Generalized functions and statistical problems of orbital mechanics

A new method for the solution of statistical problems describing the motion of ensembles of particles is discussed. The method is an alternative to the usually used Euler algorithms. The method can be reduced to transformation of statistical distributions, beginning from distributions described by generalized functions by Dirac. The Dirac function was used in orbital problems in [1, 2, 3-6, 7-12]. Analytical formulas for the steady flows of orbital media and interplanetary dust particles in the vicinity of the Earth, considering the shadowing by the Earth, are obtained. The numerical solution of the unsteady flow in vicinity of a gravitating center is studied. The graph of the unsteady drag force acting on a body at the dust region is depicted.