The Mesosphere/ Lower Thermosphere (MLT) is the region of the atmosphere in the altitude range from 60 km to 110 km. This region becomes more and more important for climate predictions and weather forecasts with the extension of simulation models to higher altitudes. The global dynamics of the MLT is driven by gravity waves. Gravity waves are generated in the lower atmosphere and transport momentum to the MLT, where these waves break and dissipate. The resulting gravity wave drag influences the wind fields and, thus, the global circulation in this region. However, gravity waves are not yet sufficiently well represented in global circulation models, because their scales are often below the grid size of the simulation models, requiring that gravity waves are parameterized. The parameterization is one of the major uncertainties in current simulation models. Thus, observational data are required to better understand the underlying processes and to constrain gravity waves in the global circulation models. However, current gravity wave observing satellites for the MLT exceeded their operational lifetimes and succeeding missions are sparse. The observational gap in the near future is already conceivable. The goal of this work is to propose a novel satellite mission with the corresponding remote sensing instrument that can reduce the data gap through a low-cost, agile, and scalable satellite. The satellite is based on the 3U CubeSat form factor that limits the mass to 4 kg and the launch volume to 34cm x 10 cm x 10 cm. CubeSats are nano satellites that can be launched on many different rockets through a standardized interface that eases the access to space. The here proposed AtmoCube-1 mission is described on a conceptual level. The focus of this work lies on the development of the remote sensing instrument that enables the characterization of gravity waves through temperature soundings in the MLT with a limb viewing geometry. The instrument measures the oxygen atmospheric band emission around 762 nm with a high spectral resolution in a small bandwidth to derive the kinetic temperature in the MLT from the temperature dependence of individual rotational fine structure lines. Thereby, the instrument uses a monolithic and temperature stabilized Fourier-transform spectrometer of the type Spatial Heterodyne Spectrometer that is characterized by a high resolving power and a high etendué at a small form factor. Thus, this instrument can be miniaturized to fit into the volume of a CubeSat. The development of the instrument and of the satellite mission started with this work. Accordingly, the specification of the satellite instrument is a major part of this work, followed by the actual development of the instrument within the mission AtmoHIT. The Atmospheric Heterodyne Interferometer Test (AtmoHIT) is an experiment on-board the sounding rocket REXUS 22 that was launched in Kiruna, Sweden, in March 2017, within the Rocket/Ballon Experiments for University Students program. AtmoHIT had the goal to verify the satellite instrument under near-space conditions by measuring the oxygen atmospheric band. The temperature stabilized design of the spectrometer has been verified in a thermal vacuum chamber test before the flight, where also the operations in the temperature range from -20 degC to 46 degC have been confirmed. Vibration tests indicated that the instrument can sustain the loads during the flight, which was demonstrated with the successful rocket flight campaign. The campaign showed also that the instrument operates under near-space conditions. The oxygen atmospheric band was measured, demonstrating the functionality of the instrument. An anomaly occurred during the separation of the payload module and the rocket motor that resulted in a strongly tumbling payload. Thus, the goal of temperature sounding in the MLT could not be fulfilled. Nevertheless, the sounding rocket campaign was deemed successful, because it showed that the instrument performed as expected. This work concludes by a discussion of the major results from the instrument development and possible enhancements to the instrument. The here developed methods and design tools are already employed in the related projects AtmoSHINE and AtmoWINDS that eventually lead to the launch of the AtmoCube-1 satellite.