D. W. Schuerman studied in [6] the stability of the libration points in the first approximation and proved the non stability of all the collinear points in sense of Lyapunov. Hence each dust particle which got in the domain of the libration point must sooner or later leave it. Movement of the dust particles near Lf Let us denote the inner libration point between the Sun and the Earth as Lp We were interested in the following questions: • how long the dust particle can be near the point L j; • what is the shape of the cloud of particles which formerly filled a spherical volume with the center in Lj after some time T; • what are the possible paths of the particles movement near Lp
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