Abstract
Practical space exploration has a priority the issues of safety of space missions. And an important fundamental problem arises — the study of the evolution and the stability of a space debris cloud, consisting of artificial objects remnants, or debris of extra-terrestrial origin.We discuss a new behavior of mechanical system near an unstable equilibrium position — the trajectories located in the selected neighborhood of unstable equilibrium. As an important application, we consider perturbed motion in collinear libration points vicinity of the restricted circular three-body problem.Numerical simulations for the parameters of the Earth–Moon system convincingly illustrate our theoretical study. This mathematical model allows us predicting how long the debris with certain energy can fly in vicinity of unstable collinear libration point, being close to the localized trajectory. This must be taken under consideration when planning the space missions. And also the localized trajectories may be useful when spaceship flies around the collinear libration point.
Published Version
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