Dynamical theory of the rotation of the Earth

Abstract

From recent values of improved accuracy of the apparent secular accelerationsvandv'of the Moon and Sun, the lunar and solar tidal couplesNandN'can be found. The appropriate dynamical theory shows that the moment of inertia of the Earth,C, has been diminishing at an average rate of -1.67 x 1027cm2g s-1during the past 3300 years, giving rise to a non-tidal angular accelerationω∙i= 1.52 x 10-22s-2in addition to the retardations ofωresulting from the lunar and solar couples. The intrinsic couple associated withĊ, the time-rate of change ofC, is considerably greater than the solar tidal couple on all values ofvandv'so far determined. For an initially all-solid Earth, use of known seismic data shows that the moment of inertia has decreased during the past 3 Ga at an average rate of -1.72 x 1027cm2g s-1since a liquid core first began to form, a figure in close agreement with the value based on ancienteclipse data. On the time-honoured hypothesis that the core has resulted from iron separating downwards in an originally homogeneous Earth, the rate of decrease ofCis -0.873 x 1027cm2g s-1, only about one-half of that based on ancient-eclipse data, while if applied to these data the ratioN/N'= 11.35, which is more than twice the theoretical ratio on any tidal hypothesis. These results show that the iron-core theory is physically unacceptable.