The investigation of the Martian atmosphere is of key importance for an understanding of the planets present and past. Passive limb observations of thermal radiation at submillimeter wavelengths in the 320-350-GHz range by use of a state-of-the-art satellite receiver on a low Mars orbit allow important parameters such as the mixing ratios of H2O, HDO, 12CO, 13CO, O3, and H2O2 as well as the thermal profile to be retrieved with high precision and unprecedented vertical range and resolution, providing valuable information for better understanding of the planet's water cycle, atmospheric dynamics, and photochemistry. The feasibility of these kinds of measurement is demonstrated by means of model simulations based on realistic atmospheric, spectroscopic, and instrumental parameters. Temperature can be retrieved to approximately 90 km with half-scale height vertical resolution from single-scan measurements of emission lines of the long-lived species 12CO and 13CO. The global water-vapor distribution can be measured even under dry or wet conditions with good vertical resolution from the surface to approximately 45 km, and simultaneous observations of HDO allow useful information on the D/H ratio up to an altitude of approximately 30 km to be derived. The sensitivity of the limb-sounding technique also permits information on the photochemically important minor species O3, and H2O2 to be obtained. It is shown that spectral averaging may improve precision, altitude range, and resolution of the retrieved profiles. Other frequency bands are explored, and the 435-465-GHz range is suggested as a possible alternative to the 320-350-GHz range.