An application of the scaled Runge-Kutta algorithms to some problems of celestial mechanics

New Runge-Kutta algorithms are applied for determining the solution of a system of ordinary differential equations at any point within a given integrating step. In this paper we propose the application of these new algorithms in order to determine, with the smallest possible cost, the exact point of intersection of a symmetric orbit, with the axis or plane of symmetry, which appear in various problems of celestial mechanics.