Aerodynamic Stability of Satellites in Elliptic Low Earth Orbits

Abstract

Topical observations of the thermosphere at altitudes below 200 km are of great benefit in advancingthe understanding of the global distribution of mass, composition, and dynamical responsesto geomagnetic forcing, and momentum transfer via waves. The perceived risks associated withsuch low altitude and short duration orbits has prohibited the launch of Discovery-class missions.Miniaturization of instruments such as mass spectrometers and advances in the nano-satellite technology,associated with relatively low cost of nano-satellite manufacturing and operation, open anavenue for performing low altitude missions. The time dependent coefficients of a second ordernon-homogeneous ODE which describes the motion have a double periodic shape. Hence, they willbe approximated using Jacobi elliptic functions. Through a change of variables the original ODEwill be converted into Hill’s ODE for stability analysis using Floquet theory.We are interested in how changes in the coefficients of the ODE affect the stability of the solution.The expected result will be an allowable range of parameters for which the motion is dynamicallystable. A possible extension of the application is a computational tool for the rapid evaluation ofthe stability of entry or re-entry vehicles in rarefied flow regimes and of satellites flying in relativelylow orbits