On the numerical integration of orbital problems with high order Runge–Kutta–Nyström methods Original Research Article

In space dynamics a common problem deals with precise long-term predictions for satellite orbits. In such situations, especially if one demands the numerical solution of the differential equations with great precision, it is preferable to use high-order methods. Recently, González, Martı́n and Farto have developed new methods of Runge–Kutta type and low order for the numerical integration of perturbed oscillators. In this work, we present an embedded eighth order method and we study the efficiency of such method when compared with some RKN codes.