Decay of satellite orbits using K-S elements in an oblate diurnally varying atmosphere with scale height dependent on altitude

A non-singular analytical theory for the motion of near-Earth satellite orbits with the air drag effect is developed in terms of the K-S elements utilizing an analytical, oblate diurnally varying atmospheric model with varying scale height, dependent on altitude. The series expansions include up to fourth-order terms in eccentricity (e) and c, a small parameter dependent on the flattening of the atmosphere. Only two of the nine equations are solved analytically to compute the state vector at the end of each revolution due to symmetry in the K-S element equations. Numerical studies are done over a wide range of orbital parameters. A numerical comparison with numerically integrated values of the change in the orbital parameters: semi-major axis and eccentricity is made with the extended theory up to fourth-order terms of Swinerd and Boulton. It is observed that the theory in terms of the K-S elements provides better accuracy than the extended theory of Swinerd and Boulton, when compared with the numerically integrated values.