In "Three-body", why can't three-body people predict three-body motion?

What we call three-body generally refers to solving the motion analytical solutions of three moving celestial bodies under Newton's gravity, which is a common term in classical celestial mechanics. If the mass of one celestial body in the three-body can be ignored, it is still a three-body at this time, but the third body has no gravitational effect on the other two celestial bodies, which is called a restricted three-body. By definition, the three-body planet in Liu's novels should be at least a restricted four-body problem (three stars and a planet with negligible mass). If general relativity is involved, it is a problem of relativistic celestial mechanics. At present, the two-body problem of relativistic celestial mechanics has not been well solved. Off-topic, there are really few universities in China that can offer courses in celestial mechanics. In my impression, only the astronomy majors of Nanjing University and Beijing Normal University can offer courses on celestial mechanics. Many universities in China have aerospace majors, but there are differences between aerospace dynamics and celestial mechanics, with different emphasis. There are so few universities specializing in astronomy in China that it is difficult to carry on the theory of celestial mechanics, so celestial mechanics is now more or less combined with astrophysics. Whether there is an analytic solution or a uniformly convergent series solution for the three-body has been under consideration since the birth of Newtonian mechanics, Newton, Lagrange and Laplace. Laplace-Lagrange equation established by Laplace proves the stability of planets of the solar system under long-term perturbation.

1887, King Oscar II of Sweden launched a cash prize contest to find a solution to the stability of the solar system. Poincare took part in this competition, and by using the Poincare cross section invented by himself, the conclusion that the three-body is extremely sensitive to the initial value is given. From a mathematical point of view, it is normal that the three-body can not give an analytical solution, just like any nonlinear differential equation. If a nonlinear differential equation is given casually, there is probably no analytical solution. The reason why trisomy is so famous is that it has a wide range of applications. The stability of planets of the solar system, the gravitational effect of stars in clusters and the motion of satellites are all inseparable from Newton's celestial mechanics. Another well-known differential equation, Navistokes equation of fluid mechanics, is also widely used, so one of the seven Millennium-winning problems set up by Clay Institute of Mathematics in the United States is to find the existence and smoothness of Navistokes equation, but now only Russian mathematician perelman has solved Poincare conjecture, Navistokes equation and the other five problems. Although the three-body can't give practical analytical or series solutions, it can give numerical solutions, which is also a common N-body simulation in astronomy. The numerical solutions of differential equations, from the undergraduate course of numerical analysis to Euler algorithm and Runge-Kutta algorithm of ordinary differential equations, to the finite difference algorithm of partial differential equations, and even the symplectic algorithm and finite element algorithm invented by Mr. Feng Kang in China, are mature and varied. However, the numerical algorithm needs initial conditions and boundary conditions to solve the numerical solution of differential equations. There is confusion about the three-body and the sensitivity to initial values mentioned above. Chaos refers to the long-term unpredictability caused by the sensitivity of nonlinear systems to initial values. Chaos is not chaos, but certainty and unpredictability. There are observation errors in astronomical observation, truncation errors in algorithm and rounding errors in computer calculation, which make the calculation different from the real situation, and the system itself is sensitive to initial values. After a certain time (Lyapunov time scale), the output will be very different. If there really is an observation with no error, an algorithm with no truncation error and a computer with no rounding error, then we can get an always accurate numerical solution through the computer, but this is impossible. Therefore, in the traditional numerical calculation of solar system stability, it usually takes millions or tens of millions of years. Because there are errors, there are many calculations, and the later results are different from the real ones, which is meaningless.