The reason why the three-body problem cannot be solved is that gravity is a nonlinear force (specifically, it is “inverse square”), and in a three-body system each body exerts its force on the other two. This produces nonlinear feedback and results in chaotic motion of the moons’ orbits. But we have now “solved” the three-body problem by demonstrating that the orbits are inherently unpredictable. Such a solution would have been considered nothing short of sacrilege a few years ago.
