Low Earth Orbiting (LEO) Satellite and Orbital Decay

Abstract

In this article we present a simple but elegant numerical calculation to study the motion of a low earth orbiting (LEO) satellite in gravitational potential and under the influence of quadratic drag force. We solve a set of coupled differential equations to calculate the instantaneous position and velocity of the satellite and calculate the change in radial distance for different aerodynamic coefficients and altitude. We validate our numerical results with theoretical result in the high altitude where the density of air and consequently the drag force is minimum. However the LEO orbits placed in the range of 200 to 400 km faces significant effect of drag force. Satellites at an altitude of 200 km quickly decay and re-entry to earth’s atmosphere occurs. We finally do a short numerical calculation with the parameters of ISS satellite at an altitude of 400 km and compare with the existing results.