scholarly journals Rigid-Earth Nutation Models

2000 ◽  
Vol 180 ◽  
pp. 190-195
Author(s):  
J. Souchay
Keyword(s):  
Transfer Function ◽  
Rigid Body ◽  
Earth Model ◽  
High Quality ◽  
Frequency Dependent ◽  
Relative Improvement ◽  
The Earth ◽  
Rigid Earth

AbstractDespite the fact that the main causes of the differences between the observed Earth nutation and that derived from analytical calculations come from geophysical effects associated with nonrigidity (core flattening, core-mantle interactions, oceans, etc…), efforts have been made recently to compute the nutation of the Earth when it is considered to be a rigid body, giving birth to several “rigid Earth nutation models.” The reason for these efforts is that any coefficient of nutation for a realistic Earth (including effects due to nonrigidity) is calculated starting from a coefficient for a rigid-Earth model, using a frequency-dependent transfer function. Therefore it is important to achieve high quality in the determination of rigid-Earth nutation coefficients, in order to isolate the nonrigid effects still not well-modeled.After reviewing various rigid-Earth nutation models which have been established recently and their relative improvement with respect to older ones, we discuss their specifics and their degree of agreement.

scholarly journals On the Adoption of Empirical Corrections to Woolard's Nutation Theory

1980 ◽  
Vol 78 ◽  
pp. 117-124 ◽  
Author(s):  
D. D. McCarthy ◽  
P. K. Seidelmann ◽  
T. C. Van Flandern
Keyword(s):  
Solid Earth ◽  
Earth Tides ◽  
Earth Model ◽  
Working Standard ◽  
Astronomical Observations ◽  
International Astronomical ◽  
Solid Earth Tides ◽  
Rigid Earth ◽  
Empirical Corrections

Commission 4 of the International Astronomical Union has deferred the question of revisions to the constants and theory of nutation in anticipation that there might be recommendations from Symposium No. 78 in Kiev. The present rigid-Earth theory of nutation does not adequately represent current precise astronomical observations for the major nutation terms. Discrepancies between the presently adopted theory and observations can accumulate to 0″1 in right ascension and significantly affect the determination of UT1 and materially influence the derivation of the new fundamental catalog of star positions and proper motions, FK5 There appears to be no obvious choice for a non-rigid-Earth model at present. The analysis of solid-Earth tides shows nutation coefficients in substantial agreement with astronomical observations and these values have been used in the reduction of radio interferometric and laser ranging observations. In the absence of a non-rigid-Earth model which can satisfy all requirements it is suggested that the coefficients found from the investigation of solid-Earth tides be adopted as a working standard until such a model can be adopted as a basis for nutation.

scholarly journals Precession of the non-rigid Earth: Effect of the mass redistribution

2019 ◽  
Vol 626 ◽  
pp. A58 ◽  
Author(s):  
T. Baenas ◽  
A. Escapa ◽  
J. M. Ferrándiz
Keyword(s):  
Dynamical Problem ◽  
Earth Model ◽  
Linear Effect ◽  
The Earth ◽  
Mass Redistribution ◽  
Love Numbers ◽  
Oceanic Tides ◽  
Analytical Formulae ◽  
Rigid Earth ◽  
Relative Change

This research is focused on determining the contribution to the precession of the Earth’s equator due to the mass redistribution stemming from the gravitational action of the Moon and the Sun on a rotating solid Earth. In the IAU2006 precession theory, this effect is taken into account through a contribution of −0.960 mas cy−1 for the precession in longitude (with the unspecific name of non-linear effect). In this work, the revised value of that second-order contribution reaches −37.847 mas cy−1 when using the Love numbers values given in IERS Conventions, and −43.945 mas cy−1 if those values are supplemented with the contributions of the oceanic tides. Such variations impose a change of the first-order precession value that induces relative changes of the Earth’s dynamical ellipticity of about 7.3 and 8.5 ppm, respectively. The corresponding values for the obliquity rate are 0.0751 and 0.9341 mas cy−1, respectively, in contrast to 0.340 mas cy−1 considered in IAU2006. The fundamentals of the modeling have been revisited by giving a clear construction of the redistribution potential of the Earth through the corresponding changes in the Earth tensor of inertia. The dynamical problem is tackled within the Hamiltonian framework of a two-layer Earth model, introduced and developed by Getino and Ferrándiz. This approach allows for the achievement of closed-analytical formulae for the precession in longitude and obliquity. It makes it possible to obtain numerical values for different Earth models once a set of associated Love numbers is selected. The research is completed with a discussion on the permanent tide and the related estimation of the variation of the second degree zonal Stokes parameter, J2, and also the indirect effects on nutations arising from the relative change of the Earth’s dynamical ellipticity.

Implications of second order nutation terms in IAU2000 framework

2021 ◽  
Author(s):  
Alberto Escapa ◽  
Juan Getino ◽  
Jose Manuel Ferrándiz ◽  
Tomás Baenas
Keyword(s):  
Transfer Function ◽  
Second Order ◽  
Earth Structure ◽  
First Order ◽  
The Earth ◽  
Fluid Core ◽  
Rigid Earth

<p>IAU2000 (Mathews et al. 2002) incorporates some second order terms in the sense of perturbation theories in its formulation. In particular, the second order Poisson amplitudes independent of the Earth structure. They are borrowed from the rigid Earth theory REN2000 by Souchay et al. (1999). Their inclusion, however, is inconsistent (Escapa et al. 2020) since they are convolved with the MHB2000 transfer function, rendering them Earth dependent.</p><p>In that IAU2000 scheme, second order contributions depending on the Earth structure are totally ignored, as it is the case in the rigid Earth theory (Souchay et al. 1999). That structure dependent terms affect both a part of Poisson second order amplitudes and all the Oppolzer ones. Getino et al. (2021) have shown that the numerical contribution of the ignored Poisson terms is not negligible. In addition, the dependence of the respective amplitudes on the fluid core present quite different features from those of first order terms.</p><p>These facts pose some significant problems in the application of IAU2000 transfer function and the estimation of basic Earth parameters when second order terms are included, which are discussed in this communication.</p>

scholarly journals Agreements and Disagreements between Theories of Rigid Earth Nutation

1997 ◽  
Vol 165 ◽  
pp. 319-324
Author(s):  
J. Souchay
Keyword(s):  
Very Long Baseline Interferometry ◽  
Laser Ranging ◽  
Lunar Laser Ranging ◽  
Theoretical Determination ◽  
Long Baseline ◽  
The Earth ◽  
Lunar Laser ◽  
Rigid Earth ◽  
Good Agreement

AbstractThe necessity to elaborate a theory of nutation and precession matching the accuracy of very modern techniques as Very Long Baseline Interferometry and Lunar Laser Ranging led recently to various works. We discuss here the good agreement between those related to the nutation when considering the Earth as a solid body. In comparison we show the uncertainty concerning the modelisation of the transfer function leading to theoretical determination of the nutation coefficients when including dominant geophysical characteristics.

On the dynamics of physical heights and their use for the determination of accurate orthometric/normal heights

2021 ◽  
Author(s):  
Walyeldeen Godah ◽  
Malgorzata Szelachowska ◽  
Jan Krynski
Keyword(s):  
River Basin ◽  
Temporal Variations ◽  
Earth Model ◽  
Specific Reference ◽  
Normal Height ◽  
The Earth ◽  
Love Numbers ◽  
Normal Heights ◽  
Vertical Deformations

<p>Physical heights, e.g. orthometric and normal heights, are, so far, practically considered as static heights in the majority of land areas over the world. They were traditionally determined without considering the dynamic processes of the Earth induced from temporal mass variations within the Earth’s system. The Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GRACE-FO) satellite missions provided unique data that allow the estimation of temporal variations of geoid heights and vertical deformations of the Earth’s surface, and thereby the dynamics of physical heights. They revealed that for the large river basin of a strong hydrological signal (e.g. the Amazon river basin), peak to peak variations of orthometric/normal height changes reach 8 cm. The objective of this research is to discuss the need of considering the dynamics of physical heights for the determination of accurate orthometric/normal heights. An approach to determine the dynamics of physical heights using the release 6 (RL06) GRACE-based Global Geopotential Models (GGMs) as well as load Love numbers from the Preliminary Reference Earth Model (PREM) was proposed. Then, the dynamics of orthometric/normal heights was modelled and predicted using the seasonal decomposition (SD) method. The proposed approach was tested over the area of Poland. The main findings reveal that the dynamics of orthometric/normal heights over the area investigated reach the level of a couple of centimetres and can be modelled and predicted with a millimetre accuracy using the SD method. Accurate orthometric/normal heights can be obtained by combining modelled dynamics of orthometric/normal heights with static orthometric/normal heights referred to a specific reference epoch.</p><p><strong>Keywords:</strong> dynamics of physical heights, GRACE, accurate orthometric/normal heights, temporal variations of geoid/quasigeoid heights, vertical deformations of the Earth’s surface</p>

scholarly journals Solved and unsolved questions in the non-rigid Earth nutation study

2007 ◽  
Vol 3 (S248) ◽  
pp. 374-378
Author(s):  
C. L. Huang
Keyword(s):  
Inner Core ◽  
Outer Core ◽  
Earth Model ◽  
Future Studies ◽  
Atmospheric Loading ◽  
The Earth ◽  
Core Boundary ◽  
Oceanic Tides ◽  
Rigid Earth ◽  
Electro Magnetic

AbstractAt the IAU 26th GA held in Prague in 2006, a new precession model (P03) was recommended and adopted to replace the old one, IAU1976 precession model. This new P03 model is to match the IAU2000 nutation model that is for anelastic Earth model and was adopted in 2003 to replace the previous IAU1980 model. However, this IAU2000 nutation model is also not a perfect one for our complex Earth, as stated in the resolution of IAU nutation working group. The Earth models in the current nutation theories are idealized and too simple, far from the real one. They suffer from several geophysical factors: the an-elasticity of the mantle, the atmospheric loading and wind, the oceanic loading and current, the atmospheric and oceanic tides, the (lateral) heterogeneity of the mantle, the differential rotation between the inner core and the mantle, and various couplings between the fluid outer core and its neighboring solids (mantle and inner core). In this paper, first we give a very brief review of the current theoretical studies of non-rigid Earth nutation, and then focus on the couplings near the core-mantle boundary and the inner core-outer core boundary, including the electro-magnetic, viscous, topographic, and gravitational couplings. Finally, we outline some interesting future studies.

scholarly journals New series of rigid and non rigid Earth nutation. Comparison with observations

1996 ◽  
Vol 172 ◽  
pp. 239-242
Author(s):  
J. Souchay
Keyword(s):  
Transfer Function ◽  
Earth Model ◽  
Model Based ◽  
Recent Developments ◽  
Rigid Earth

After analysing the recent developments of the theory of the nutation for a simplified rigid Earth model (Kinoshita and Souchay, 1990) with new corrections and new contributions (Williams, 1994; Souchay and Kinoshita, 1996), we will study the effect of these developments on the calculation of the coefficients of nutation for a non rigid Earth model, based on the transfer function given by Wahr (1979). The relative improvements characterized by the residuals with the observations are explained in the following.

The influence of rotation on the free oscillations of the Earth

1975 ◽  
Vol 279 (1292) ◽  
pp. 583-624 ◽  
Keyword(s):  
Rigid Body ◽  
Normal Mode ◽  
Body Force ◽  
Normal Modes ◽  
Earth Model ◽  
Static Response ◽  
The Earth ◽  
Rigid Body Modes ◽  
Effects Of Rotation ◽  
Zero Frequency

We pursue an abstract investigation of the theory of the infinitesimal free elasticgravitational oscillations of a fairly general rotating Earth model. By considering in some detail the transition to the non-rotating case, we are able to delineate certain of the intrinsic effects of rotation on the normal mode eigensolutions, and to show how profoundly rotation alters the fundamental mathematical and physical properties of these eigensolutions. In particular, we show that the displacement eigenfunctions of a rotating Earth model are not mutually orthogonal, and that the corresponding normal modes of oscillation cannot in general be represented by pure standing waves. We consider the excitation of the normal modes of oscillation of a rotating Earth model by a transient imposed body force distribution, and we show that the complex dynamical amplitude of each normal mode may, in many geophysical applications, be determined separately, in spite of the lack of orthogonality among the displacement eigenfunctions. The calculation of the associated static response after the decay of the normal modes of oscillation is, on the other hand, complicated considerably by the absence of orthogonality. We specifically examine the influence of rotation on the zero-frequency rigid body translational and rotational modes of any non-rotating Earth model, and show how to account for the corresponding rigid body modes of any rotating Earth model in excitation calculations.

5. On Centrobaric Bodies

1866 ◽  
Vol 5 ◽  
pp. 190-192
Author(s):  
W. Thomson
Keyword(s):  
Rigid Body ◽  
Natural Philosophy ◽  
The Body ◽  
Centre Of Gravity ◽  
The Earth ◽  
Line Passing ◽  
Single Force

This is an abstract of an investigation which will be published in full in “Thomson and Tait's Natural Philosophy.” It contains the application of Green's wonderful results regarding the potential to the determination of the centre of gravity of a system when there is such a point. Some of the more remarkable propositions, which are thus established are as follows:—If the action of terrestrial or other gravity on a rigid body is reducible to a single force in a line passing always through one point fixed relatively to the body, whatever be its position relatively to the earth or other attracting mass, that point is called its centre of gravity, and the body is called a centrobaric body.

HADIS KURAIB DALAM KONSEP RUKYATUL HILAL

1970 ◽  
Vol 13 (2) ◽  
Author(s):  
Muslih Husein
Keyword(s):  
The West ◽  
The Earth ◽  
New Moon ◽  
The Republic

Hisab dan rukyat, hakikatnya, adalah cara untuk mengetahui pergantian bulan. Kajian ini memperlihatkan beberapa temuan. Pertama, korelasi antara hadis Kuraib dan terjadinya perbedaan penetapan awal Ramadan, Syawal, dan Dzul Hijjah di Indonesia. Kementerian Agama Republik Indonesia telah menetapkan bahwa Indonesia secara keseluruhan menjadi satu wilayah hukum (wilayatul hukmi). Kedua, tentang keberhasilan rukyat al-hilal di satu kawasan yang diberlakukan bagi kawasan lain di muka bumi. Perlu diketahui bersama bahwa visibilitas pertama hilal tidak meliputi seluruh muka bumi pada hari yang sama, melainkan membelahnya menjadi dua bagian: (1) bagian sebelah Barat yang dapat melihat hilal dan (2) bagian sebelah Timur yang tidak dapat melihat hilal.Hisab and rukyat is a way to know the turn of the month. This study shows several findings. First is the correlation between Kuraib traditions and differences in the determination of the beginning of Ramadan, Shawwal, and Dhul-Hijjah in Indonesia. Ministry of Religious Affairs of the Republic of Indonesia has stated that Indonesia as a whole into a single jurisdiction (wilayatul hukmi). Second, on the success rukyat alhilal in one area that applied to other regions of earth. Important to know that the first visibility of the new moon does not cover the entire face of the earth on the same day, but splitting it into two parts: (1) part of the West to see the new moon, and (2) part of the East were not able to see the new moon.

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