Orbital decay in the classroom

Abstract

The objective of this paper is to provide a pedagogical framework for the phenomenon of orbital decay of satellites in low Earth orbit. The dynamics of orbital decay are derived considering atmospheric drag as the only dissipative mechanism and using an educational approach suitable for undergraduate calculus-based physics and engineering courses. The resulting nonlinear first-order differential equation for the altitude as a function of time is solved numerically for the isothermal-barotropic atmospheric model with a fixed scale height. The model is validated using the uncontrolled reentry data of the Chinese space station Tiangong-1