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I've made a Mathematica n-body simulation of the first few planets in our Solar System and thought it would be a good idea to try and simulate a spacecraft transfer from Earth to Mars. I've thought about using a patched conic approximation, but I was wondering if there is anything more along the lines of an "n-body approximation" where, say for example, the gravitational acceleration from the Earth, Mars and the Sun influence the transferring spacecraft all at the same time (i.e. no disjoint 2-body approximations and spheres of influence). Has anyone developed such a method?

By the way, how accurate is the patched conic approximation? I know it was used during the Moon missions, but what about getting to planets such as Uranus or Neptune? Does its accuracy drop off with distance, and is this drop linear?