The three body problem is studied in the field of nonlinear ordinary differential equations with initial conditions: bifurcation theory, an exceedingly difficult branch of advanced mathematics.

https://books.google.ro/books?id=YhXnBwAAQBAJ&printsec=frontcover&dq=wiggins+introduction+to&hl=en&sa=X&ved=0ahUKEwj2yPuosdblAhVC3qQKHUXdByMQ6AEIMDAB#v=onepage&q=wiggins%20introduction%20to&f=falseHere are the known facts concerning the three body problem in the context of bifurcation theory:

https://forum.tfes.org/index.php?topic=10175.msg160183#msg160183https://forum.tfes.org/index.php?topic=14559.msg191038#msg191038The most intriguing is the discovery made by Professor Robert W. Bass.

Dr. Robert W. Bass

Ph.D. (Mathematics) Johns Hopkins University, 1955 [Wintner, Hartman]

A. Wintner, world's leading authority on celestial mechanics

Post-Doctoral Fellow Princeton University, 1955-56 [under S. Lefschetz]

Rhodes Scholar

Professor, Physics & Astronomy, Brigham Young University

"In a resonant, orbitally unstable or "wild" motion, the eccentricities of one or more of the terrestrial planets can increase in a century or two until a near collision occurs. Subsequently the Principle of Least Interaction Action predicts that the planets will rapidly "relax" into a configuration very near to a (presumably orbitally stable) resonant, Bode's-Law type of configuration. Near such a configuration, small, non-gravitational effects such as tidal friction can in a few centuries accumulate effectively to a discontinuous "jump" from the actual phase-space path to a nearby, truly orbitally stable, path. Subsequently, observations and theory would agree that the solar system is in a quasi-periodic motion stable in the sense of Laplace and orbitally stable. Also, numerical integrations backward in time would show that no near collision had ever occurred. Yet in actual fact this deduction would be false."

"I arrived independently at the preceding scenario before learning that dynamical astronomer, E. W. Brown, president of the American Astronomical Society, had already outlined the same possibility in 1931."

Dr. Robert Bass, Stability of the Solar System:

https://web.archive.org/web/20120916174745/http://www.innoventek.com:80/Bass1974PenseeAllegedProofsOfStabilityOfSolarSystemR.pdfDr. E.W. Brown

Fellowship, Royal Society

President of the American Mathematical Society

Professor of Mathematics, Yale University

President of the American Astronomical Society

What this means is that the interval of assured reliability for Newton's equations of gravitational motion is at most three hundred years.

If any proofs can be provided that the solar system underwent cataclysmic planetary collisions in recent historical times, this fact would render any kind of heliocentric orbital calculations as completely useless.

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg1936055#msg1936055 (part I)

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg1938384#msg1938384 (part II)

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg1938393#msg1938393 (part III)

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg1938396#msg1938396 (part IV)