Analytical approach using KS elements to high eccentricity orbit predictions including drag

A new non-singular analytical theory for the contraction of high eccentricity satellite orbits under the influence of air drag is developed in terms of the KS elements using an oblate atmosphere with variation of density scale height with altitude. The series expansions include up to fourth power in terms of an independent variable Λ (function of the eccentric anomaly) 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 and change in energy at the end of each revolution, due to symmetry in the equations of motion. It is observed that the analytically computed values of the semi-major axis (a) and eccentricity (e) match very well with the numerically integrated values up to 1000 revolutions over a wide range of the drag perturbed orbital parameters. Inclusion of the density scale height variation with altitude is found to increase the decay of the high eccentricity orbits up to eight percent. The theory can be used effectively for the orbital decay of aero-assisted orbital transfer orbits during mission planning.