We present a passive method for the retrieval of atmospheric pressure profiles based on the measurement of the apparent flattening of the solar disk as observed through the atmosphere by a spaceborne imager. This method was applied to simulated sunsets. It relies on accurate representation of the solar disk, including its limb darkening, and how its image is affected by atmospheric refraction. The Zernike polynomials are used to quantify the flattening in the Sun images. The inversion algorithm relies on a transfer matrix providing the link between the atmospheric pressure profile and a sequence of Zernike moments computed on the sunset frames. The transfer matrix is determined by a training dataset of pressure profiles generated from a standard climatology. The performance and limitations of the method are assessed by two test cases. Pressure profiles similar to the training dataset show that retrieval error can be up to 10 times smaller than the natural variability in the lower mesosphere, and up to 500 times smaller in the upper troposphere. Tests with other independent profiles emphasize the need for better representativeness of the training dataset.