The Secular Decrease of Obliquity due to Dissipative Core--Mantle Coupling

Abstract

Summary Aoki suggested, and later (Aoki; Kakuta & Aoki) presented a theoretical model in support of calculations, that frictional (electromagnetic or viscous) torques acting across the precessing Earth's core-mantle boundary could tilt the equator toward the ecliptic plane at an astronomically-detectable rate. An upper limit to any such rotation is set by the most recent analysis of lunar occultation observations by Duncombe & van Flandern which yields a discrepancy of no more than 0.01 f 0.05 cy-' between the observed secular rate of change of the obliquity and that due to calculated planetary perturbations of the ecliptic plane. This problem in the dynamics of the Earth's ortation is here re-examined, motivated by the shortcomings of Aoki's theory (principally the neglect of inertial fluid coupling between the core and mantle) and by the importance even so slow a geophysically-induced decrease of the obliquity would have for Earth-Moon history and galactic astronomy. An extension of PoincarBs model of a perfect liquid core inside a rigid mantle, allowing for the combined effects of inertial and dissipative coupling during precession, gives a rate of decrease of the obliquity 5 0~0004cy-', far below the level of detectability by current astronomical observations. Unless the actual value of the core viscosity approaches the upper limit of 10mZs-' set by Toomre, core-mantle coupling can be ignored in modelling the dynamical evolution of the Earth-Moon system. The relationship of this problem to that of the precession-driven geomagnetic dynamo is briefly discussed.