Construction of confidence regions in problem on probabilistic study into motion of minor bodies of the solar system

Different approaches to constructing regions of possible motions of minor bodies are examined. An economical approach to the minimization of the number of points of the initial region by means of defining this region with its boundary surface is offered, and the estimations of its efficiency are given. The methods for estimating the admissibility of the linear approach are considered. For this purpose, simple methods for calculating the nonlinear factors are offered, which makes it possible to classify a problem to be solved as either strongly or weakly nonlinear. Recommendations are given on the possibility of reducing the concrete estimation problem to a weakly nonlinear one, where the more economical linear approach can be used. The combined method of mapping the initial region in time is also offered which unites the linear and nonlinear approaches. By example of two asteroids, the area of applicability of linear mappings is estimated.