An Improved Analytical Drag Theory for the Artificial Satellite Problem

This paper presents a solution for satellite orbits in a non-rotating atmosphere which takes into account the coupled effects of atmospheric drag, and the second, third, and fourth zonal harmonics. It is an extension to the Analytical Drag Theory developed by Lane in 1965. Limitations to the theory for small eccentricities and small inclinations no longer appear. Certain terms with coefficients of the forn B02t2 and Bo2T3 (where Bo is the drag coefficient and t is the time), which were not present in either Lane's paper or in the Brouwer-Hori theory, were found to be significant for low satellites and have been included, the criterion used in this paper is that terms contributing more than 600 meters in position error over a prediction span of at least ten days (unless decay occurs earlier) would be retained. Where J2 is the coefficient of the second harmonic in the earth's gravitational potential, the result is complete through second order (522) in the secular terms and, except for the long period terms in the mean anomaly, through first order (J2) in periodic terms. The drag coefficient is assumed to be no larger than J2.