The “three-body” problem and the “figure-eight” solution (with a planet)

The three body system in the figure-8 configuration is rather stable. A fourth body (a planet) with a mass 1/1000 times that of each sun, doesn’t destroy the suns’ “figure-8“ trajectories. The sun/planet mass ratio used in this simulation is similar to that between our Sun and Jupiter. With a very slight change in the initial position of the planet, its dynamical evolution is completely different. The strong dependence on initial conditions is a typical phenomenon of chaos. For almost all initial conditions the planet is eventually ejected from the system as its total energy becomes positive. That extra energy comes at the expenses of some energy lost by the suns (small in relative terms). This effect is usually called “gravitational slingshot” and it is currently used to drive artificial satellites through the solar system. The background music is “Dawnings“ (2002) SELECTED REFERENCES (the most “readable“ ones): A remarkable periodic solution of the three-body problem in the case of equal masses A. Chenciner, A New Solution to theThree-Body Problem R. Montgomery Braids in Classical Dynamics [1993] C. Moore The Three-Body Problem R. Montgomery - (Scientific American August 2019) The three-body problem Z.E. Musielak B. Quarles An Introduction to the Classical Three-Body Problem Govind S. Krishnaswami, Himalaya Senapati Dynamical properties of the figure eight solution of the three-body problem C. Simó Newtonian Periodic Three-Body Orbits with Zero Angular Momentum V. Dmitrašinović, A. Hudomal, M. Shibayama, A. Sugita Celestial Mechanics Note Set 3: General Three Body Problem and the Orbital Configurations of Euler and Lagrange J.D. Mireles James ~jmirelesjames/ PHYS 7221 - The Three-Body Problem (special Lecture) F. Juhan TEXTBOOK New Foundations for Classical Mechanics - 2nd edition - 1999 D. Hestenes see section 5 of chapter 6 “The Newtonian Many Body Problem“ starting at