A Second-Order Artificial Satellite Theory Based on an Intermediate Orbit

An analytical second-order theory is developed for the motion of a satellite of an oblate planet whose gravitational potential includes the second, third, and fourth zonal harmonics. it is assumed that J2 is a small quantity of the first order, and that J2 and J4 are of the second order. The secular and the periodic perturbations are obtained to the third and to the second order, respectively. The former are contained in the Delaunay variables ", g", h", which are linear functions of the time, while the latter are given as additions to the Hill variables r", r", G", u", h" in the form of trigonometric series with constant coefficients. The theory is distinguished by a relative simplicity and compactness of the final algorithm achieved by the use of the following special devices and techniques: (i) an intermediate orbit, (ii) Hori's perturbation method, and (iii) the Hill variables. A comparison with the results of numerical integration of the equations of motion indicates that the theory is capable of predicting the position of a close Earth satellite to better than one meter over one-hundred revolutions.