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We have discovered that application of the method of variation of parameters to the KustaanheimoStiefel (K-S) regularization drastically reduces the orbital integration errors of the perturbed two-body problem for arbitrary types of perturbations. This is because not only the errors of position, whose linear growth was determined previously (Paper I), but those of the physical time grow only linearly with respect to the —ctitious time even if using traditional integrators such as the Runge-Kutta, extrapolation,

Long-Term Integration Error of Kustaanheimo-Stiefel Regularized Orbital Motion. II. Method of Variation of Parameters