On nonlinear random effects in astrodynamics.

Results are given for the approximate determination of the distribution of the random vector function describing a nonlinear random astrodynamic effect. Their application for study of the distribution of the semi-major axis and eccentricity of an orbit as functions of random initial coordinates and velocities, distributed according to the normal law, are considered. Inequalities for estimation of the proximity of distribution laws according to the proximity of the generating functions are established. A method for determining the distribution law of the random vector-argument function by the use of its expansion in Fourier series with respect to Chebyshev-Hermite functions is developed.