The distributions of stream meteoroids in the near-Earth space is investigated analytically using the method of general functions (MGF). The analytical formulas for the focusing and shadowing effects by the Earth are obtained. These results reflect clearly the main features of meteoroid distributions, and can be used for interpretations of on-board measurements and ground observations by meteor radars and optical telescopes. The results can also be used for estimations of spacecraft safety. Then there are presented new results on transitory dust dynamics obtained by MGF. The temporary distributions and a gravitational drag for a moving gravitating center are evaluated in linear approach (without self-gravitation).