On semi-analytical method for construction bounded motion in central force field

The known intergrable in quadratures problem is examined about motion in the central field. The force function of the problem depends only on distance of material point to the chosen origin of the coordinates. In general case of arbitrary central force no rigorous analytical solution of the problem can be obtained due to the complexity of the integrals. In the present work for a case, when distance changes in finite limits, the semi-analytical method for construction of approximate solution, getting dependences of polar coordinates on time, is offered using elliptical functions and integrals. A model problem is as an example considered for perturbing motion of hypothetical equatorial satellites of the Jupiter and of the Moon as well as motion of single star in the main plane of galaxy. The estimation of methodical accuracy is obtained by comparing to the numerical solution.