Near-Circular Orbits in a Central Force Field with Variable Drag

Near-circular satellite orbits under the influence of a drag force, which vary with time was studied. The formulas for satellite orbits under the influence of variable drag coefficient were derived using a perturbation expansions in the drag coefficient and the eccentricity. The accuracy of these new formulas was verified and they were found to be as accurate as those that were derived for nearly circular orbits with constant drag coefficients. A test is performed to find the accuracy of the analytical models presented in the preceding sections and their range of applicability. To do so, the orbits obtained from the analytical formulas are compared with those obtained from the numerical simulation of the exact equation of motion using the same variable drag coefficient function. In all cases, the simulations started from a circular orbit of 6700 km from the Earth center for a duration of 160 revolutions. The results obtained show excellent agreement between the analytical formulas for these orbits and the numerical simulation of the exact equations of motion.