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" 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 in
by 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