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The belief that there's no exact solution to the three-body problem is common but wrong. There is one, and it was found about a hundred years ago. The history o
by troymc 8y ago
The belief that there's no exact solution to the three-body problem is common but wrong. There is one, and it was found about a hundred years ago. The history of the problem, and its solution, are all described in the book Poincare and the Three Body Problem, published by the American Mathematical Society. It includes a section about potential reasons for the pervasive belief that no solution exists.
- rocqua 8y ago" A complete solution for a particular three-body problem would provide the positions for all three particles for all time, given three initial positions and initial velocities. In general, no closed-form solution for such a problem exists, and the time evolution of the system is believed to be chaotic. " from wikipedia [1]. Not a fool-proof source, but it seems to disagree with you. It does seem the case that whether the system is chaotic isn't yet determined. [1] https://en.wikipedia.org/wiki/Three-body_problem#Gravitational_systems https://en.wikipedia.org/wiki/Three-body_problem#Gravitation...
- privong 8y agoThere is a series solution to the 3-body problem, which can in principle be computed to an arbitrary level of precision. So while there's no closed-form solution (as the wikipedia article notes), there is a solution. However, my understanding is that this series solution converges slowly enough as to not be useful in practice.
- rocqua 8y agoAh, that is interesting. I figure Numerical ODE solvers might be faster. But there is philosophical value in a series that is proven to converge for any time t. Do you happen to recall whether it is uniform convergence?
- privong 8y agoI don't have more than a cursory knowledge of the solution, but the Three-body problem wikipedia page should have enough info to get you set in the right direction: https://en.wikipedia.org/wiki/Three-body_problem#Sundman's_theorem https://en.wikipedia.org/wiki/Three-body_problem#Sundman's_t... It says that the series should converge for all t, except for systems which begin with zero angular momentum. It additionally states that: > in 1930, David Beloriszky calculated that if Sundman’s series were to be used for astronomical observations, then the computations would involve at least 10^8000000 terms