Some remarks on polar wandering


  • Peter Goldreich,

  • Alar Toomre


This paper lends fresh support to the hypothesis that large angular displacements of the earth's rotation axis relative to the entire mantle have occurred on a geological time scale, owing to the gradual redistribution (or decay or manufacture) of density inhomogeneities within the earth by the same convective processes that are responsible for continental drift. The first of our three contributions is a pedagogic theorem that rigorously illustrates this mechanism of polar wandering for a ‘quasi-rigid body’. That theorem states that any slow changes in shape of such a body preserve as an adiabatic invariant the solid angle traced out by its angular momentum vector as viewed from its principal axes. Thus, if the body were once set spinning about the axis with the greatest moment of inertia, it would always continue to spin almost exactly about the same principal axis no matter how that axis moves through the deforming body. The second and main contribution is our refutation of the widely accepted notion that the earth's figure shows unmistakable signs of the faster spin rate of the past. If correct, the degree of permanence of the rotation bulge so inferred by G. J. F. MacDonald (1963, 1965) and D. P. McKenzie (1966) would have been an effective impediment against any significant polar wandering of the earth as a whole. However, we show here that, after subtraction of the hydrostatic flattening, the remaining or nonhydrostatic part of the earth's inertia ellipsoid is distinctly triaxial. Such a triaxial shape, as well as the coincidence of the present rotation axis with the principal axis having the largest of the nonhydrostatic moments of inertia, is indeed to be expected of any randomly evolving, nearly spherical object without too much ‘memory’ for its past axis of rotation. Finally, we discuss briefly some statistical aspects of polar wandering on the assumption that the earth is such an object.