Nearly Circular Equatorial Orbits About an Oblate Body with Atmosphere

This paper studies nearly circular equatorial orbits of satellites in the gravitational field of an oblate body that includes the J(2) term and quadratic drag. We derive analytic expressions for the orbit of a satellite under these conditions even if the local atmospheric density is provided in tabular form. This work includes four distinct atmospheric density models. A closed-form solution of the orbit equation for each model is compared with the numerical integration of the equations of motion with a test model of the atmospheric density, disclosing the accuracy of the analytic solution that follows from each model. For an orbital decay of 900 in over 160 revolutions, the least accurate model revealed an error of 5 m, whereas the most accurate model produced an error of 0.4 m.