A computer program called “42” simulates the attitudes and trajectories of multiple spacecraft flying in formation anywhere in the Solar System. The rotational dynamics are represented by high-fidelity models of spacecraft, each comprising as many as three connected rigid bodies and containing as many as four flywheel mechanisms for storing angular momentum for controlling attitude. The translational dynamics are represented partly by Encke’s method of orbit perturbation, which enables the use of a reference trajectory shared by multiple spacecraft and, in so doing, enables separation of gigameter-scale trajectory features from nanometer-scale formation adjustments to preserve the numerical accuracy needed for simulating precise multi-spacecraft formations.