Various simplified representations of the motion of Galilean satellites are considered which are used in simulations of the near and distant satellites of Jupiter. For the near satellites it has been shown that of all simplified models the highest accuracy is attained with a model in which the motion of Galilean satellites is described by formulas of circular motion, and the accuracy is such that the model can well be used for preprocessing of observed data. The problem of short-period perturbations has been stated which arises in a high-accuracy simulation of the motion of distant satellites in view of the motion of fast circumjovial large satellites. It has been shown that this problem is solved most effectively with the use of Gaussian rings.
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