ABSTRACT
The problem of calculating how a collection of N masses move under classical gravitational force has been around for hundreds of years, and the only case for which the shape of the paths can always be expressed with elementary functions is when N = 2. The two-body problem is solved when the masses follow paths that are conic sections: Ellipse, parabola, hyperbola. Since we know the elementary function for the path shape, we can test any numerical method against that exact solution.
