A semi-analytical solution for the motion of a low altitude Earth satellite under J2-gravity and air drag perturbations

The motion of the low altitude Earth satellites is important for space applications, since these altitudes are crowded by a large number of artificial satellites. At this region the Earth’s oblateness and the drag force play an important role and capture the dynamics of the problem. The present work investigates the motion of a low altitude Earth satellite under the combined effect of the Earth’s gravity, up to the fourth zonal harmonic, and the drag force. The equations of motion are formulated under the considered force model. The problem under concern is treated using two different techniques, Cowell's and Average methods. We used the TLE data of the International Space Station (ISS) to compare the analytical method (average method) and the numerical Cowell’s method. To better understanding the problem, we carried out several numerical explorations. A Mathematica code is constructed to simulate the numerical examples. Comparing the two methods, we found that Cowell’s method gave more acceptable results.