Tides and Tidal Stress: Applications to Europa

Abstract

A review of analytical techniques and documentation of previously inaccessible mathematical formulations is applied to study of Jupiter's satellite Europa. Compared with numerical codes that are commonly used to model global tidal effects, analytical models of tidal deformation give deeper insight into the mechanics of tides, and can better reveal the nature of the dependence of observable effects on key parameters.I develop analytical models for tidal deformation of multi-layered bodies. Previous studies of Europa, based on numerical computation, only to show isolated examples from parameter space. My results show a systematic dependence of tidal response on the thicknesses and material parameters of Europa's core, rocky mantle, liquid water ocean, and outer layer of ice. As in the earlier work, I restrict these studies to incompressible materials. Any set of Love numbers h2 and k2 which describe a planet's tidal deformation, could be fit by a range of ice thickness values, by adjusting other parameters such as mantle rigidity or core size, an important result for mission planning.Inclusion of compression into multilayer models has been addressed analytically, uncovering several issues that are not explicit in the literature. Full evaluation with compression is here restricted to a uniform sphere. A set of singularities in the classical solution, which correspond to instabilities due to self-gravity has been identified and mapped in parameter space.The analytical models of tidal response yield the stresses anywhere within the body, including on its surface. Crack patterns (such as cycloids) on Europa are probably controlled by these stresses. However, in contrast to previous studies which used a thin shell approximation of the tidal stress, I consider how other tidal models compare with the observed tectonic features. In this way the relationship between Europa's surface tectonics and the global tidal distortion can be constrained.While large-scale tidal deformations probe internal structure deep within a body, small-scale deformations can probe internal structure at shallower depths. I have used photoclinometry to obtain topographic profiles across terrain adjacent to Europan ridges to detect the effects of loading on the lithosphere. Lithospheric thicknesses have been determined and correlated with types and ages of terrain.