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The interstellar dust (ISD) grains penetrate into the heliosphere due to the relative motion of the Sun. Chemical composition of the ISD grains in the interstellar medium is carbonaceous materials and astronomical silicates and their characteristic sizes are in range approximately from 0.01 mcm to 1 mcm. The motion of dust particles in the heliosphere is influenced by three forces: the solar gravitational force, the radiation pressure force and the electromagnetic force. As a result, peculiarities of the ISD distribution appear in the interplanetary medium. The main goal of this work is to study the peculiarities of the ISD distribution. For that we employed two methods: Lagrangian Osiptsov method [1] and more conventional Monte-Carlo modeling. To understand the locations of interstellar grains accumulations may be actual for the planning of the interstellar Probe mission and also in the context of the astronomical observations, because dust grains absorb and scatter the light.