Low thrust oscillatory ascending spiral trajectories as affected by air drag

Abstract

The ascending spiral trajectory of a satellite subject to air drag and a low constant tangential thrust is derived by the asymptotic method in nonlinear mechanics. Based on the assumptions of a non-rotating, spherically symmetric atmosphere and an exponential distribution of atmospheric density, closed-form solutions for the first-order approximation are obtained. The oscillatory nature of the spiral trajectory is exposed and the oscillations are shown to damp out as the satellite spirals out.