Analytical second-order drag theory with application for lifetime determination of artificial satellites in low earth orbits

A second-order atmospheric drag theory based on the usage of TD88 model is constructed. It is developed to the second order in terms of TD88 small parameters Kn,j. The short periodic perturbations, of all orbital elements, are evaluated. The secular perturbations of the semi-major axis and of the eccentricity are obtained. The theory is applied to determine the lifetime of the satellites in the low Earth orbits, e.g. ROHINI (1980 62A), and to predict the lifetime of the microsatellite MIMOSA. The secular perturbations of the nodal longitude and of the argument of perigee due to the Earth's gravity are taken into account up to the second order in Earth's oblateness.