The change in satellite orbital inclination caused by a rotating atmosphere with day-to-night density variation

The theory specifying the change i in a satellite's orbital inclination due to atmospheric rotation, in terms of the decrease in orbital period T, has been extended to an atmosphere with sinusoidal variation of density between day and night. It is found that with certain special sets of values for the orbital parameters, the day-to-night variation in the Earth's atmosphere can alter the equation for i/T by as much as 25% though only for a few days. Appreciable changes in i/T persisting for several months can only occur for certain resonant orbits: the maximum change is then about 8%. Near-resonance is very unlikely, but the resonance conditions are derived so that orbits can be recognised and avoided.