentric Theory, are so sensitive that the slightest change or imperfection will tear the entire system apart. As a very illustrative demonstration, take a look at this online Three Body Problem simulator that uses the simplest possible figure eight pattern, which requires three identical bodies of equal mass that move at very specific momentum and distance in relation to each other.

Demo: Figure-Eight Three Body Problem



Adjust the slider values in the upper left to something very slight to find what happens. What you will see is a demonstration of Chaos Theory. Any slight modification to the system creates a chain reaction of random chaos.

This is precisely the issue of modeling the Heliocentric System, and why its fundamental system cannot exist. Only very specific and very sensitive configurations may exist. The slightest deviation, such as with a system with unequal masses, or the minute influence from a gravitating body external to the system, will cause the entire system to fly apart. The reader is invited to decide for his or her own self whether those scenarios would occur in nature as described by popular theory.

Highly Sensitive Orbits
From 'Mathematics Applied to Deterministic Problems in Natural Sciences' we read another account of Poincaré's discoveries:

N-Body Solution Galleries
Wolfram Science

https://www.wolframscience.com/nks/notes-7-4--three-body-problem/ (Archive)



Institute of Physics Belgrade

http://three-body.ipb.ac.rs/ (Archive)

n-Body Choreographies

http://rectangleworld.com/demos/nBody/ (Archive)

Scholarpedia.org

http://www.scholarpedia.org/article/Three_body_problem (Archive)

Euler Math Toolbox

http://euler.rene-grothmann.de/Programs/Examples/Three-Body%20Problem.html (Archive)

Supercomputing Challenge
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)

The PDF report explains with additional details that all attempts at observing orbit were unsuccessful.

Universe Sandbox 2
Universe Sandbox 2 (Universe Sandbox ²) is a physics based space simulation developed and published by Giant Army. 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.

The reader should read the following from a developer blog post and decide whether the program is using a full simulation of gravity:

Working Through the N-Body Problem in Universe Sandbox ² (Archive)