Dynamical Theory of the Rotation of the Earth
Abstract
From recent values of improved accuracy of the apparent secular accelerations ν and ν' of the Moon and Sun, the lunar and solar tidal couples N and N' 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 10^{27} cm^2 g s^{1} during the past 3300 years, giving rise to a nontidal angular acceleration dot{ω}_i = 1.52 x 10^{22} s^{2} in addition to the retardations of dot{ω} resulting from the lunar and solar couples. The intrinsic couple associated with dot{C}, the timerate of change of C, is considerably greater than the solar tidal couple on all values of ν and ν' so far determined. For an initially allsolid 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 10^{27} cm^2 g s^{1} since a liquid core first began to form, a figure in close agreement with the value based on ancienteclipse data. On the timehonoured hypothesis that the core has resulted from iron separating downwards in an originally homogeneous Earth, the rate of decrease of C is 0.873 x 10^{27} cm^2 g s^{1}, only about onehalf of that based on ancienteclipse data, while if applied to these data the ratio N/N' = 11.35, which is more than twice the theoretical ratio on any tidal hypothesis. These results show that the ironcore theory is physically unacceptable.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 December 1986
 DOI:
 10.1098/rspa.1986.0120
 Bibcode:
 1986RSPSA.408..267L
 Keywords:

 Earth Rotation;
 EarthMoon System;
 Geodynamics;
 Moments Of Inertia;
 Solar Velocity;
 Acceleration (Physics);
 Angular Velocity;
 Earth Core;
 Secular Variations;
 Geophysics