К ОБРАТНОЙ ЗАДАЧЕ НЕБЕСНОЙ МЕХАНИКИ

This work is devoted to the inverse problem of celestial mechanics, the study of whichhas become relevant in connection with the intensive exploration of outer space and the study of thegravitational and other force fields of the planets of the Solar system, other celestial bodies and gravitationalsystems. The inverse problem of celestial mechanics is the problem of determining the potential thatgenerates a given set, or family of orbits.Szebehely equation is a first - order linear partial differential equation for the potential of anautonomous conservative system with two degrees of freedom that generates a given one-parameter familyof plane orbits, is widely known. This equation gave rise to a whole series of studies in the field of celestialmechanics.There is a number of papers devoted to the generalization of the Szebehely equation and its variousanalogues. A number of studies have presented properties and interpretations of the Szebehely equationfrom the point of view of analytical mechanics, some of which are summarized in this article.The extended review is made in order to emphasize the importance of further research of the inverseproblem of celestial mechanics and its application to the study of actual problems of the dynamics of variousgravitational systems.