The existence of the clouds of interplanetary dust in the neighborhood of the triangular libration points of the Earth-Moon system is discussed. In 1961 polish astronomer K. Kordylewski took photos of the dust clouds in the neighborhood of the libration point L5. We show the possibility of the existence of four dust clouds, moving in the vicinity of the stable periodical orbits, capturing these libration points, and the best conditions to observe these clouds.
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