The motion of the Earth's principal axes of inertia, caused by tidal and rotational deformations

Barkin, Yu. V.; Ferrándiz, José M.

doi:10.1080/10556790008208165

Cited by 3 publications

(7 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(2) The main tidal variations can be clearly assigned and are given by The analysis of the geometry and kinematics of the temporal behaviour of the principal axes of inertia of the Moon due to tidal variations in its tensor of inertia has attracted great interest. A marked change in the orientations of these axes can be expected [13].…”

Section: Discussionmentioning

confidence: 99%

Terrestrial tidal variations in the selenopotential coefficients

Barkin

Ferrándiz

Navarro

2005

Astronomical & Astrophysical Transactions

Self Cite

View full text Add to dashboard Cite

The variations in the coefficients of the harmonics of second degree of the selenopotential caused by the terrestrial tides have been studied. In the paper we use analytical expressions for the tidal variations in the Stokes coefficients obtained for a model of the elastic celestial body with a concentric distribution of mass using the fundamental elastic parameter k 2 of the Moon. Taking into account the resonant properties of the Moon's motion, the variations in the selenopotential coefficients are presented in the form of Fourier series in the arguments of the theory of lunar orbital motion: l M , l S , F and D. The variations in the polar moment of inertia of the Moon due to the terrestrial tides lead to marked variations in the Moon's axial rotation, which also have been determined and tabulated. From the results obtained, it follows that the tide periodic variations in the gravitational coefficients of the Moon are an order larger than the corresponding tide variations in the geopotential coefficients.

show abstract

Section: Discussionmentioning

confidence: 99%

Terrestrial tidal variations in the selenopotential coefficients

Barkin

Ferrándiz

Navarro

2005

Astronomical & Astrophysical Transactions

Self Cite

View full text Add to dashboard Cite

show abstract

“…The fundamental equations used in this approach are basically the same as those employed in [ 16 ]. Therefore, we present a short summary of them with identical notation and refer to that paper for additional details.…”

Section: Methods and Datamentioning

confidence: 99%

“…The computation of the principal moments of inertia and the rotation matrix can be performed by solving a cubic equation whose roots are the principal moments. The main steps of the procedure are presented in several references (e.g., [ 11 , 16 , 17 ]).…”

Section: Methods and Datamentioning

confidence: 99%

“…In this paper, we use an approximate analytical method introduced by Barkin and Ferrandiz in 2000 [ 16 ] for deriving the PAI oscillations due to the Earth’s elasticity yielding to the Moon and Sun attraction and its rotation. The changes of the Earth’s PAI due to tidal and centrifugal (pole tide) deformations are included in the background models used to derive the Stokes coefficients and thus are excluded from the solution obtained in this paper by applying the same method to the time series providing the variation of the second-degree Stokes coefficients.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Drift of the Earth’s Principal Axes of Inertia from GRACE and Satellite Laser Ranging Data

et al. 2020

View full text Add to dashboard Cite

The location of the Earth’s principal axes of inertia is a foundation for all the theories and solutions of its rotation, and thus has a broad effect on many fields, including astronomy, geodesy, and satellite-based positioning and navigation systems. That location is determined by the second-degree Stokes coefficients of the geopotential. Accurate solutions for those coefficients were limited to the stationary case for many years, but the situation improved with the accomplishment of Gravity Recovery and Climate Experiment (GRACE), and nowadays several solutions for the time-varying geopotential have been derived based on gravity and satellite laser ranging data, with time resolutions reaching one month or one week. Although those solutions are already accurate enough to compute the evolution of the Earth’s axes of inertia along more than a decade, such an analysis has never been performed. In this paper, we present the first analysis of this problem, taking advantage of previous analytical derivations to simplify the computations and the estimation of the uncertainty of solutions. The results are rather striking, since the axes of inertia do not move around some mean position fixed to a given terrestrial reference frame in this period, but drift away from their initial location in a slow but clear and not negligible manner.

show abstract

“…Let us notice that the definition of the body frame has no special difficulties under the assumption of linear elasticity, since the deformations have known expressions depending on constant Love numbers, and the variations of the principal axes and moments of inertia can be derived analytically (BARKIN and FERRÁ NDIZ 2000). More properties of the rotation of weakly deformable bodies are given by BARKIN (1998BARKIN ( , 2000a.…”

Section: Two-layer Earth Modelsmentioning

confidence: 99%