Analytical determination of near-earth satellite trajectories using a realistic air resistance model

An analytical method for calculating the trajectories of near-earth satellites is presented which is substantially more accurate than other methods and faster than the most efficient numerical methods while providing predictions of comparable precision. The utilized model for the disturbing forces along the orbital trajectory includes the rotationally symmetric final disturbing potential up to and including the zonal harmonic J4. It also includes a recently developed, realistic, analytically integrable air resistance model which takes into account a variable aerodynamic cross section and air thickness which varies with atmospheric parameters. The equations of variation of the orbital elements are integrated using the general mean value method. The theory was translated into a computer program, whose utility is shown by a sample prediction of the fall of COSMOS 1402.