Abstract
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 m 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.
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