  Topical observations of the thermosphere at altitudes below $200 \, km$ are
of great benefit in advancing the understanding of the global distribution of
mass, composition, and dynamical responses to geomagnetic forcing, and momentum
transfer via waves. The perceived risks associated with such 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 an avenue for performing low
altitude missions. The time dependent coefficients of a second order
non-homogeneous ODE which describes the motion have a double periodic shape.
Hence, they will be approximated using Jacobi elliptic functions. Through a
change of variables the original ODE will 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
dynamically stable. A possible extension of the application is a computational
tool for the rapid evaluation of the stability of entry or re-entry vehicles in
rarefied flow regimes and of satellites flying in relatively low orbits.
