Calculation of the compression of ellipsoidal layers and stress distribution in the outer shells of the earth and Mars

A method is presented for calculating the stress-strain state in the elastic lithospheric shells of the earth and Mars. The planetary stress fields in the shells of the earth and Mars are shown to have a well defined structure, which may change in time as the planet rotation speed decreases. Stress intensities in the earth lithosphere noticeably exceed those in the Mars lithosphere. In the case of the earth, maximum tangential stresses reach hundreds of bars. These stresses, however, are largely qualitative, since the rheological properties of the planetary lithospheres have not been determined with a high degree of reliability.