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The National Aeronautics and Space Administration Ionospheric Connection Explorer (ICON) mission will study the close relationship between the ionosphere, the atmospheric weather, and space weather using in situ and remote sensing instruments proving plasma density, temperature, ion drift velocity, and thermospheric wind velocity over the equatorial region. In particular, the far ultraviolet (FUV) instrument will image the terrestrial limb in two wavelength channels. During nighttime, only the channel characterizing the bright 135.6-nm emission of atomic oxygen will be used. The purpose of this study is to simulate FUV nightglow measurements under quiet as well as disturbed ionospheric conditions. Classical medium-scale traveling ionospheric disturbances (MSTIDs), which are understood as the ionospheric signature of atmospheric gravity waves, are one of the main sources of ionospheric variability. Here, we simulate their potential appearance in the FUV instrument data. The simulation model produces FUV images used as input to identify and characterize MSTIDs. MSTID propagation parameters can be retrieved under specific geometrical configurations between the FUV lines of sight and propagation direction of the MSTID, which differs depending on the limb or sublimb observing geometry. The largest MSTID signature is expected during equinoxes under solar maximum periods, for MSTID periods of less than 30\ min. The weak brightness of the 135.6-nm multiplet under solar minimum conditions is the main limitation to the MSTID detection on the nightside. Future MSTID detection algorithms would have to cope with very low signal-to-noise ratio, in particular during solstices and under solar minimum conditions.