Long-term rotation and mantle dynamics of the Earth, Mars, and Venus

In response to internal and surface tectonic processes the terrestrial planets have the ability to displace the axis of rotation with respect to the mantle. This behavior is quantified by means of a nondimensional number, defined here as the rotational number Ro, that allows classification of the planets into two categories, the first containing Mars and the Earth, where true polar wander is a feasible mechanism, and the second, to which Venus belongs, where rotation equilibrium is attained by means of mega-wobbles driven by internal mass anomalies. The number Ro is related to the timescale characterizing the readjustment of the equatorial bulge during long-term polar motion and to the length of the sidereal day. If these two timescales are well separated, the planet experiences true polar wander. Nonlinear Liouville equations for stratified viscoelastic bodies with linear Maxwell theology are solved in order to assess the relevance of surface and mantle processes in driving long-term rotation instabilities in the terrestrial planets. The amount of true polar wander estimated for the Earth and Mars is reproduced correctly by our modeling with mantle viscosities and lithospheric thickness consistent with other studies. The major difference between the Earth and Mars is the driving mechanism, subduction for the Earth and lithospheric loading for Mars. When mantle viscosities similar to those of the Earth are considered for Venus, the most updated estimate for the offset of about 0.50 between the rotation axis and the axis of maximum inertia is well reproduced during the mega-wobbles induced by internal mass redistribution. We show that the degree 2 topography of these three planets can be affected by their rotation, which is responsible for the dominance of the sectorial component on the Earth and Mars and for the zonal component on Venus.