I am curious to know a simple example that provide me evidence that there are no solution (maybe chaotic) for the so-called three-body problem, and an explanation from an informative point of view of what means a phrase that I've read in Wikipedia's article dedicated to the Moons of Saturn.
I know from an informative point of view that there is an unsolved problem in physics concerning the motion in a gravitational field of more of two bodies, is the so-called three-body problem, see this Wikipedia. On the other hand Wikipedia's article dedicated to the Moons of Saturn tell us in the first paragraph that Saturn has 62 moons with confirmed orbits.
Question. A) Can you answer as a reference request or with yourself didactic example (I would like to know a simple example, explained from an informative point of view for mathematicians) about an example of motion of three or more bodies where is evidenced that there is no solution, or well it is chaotic?
B) What is the meaning of a confirmed orbit in the quote that I've cited in my second paragraph? It means that with numerical analysis or different evidence (measurement of periods or photographs of such moons) that physics known that a moon has a confirmed orbit or what is my misunderstanding? Many thanks.
I am asking B) because I don't know if the orbits of such moons are solutions of an equation or these are determined from a different way.