Rotational dynamics of tidally deformed planetary bodies and validity of fluid limit and quasi-fluid approximation

In past studies, the reorientation or true polar wander (TPW) of visco-elastic bodies has been studied with approximated solutions. Two types of methods are commonly adopted: those based on the quasi-fluid approximation e.g. Ricard et al., 1993 and those based on the fluid limit approximation which only consider the final orientation (e.g. Matsuyama and Nimmo, 2007). Recently, Hu et al., (2017b) established a method which provides a dynamic solution for calculating the reorientation of tidally deformed bodies. However, they did not provide the links between the complete solution and the fluid limit solution. This paper provides a semi-analytical method for calculating the reorientation of tidally deformed bodies and shows the relation between the complete and the approximated solutions. Furthermore, we provide a criterion, the fluid limit process number F, to test for a given model and estimated TPW speed if the quasi-fluid approximation or fluid limit solution is valid. This number is a quantitative description of how close the body stays in hydrostatic equilibrium during a reorientation process. We use this number to obtain the largest allowed TPW speed of Mars as a function of viscosity, for which the approximated solutions may be used.