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Topical observations of the thermosphere at altitudes below $200 \, km$ areof great benefit in advancing the understanding of the global distribution ofmass, composition, and dynamical responses to geomagnetic forcing, and momentumtransfer via waves. The perceived risks associated with such low altitude andshort duration orbits has prohibited the launch of Discovery-class missions.Miniaturization of instruments such as mass spectrometers and advances in thenano-satellite technology, associated with relatively low cost ofnano-satellite manufacturing and operation, open an avenue for performing lowaltitude missions. The time dependent coefficients of a second ordernon-homogeneous ODE which describes the motion have a double periodic shape.Hence, they will be approximated using Jacobi elliptic functions. Through achange of variables the original ODE will be converted into Hill's ODE forstability analysis using Floquet theory. We are interested in how changes inthe coefficients of the ODE affect the stability of the solution. The expectedresult will be an allowable range of parameters for which the motion isdynamically stable. A possible extension of the application is a computationaltool for the rapid evaluation of the stability of entry or re-entry vehicles inrarefied flow regimes and of satellites flying in relatively low orbits.

Aerodynamic Stability of Satellites in Elliptic Low Earth Orbits