Contraction of high eccentricity satellite orbits using KS elements in an oblate atmosphere

Abstract

A non-singular analytical theory for the contraction of high eccentricity orbits (eccentricity e > 0.5) under the influence of air drag is developed in terms of the KS elements, using an oblate exponential atmospheric model. With the help of MACSYMA software, the series expansions include up to the sixth power in terms of an independent variable λ, introduced by Sterne as cos E =1 − H λ 2 a e , where E and a are the eccentric anomaly and semi-major axis of the orbit and H, the density scale height, is assumed constant. The solution is tested numerically over a wide range of orbital parameters: perigee height (H p), e and inclination (i) up to 100 revolutions and is found to be quite accurate. The % error in the semi-major axis computation when compared with numerically integrated values, for test cases whose perigee heights vary from 150 to 300 km and eccentricities increase from 0.6 to 0.8, is found to be less than one. The decay rates of a and e are found to be lower than those obtained with spherically symmetrical atmospheric models and increasing with increase in inclination. The theory can be effectively used for the orbital decay of Molniya type of communication satellites, decay of geostationary transfer orbits and during mission planning of aeroassisted orbital transfer orbits.