Abstract
In this paper the authors provide a study of the phenomenon of the gravitational capture by using the models of the circular and elliptic restricted three-body problem. In the first part the inadequacy of the circular restricted three-body problem in the study of the phenomenon of the capture in the case of NEAs is shown. In the model of the spatial elliptic restricted three-body problem criteria of the capture are deduced by using the pulsating Hill-regions.
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