Free Wobble of the Triaxial Earth: Theory and Comparisons with International Earth Rotation Service (IERS) Data

Abstract

Earth's free wobble is often referred to as the Euler wobble (for the rigid case) or the Chandler wobble for the real case. In this study, we investigate the theory of the free wobble of the triaxial Earth and demonstrate that: (1) the Euler period should actually be expressed by the complete elliptic integral of first kind, and (2) the trace of the free polar motion is elliptic, with the orientations of its semi-minor and major axes being approximately parallel to the Earth's principal axes A and B, respectively. Numerical calculations show that, due to the triaxiality of the Earth, the spin rate x 3 fluctuates with the semi-Euler/ Chandler period, although its amplitude (about 10 -19 rad/s) is rather small and beyond the present measurement accuracy; the tilt of the instantaneous spin axis (or the amplitude of the free wobble), h, has a fluctuation whose amplitude is around 0.34 milli-arcsecond (mas), which could be detected by present observations. Thus, we conclude that the Earth's triaxial nature has little impact on x 3 , but has an influence on the polar motion which should not be ignored. On the other hand, our study shows that there is a mechanism of frequency-amplitude modulation in the Chandler wobble which might be a candidate to explain the correlation between the amplitude and period of the Chandler wobble. We compare the theoretical polar parameters (m 1 , m 2 ) with the observed values for the Chandler components obtained from the data EOP (IERS) C 04, and find that they coincide with each other quite well, especially for recent years. In addition, a polar wander towards 76.7°W, which is in agreement with previous results given by other scientists, is also obtained.

The Dawn Gravity Investigation at Vesta and Ceres

“…One means of testing for an un-damped obliquity would be to look for a free wobble, or non-principal axis rotation (Munk and MacDonald 1960;Lambeck 1980;Chen et al 2009). The wobble period is short compared to the spin pole precession period, and thus the wobble damping time is short compared to the obliquity damping time.…”

Forced obliquities and moments of inertia of Ceres and Vesta

“…One means of testing for an un-damped obliquity would be to look for a free wobble, or non-principal axis rotation (Munk and MacDonald, 1960;Lambeck, 1980;Chen et al, 2009 period is short compared to the spin pole precession period, and thus the wobble damping time is short compared to the obliquity damping time. A hypothetical excitation event, such as a relatively recent impact (Peale, 1976), could have produced both a free wobble and a free obliquity.…”

Commission 19: Rotation of the Earth

“…A triaxial Earth rotation theory to incorporate all relevant physical processes was studied. The dynamic equations are formulated and the normal modes for an Earth model with a triaxial anelastic mantle, a triaxial fluid core, and dissipative oceans are obtained (Chen et al, 2009(Chen et al, , 2010Shen et al, 2011).…”