Motion in Oblate Spheroidal Coordinates: Applications to Gravity Perturbed Trajectories of Space Dynamics

In this paper, initial value problem for dynamical astronomy will be established using Oblate spheroidal coordinates. A computational algorithm is developed for the initial value problem of gravity perturbed trajectories of the space dynamics. Applications of the algorithm for the problem of final state prediction are illustrated by numerical examples of some test orbits of different eccentricities. The numerical results are extremely accurate and efficient in predicting final state for gravity perturbed trajectories which is important for scientific researches and the best representation of this application. Moreover, an additional efficiency of the algorithm is that, for each of the test orbits, the stepsize used for solving the differential equations of motion is at most 70% of the step size used for obtaining its reference final state solution.