The article was published in the journal: Astronomical Journal. — 1961. - T. 38. - Vyp. 4. - M. Academy of Sciences of the USSR . — C. 738-753. The problems of celestial mechanics are considered, provided that the initial conditions and masses of bodies are random quantities. In the first section, the amount of the time interval during which it is possible to pre-calculate the elliptic motion is set. In the second section is the distribution of the probabilities of deviations of the problem of two bodies from the Kepler motion, if the distribution of the initial values of coordinates and velocities, the distribution of body masses and the probabilistic characteristics of the random perturbing force are known. The third section gives a generalization of the previous method to the problem. Calculation of elliptic motion. Random initial conditions and random parameters in a two-body problem. Generalization to Task.