Final state predictions for J2 gravity perturbed motion of the earth's artificial satellites using orthogonal curvilinear coordinates

In this paper, initial value problem for dynamical astronomy will be established using four orthogonal curvilinear coordinates: Spherical Polar, Prolate Spheroidal, Bipolar and Bispherical coordinates. A computational algorithm is developed for the finial state predictions for J2 gravity perturbed motion of the Earth's artificial satellites using these orthogonal curvilinear coordinates. This algorithm is important in targeting, rendezvous maneuvers as well for scientific researches. The applications of the algorithm are illustrated by numerical examples of some test orbits of different eccentricities. The numerical results are extremely accurate and efficient.