KSP doesn't need top do a full N-body simulation. The force any craft we can build exerts on the astronomical objects in the Kerbol system is insignificant. (Gilly, the smallest mass in the Kerbol system, has a mass of 1.2x10^17 kg, the largest craft i have made to date is only 7x10^5 kg) Furthermore one can make the approximation that the planets and moons have ideal Keplerian orbits without making the same assumption for any spacecraft. Once those assumptions are made its fairly easy to do a numerical simulation of the trajectory that allows more than the 1-body system that KSP uses currently, without the (17+x)^2 calculations that a full N-body simulator such as Universe Sandbox would have to do. Each time step would have to find force of each natural object on the space craft, but it would not have to find the force of each natural object on other natural objects, leaving only the vector sum of the 17 bodies in the Kerbol system. However the ability to see where your spacecraft's trajectory would be harder to figure out.
