Evolution of the Earth's principal axes and moments of inertia: the canonical form of solution

Ray

et al. 2014

J Geod

The Earth's dynamic figure parameters, namely the principal moments of inertia and dynamic ellipticities of the whole Earth, the fluid outer core and the solid inner core, are fundamental parameters for geodetic, geophysical and astronomical studies. This study aims to re-estimate the mass and the dynamic figure parameters of the Earth on the basis of some global gravity models (EGM2008, EIGEN-6C and EIGEN-6C2) recently released with unprecedented accuracies, as well as an improved value of the gravitational constant G recommended by the Committee on Data for Science and Technology (CODATA). With the potential coefficients of EGM2008, EIGEN-6C and EIGEN-6C2 rescaled to be consistent with the IAU (International Astronomical Union) and IAG (International Association of Geodesy) numerical standards, and other values of relevant parameters also being consistent with those numerical standards, we have obtained consistent estimates of the dynamic figure parameters of the stratified Earth using the theory described in Chen and Shen (J Geophys Res 115:B12419 2010). Our preferred principal moments of inertia for the whole Earth are A = (80,085.1 ± 9.6) × 10 33 kg m 2 , B = (80,086.8 ± 9.6) × 10 33 kg m 2 , and C = (80,349.0 ± 9.6) × 10 33 kg m 2 , respectively, the accu-

Section: Dynamic Figure Factor Of the Earthmentioning

confidence: 99%

Section: Mathews Et Al (1991) Provided Hydrostatic Equilibrium Valuementioning

confidence: 99%

Consistent estimates of the dynamic figure parameters of the earth

Ray

et al. 2014

J Geod

“…Conventionally, the Earth's equatorial principal moments of inertia A and B are assumed to be equivalent to simplify Euler's dynamic equations (e.g., Landau 1975;Lambeck 1980;Goldstein et al 2002). However, recent measurements have demonstrated that all the Earth's principal moments of inertia, A, B and C, are different from each other (e.g., Burša and Ś ima 1984;Liu and Chao 1991;Marchenko and Abrikosov 2001;Groten 2004). The hypothesis that A = B, although simplifying the solutions to the traditional analytical ones (e.g., Lambeck 1980), makes the actual rotation state of the Earth theoretically unclear (although we can obtain it at a certain accuracy by making various kinds of observations).…”

Section: Introductionmentioning

confidence: 98%

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

Shen

2009

Surv Geophys

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 Earth's inertia moment tensor is closely related with the second-order potential coefficients [3,4] . The solution of the principal moments of inertia can be expressed as [3,4] …”

Section: Earth's Temporal Inertia Moment Tensormentioning

confidence: 99%

“…Mass redistribution, or sometimes called mass term, is directly related with the Earth's gravity field and was once difficult to be obtained [1,2] . However, the development of high-accuracy satellite gravimetry, such as CHAMP and GRACE, has provided us the possibility to access the Earth's temporal gravity and thus the variations of the inertia moment tensor which is relevant with the second-order potential coefficients [3][4][5] . Shen et al [4] studied the secular variation in the Earth's rotation and concluded that the tilt of the rotation axis increases 2.1×10 -8 mas/a while the rotational rate has a decrease of 1.0×10 -22 rad/s 2 based on the static gravity models EGM96 and EIGEN GL-04C.…”

Section: Introductionmentioning

confidence: 99%

GRACE’s implication of temporal inertia moment and length of day

Geo-spatial Information Science

Shen²,

Li³

2009

This paper aims to study the Earth's temporal inertia moment and its influence on length of day (LOD). First, the GRACE data are processed by wavelet analysis to remove abnormal jumps and noises. Then the theoretical impacts of the second-order potential coefficients on the inertia moment and LOD are studied. Finally, the processed GRACE data are applied and results show that mass redistribution has led to decreasing tendencies of inertia moment and LOD as well as some unexpected seasonal oscillations in the recent 6 years.