Invariant imbedding equations are developed for the determination of the vertical stratification of terrestrial and other planetary atmospheres on the basis of satellite observations. The top altitude of a cloud, for example, can be estimated from the relative spectral intensities of the solar radiation reflected from the cloud in the oxygen "A" band at 7600 angstrom, and in a nearby window. The results of RM-5245-PR are extended to solve the Chandrasekhar planetary problem for atmospheres with or without internal energy sources, and with or without bottom surface reflectivity, either Lambert or nonorthotropic. The differential-integral equations may be approximated by systems of stable initial-value problems that are readily and accurately solved by digital computers. 26 pp. Refs.