A ThirdOrder Theory for the Effect of Drag on Earth Satellite Orbits
Abstract
Analytical theory for the motion of nearEarth satellite orbits with the air drag effect is developed in terms of the KS elements, utilizing an analytical oblate exponential atmospheric model. The series expansions include up to cubic terms in e (eccentricity) and c (a small parameter dependent on the flattening of the atmosphere). Due to the symmetry of the KS element equations, only one of the eight equations is integrated analytically to obtain the state vector at the end of each revolution. Numerical comparisons are made with nine test cases, selected to cover a wide range of eccentricity with perigee heights near to 300 km at three different inclinations. A comparison of three orbital parameters: semimajor axis, eccentricity and argument of perigee, perturbed by air drag with oblate atmosphere is made with the previously developed secondorder theory. It is found that with the present theory with increase in eccentricity there is improvement in semimajor axis and eccentricity computations over the secondorder theory.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 September 1992
 Bibcode:
 1992RSPSA.438..467K