I.K. Kostin, A.V. Testov

Tracking changes in the distances between space objects is one of the classical problems in applied celestial mechanics. There are several algorithms that solve this problem using the approximation of the actual motion of the space object by simpler functions. Version of such an algorithm is proposed in this article. The algorithm consists of two parts: 1. The calculation of auxiliary data, which determine the length of the approximation interval within which the approximation error does not exceed the specified limits. 2. Calculation of the parameters of approaches using pre-computed and stored auxiliary data. The proposed algorithm incrementally builds the approximation intervals, finds the real roots of the associated polynomials of fifth degree, and puts the detected roots in the output array for the analysis of information consumers. These roots define the boundaries of the intervals of monotonic variation of the distance between the space objects. The procedure for finding the roots has high computational reliability and stability. Test results showed that the algorithm described here has a good perspective of use as a model.