Sometime late in the fall of 2007, the NetLander mission will land four probes on the surface of Mars containing geodetic and seismic experiments, thereby establishing the first network of geophysics stations on the surface of a terrestrial body other than our own Earth. This mission will yield a tremendous amount of information pertaining the internal structure and orientation of Mars. Thanks to such missions, the data available for the terrestrial bodies will increase and with it our understanding of the rotational instabilities.
Although this was not always the case, it is now known that forces and deformations due to the non-rigid characteristics of the Earth constantly perturb the motion of the planet to various degrees. The fact that our planet, and all realistic bodies for that matter,is not wholly solid, that it has oceans, an atmosphere and a visco-elastic crust, mantle and core, means that the actual position of the rotational axis and rotation rate of the Earth vary from the idealized rigid body motion on virtually every time scale. The Earth constantly reshapes itself to cope with the ever changing loads and other geo-dynamic forces that act upon it. This deformation in turn leads to shifts in the position of the rotation axis with respect to the Earth’s surface, or polar motion, and to a change in rotation rate, also known as a change in length-of-day. This reshaping of a body due to geo-dynamic forces is dependent on the rheology of that body, since material properties such as rigidity and viscosity determine how a body deforms and flows under certain stresses. Although their regularities in the rotation of the Earth complicate astronomical research, for the geophysicist they are a gift. The rotational perturbations must have sources and thus provide information on the internal structure of the Earth and the geophysical processes acting on and within it. The main objective of this thesis is to examine the influences of some of the parameters that determine the polar motion of a terrestrial body, without adhering to the constraints put on them by the application to the Earth. For instance, the influence of the absolute size of a body as defined by its radius has never been examined since the radius of the Earth is known very accurately. This leads to more general and more widely applicable results as the driving parameters are examined in wide ranges.

To this end, a linearized formulation of the polar motion was used in conjunction with the Normal Mode technique, which uses the Laplace domain to calculate the elastic equivalence of the visco-elastic problem in the time domain.