To be clear—the three-body problem deals with real numbers. Computers can’t work directly with real numbers, since real numbers can’t be finitely represented. Hence when we speak about the computability of a problem “compute f(x)” that calls for a real number answer, we really mean the computability of the problem “compute f(x) to within epsilon” (where now epsilon is another input to the problem).
To be clear—the three-body problem deals with real numbers. Computers can’t work directly with real numbers, since real numbers can’t be finitely represented. Hence when we speak about the computability of a problem “compute f(x)” that calls for a real number answer, we really mean the computability of the problem “compute f(x) to within epsilon” (where now epsilon is another input to the problem).