ANALYTICAL ORBIT PREDICTIONS WITH OBLATE ATMOSPHERE USING K-S UNIFORMLY REGULAR CANONICAL ELEMENTS

摘要

A new non-singular analytical theory for the motion of near-Earth satellite orbits with the air drag effect is developed for long-term motion in terms of the K-S uniformly regular canonical elements, which are ten in number and are constant for unperturbed motion and the equations of motion permit the uniform formulation of the basic laws of elliptic, parabolic and hyperbolic motion. Series expansion method is employed and the terms up to third-order in eccentricity are included. The atmosphere is assumed to be oblate with constant density scale height. The series expansions include up to third-order terms in eccentricity. Only two of the nine equations are solved analytically to compute the state vector and change in energy at the end of each revolution, due to symmetry in the equations of motion. Comparison of the present solution with the third-order KS theory and the third-order theory of Swinerd and Boulton with respect to the numerically integrated values up to 1000 revolutions, show the superiority of the present solution over the other two theories for orbits having a wide range of eccentricity, perigee height and inclination.