Engineering topics

Willemann, R. J.

Publications and source records attributed to Willemann, R. J..

4 records

NASA NTRS1985

Planetary reorientation by surface loads

Non-hydrostatic concentrations of mass at the surface of the planet have been suggested as mechanisms of permanent reorientation for all of the terrestrial planets and for the Moon. In order for such a load to control planetary orientation, three conditions must be satisfied. The surface load must be non-hydrostatically supported; the surface load must be large compared to internal departures from a hydrostatic mass distribution; and the load must be large compared to hydrostatic departures of the planetary figure from a sphere. The third condition comes from the consideration that if the load is non-hydrostatically supported, then the same processes which support the load will also the hydrostatic figure.

Willemann, R. J.↗

NASA NTRS1982

The role of lithospheric stress in the support of the Tharsis rise

It is hypothesized that the Tharsis rise can be approximated as an axisymmetrical igneous construct. Linear theory for the deflection of planetary lithospheres is used to demonstrate that the lithospheric stresses required partially to support the construct are reasonable and consistent with the observed radial grabens around Tharsis. The computed thickness of the elastic lithosphere is between 110 and 260 km, depending of the values assumed for crustal thickness and crustal density. The computed thickness of the Tharsis load ranges from 40 to 70 km. Since in this model the height of the geoid is not specified a priori, the agreement between the observed and computed geoid is evidence for the validity of the model. The tectonics of the Tharsis region are briefly reviewed, and it is contended that all observations are consistent with the loading model.

Willemann, R. J.↗

NASA NTRS1982

Support of topographic and other loads on the moon and on the terrestrial planets

The existence of mascons on the moon indicates that the lunar elastic lithosphere can support substantial loads for about three billion years. Lunar topography also appears to be uncompensated. Observations of gravity on Mars show that the Tharsis uplift is only partially compensated. A number of authors have attributed this support to lithospheric flexure. In this paper it is shown that membrane stresses play an important role in the support of loads on the moon, Mars, and Mercury. For loads that have been expressed in terms of spherical harmonics analytical expressions for the degree of compensation are obtained as a function of the degree of the load. The results are compared with the observed dependence of the ratio of gravitational potential to topography on degree. It is also concluded that membrane stresses can support a significant ellipticity for a tidally despun planetary body.

Willemann, R. J.↗

NASA NTRS1981

Role of membrane stresses in the support of planetary topography

The role of membrane stresses and bending stresses in supporting topographic loads on planetary elastic lithospheres is examined. A dimensionless parameter is introduced in order to determine the ability of a spherical shell to support loads through membrane stresses. It is determined that when this parameter is large, membrane stresses can fully support topographic loads with flexure, and when it is small the influence of the membrane stresses can be neglected. Equations governing the behavior of a spherical shell are solved for a topographic load expressed in terms of spherical harmonics, and spherical harmonic expansions of the measured gravity and topography for Mars and the moon are compared with the theory. It is concluded that membrane stresses play an important role in the support of topographic loads on the moon and Mars. The correlation of observed gravitational potential anomalies with the topography on Mars is explained by membrane stresses in the elastic lithosphere.

Turcotte, D. L.↗