In essence this mathematical simulation of the Solar System is a form of the "N-body problem". The symbol N represents the number of bodies, which can grow quite large if one includes the Sun, 8 planets, dozens of moons, and countless planetoids, comets and so forth. However the influence of the Sun on any other body is so large, and the influence of all the other bodies on each other so small, that the problem can be reduced to the analytically solvable 2-body problem. The result for each planet is an orbit, a simple description of its position as function of time. Once this is solved the influences moons and planets have on each other are added as small corrections. These are small compared to a full planetary orbit. Some corrections might be still several degrees large, while measurements can be made to an accuracy of better than 1″.