scholarly journals Relativistic Considerations for Precession and Nutation

1998 ◽  
Vol 11 (1) ◽  
pp. 173-176
Author(s):  
S.A. Klioner ◽  
M. Soffel
Keyword(s):  
General Relativity ◽  
Rotational Motion ◽  
Earth Rotation ◽  
Equations Of Motion ◽  
Relativistic Effects ◽  
Point Of View ◽  
Extended Body ◽  
The Earth ◽  
Celestial Bodies

Abstract The whole scope of problems related with the rotational motion of celestial bodies is briefly discussed. Relativistic modeling of the Earth rotation is considered from a conceptual point of view. Relativistic effects in rotational equations of motion of an extended body in general relativity are discussed. Numerical values of the effects are given.

scholarly journals Rotational Motion of Celestial Bodies in the Relativistic Framework

1999 ◽  
Vol 172 ◽  
pp. 435-436
Author(s):  
Sergei A. Klioner ◽  
Michael Soffel
Keyword(s):  
General Relativity ◽  
Rotational Motion ◽  
Relativistic Effects ◽  
Operational Definition ◽  
Point Of View ◽  
Newtonian Mechanics ◽  
Extended Body ◽  
International Astronomical ◽  
Celestial Bodies ◽  
Relativistic Framework

There are several important reasons to consider relativistic effects in rotational motion of celestial bodies. General Relativity is now recommended by the International Astronomical Union and International Union of Geodesy and Geophysics as a theoretical framework for modeling of high-precision observational data. On the other hand, various geodynamical observations provide data which are widely used for testing General Relativity itself.In Newtonian mechanics it is well known how to describe rotational motion of an extended body. In General Relativity this is a rather subtle issue. The concept of a precessing extended rigid body in general relativity encounters fundamental difficulties and cannot be introduced even in the first post-Newtonian approximation. From a practical point of view, however, the rotational motion of the Earth even at the Newtonian level is defined operationally through the time-dependence of geocentric quasi-inertial coordinates of observing sites. An analogous operational definition can be applied in general relativity. To this end, we need a set of physically adequate reference systems.

scholarly journals On the Problem of post-Newtonian Rotational Motion

1997 ◽  
Vol 165 ◽  
pp. 383-390
Author(s):  
Sergei A. Klioner
Keyword(s):  
General Relativity ◽  
Angular Velocity ◽  
Rotational Motion ◽  
Earth Rotation ◽  
Deformable Body ◽  
Gravitational Fields ◽  
The Earth ◽  
Newtonian Approximation ◽  
Deformable Bodies ◽  
Tensor Of Inertia

AbstractThe problems of modeling of the rotational motion of the Earth are considered in the framework of general relativity. Both, rigid and deformable bodies are discussed. Rigorous definitions of the tensor of inertia, Tisserand-like axes and the angular velocity of rotation of an extended deformable body moving and rotating in external gravitational fields are proposed in the first post-Newtonian approximation. The implications of these post-Newtonian definitions on modeling of Earth rotation are analyzed.

scholarly journals Relativistic aspects of rotational motion of celestial bodies

2009 ◽  
Vol 5 (S261) ◽  
pp. 112-123 ◽  
Author(s):  
S. A. Klioner ◽  
E. Gerlach ◽  
M. H. Soffel
Keyword(s):  
High Precision ◽  
Rotational Motion ◽  
Earth Rotation ◽  
Theoretical Framework ◽  
Reference Systems ◽  
The Moon ◽  
Newtonian Theory ◽  
Recent Developments ◽  
Celestial Bodies ◽  
Near Future

AbstractRelativistic modelling of rotational motion of extended bodies represents one of the most complicated problems of Applied Relativity. The relativistic reference systems of IAU (2000) give a suitable theoretical framework for such a modelling. Recent developments in the post-Newtonian theory of Earth rotation in the limit of rigidly rotating multipoles are reported below. All components of the theory are summarized and the results are demonstrated. The experience with the relativistic Earth rotation theory can be directly applied to model the rotational motion of other celestial bodies. The high-precision theories of rotation of the Moon, Mars and Mercury can be expected to be of interest in the near future.

scholarly journals Astromimetics

2018 ◽  
Vol 5 ◽  
pp. 184954351879434 ◽  
Author(s):  
Vuk Uskoković ◽  
Victoria M Wu
Keyword(s):  
Materials Science ◽  
Fine Particles ◽  
Great Majority ◽  
Point Of View ◽  
Iron Core ◽  
Colloidal Form ◽  
The Earth ◽  
Celestial Bodies ◽  
Intended Use

Composite, multifunctional fine particles are likely to be at the frontier of materials science in the foreseeable future. Here we present a submicron composite particle that mimics the stratified structure of the Earth by having a zero-valent iron core, a silicate/silicide mantle, and a thin carbonaceous crust resembling the biosphere and its biotic deposits. Particles were formulated in a stable colloidal form and made to interact with various types of healthy and cancer cells in vitro. A selective anticancer activity was observed, promising from the point of view of the intended use of the particles for tumor targeting across the blood–brain barrier. As an extension of the idea underlying the fabrication of a particle mimicking the planet Earth, we propose a new field of mimetics within materials science: astromimetics. The astromimetic approach in the context of materials science consists of the design of particles after the structure of celestial bodies. With Earth being the most chemically diverse and fertile out of all the astral bodies known, it is anticipated that the great majority of astromimetic material models will fall in the domain of geo-inspired ones.

scholarly journals Rers2014 and Mrs2014: New High-Precision Rigid Earth Rotation and Moon Rotation Series

2015 ◽  
Vol 50 (1) ◽  
pp. 35-40
Author(s):  
V.V. Pashkevich
Keyword(s):  
Numerical Solution ◽  
Numerical Investigation ◽  
High Precision ◽  
Rotational Motion ◽  
Earth Rotation ◽  
Euler Angles ◽  
Time Intervals ◽  
The Earth ◽  
Long Time ◽  
Rigid Earth

Abstract Numerical investigation of the Earth and Moon rotational motion dynamics is carried out at a long time intervals. In our previous studies (Pashkevich, 2013), (Pashkevich and Eroshkin, 2011) the high-precision Rigid Earth Rotation Series (designated RERS2013) and Moon Rotation Series (designated MRS2011) were constructed. RERS2013 are dynamically adequate to the JPL DE422/LE422 (Folkner, 2011) ephemeris over 2000 and 6000 years and include about 4113 periodical terms (without attempt to estimate new subdiurnal and diurnal periodical terms). MRS2011 are dynamically adequate to the JPL DE406/LE406 (Standish, 1998) ephemeris over 418, 2000 and 6000 years and include about 1520 periodical terms. In present research have been improved the Rigid Earth Rotation Series RERS2013 and Moon Rotation Series MRS2011, and as a result have been constructed the new high-precision Rigid Earth Rotation Series RERS2014 and Moon Rotation Series MRS2014 dynamically adequate to the JPL DE422/LE422 ephemeris over 2000 and 6000 years, respectively. The elaboration of RERS2013 is carried out by means recalculation of sub-diurnal and diurnal periodical terms. The residuals in Euler angles between the numerical solution and RERS2014 do not surpass 3 ìas over 2000 years. Improve the accuracy of the series MRS2011 is obtained by using the JPL DE422/LE422 ephemeris. The residuals in the perturbing terms of the physical librations between the numerical solution and MRS2014 do not surpass 8 arc seconds over 6000 years

scholarly journals The Apsidal Motion Test in Eclipsing Binaries

2006 ◽  
Vol 2 (S240) ◽  
pp. 290-298
Author(s):  
Alvaro Giménez
Keyword(s):  
General Relativity ◽  
Equations Of Motion ◽  
Large Data ◽  
Point Of View ◽  
Eclipsing Binaries ◽  
Stellar Structure ◽  
Low Mass Stars ◽  
Low Mass ◽  
Level Of Knowledge ◽  
Near Future

AbstractThe use of eccentric eclipsing binaries to test stellar internal structure models, as well as the equations of motion provided by General Relativity, is reviewed. Close to 80 years have elapsed since the first ideas were produced in this field and many results have been obtained since then. It appears that, in general, a good understanding of stellar structure within the main sequence is available while the same level of knowledge can not be claimed beyond the termination age. The equations of general relativity could not be disproved with observational data though some systems cannot still be fully explained. In the near future, the analysis of evolved systems, very low mass stars, the effects of tidal resonances and the presence of third bodies has to be further explored. In addition, the analysis of large data bases obtained by means of extensive photometric surveys will certainly change the picture from an observational point of view.

scholarly journals Rotational Velocity of an Earth Model with a Liquid Core

1979 ◽  
Vol 82 ◽  
pp. 313-314
Author(s):  
S. Takagi
Keyword(s):  
Rotational Motion ◽  
Velocity Vector ◽  
Inner Core ◽  
Rotational Velocity ◽  
Equations Of Motion ◽  
Liquid Core ◽  
Outer Core ◽  
Earth Model ◽  
The Earth ◽  
Rotation Of The Earth

There have been many papers discussing the rotation of the Earth (Jeffreys and Vicente, 1957; Molodenskij, 1961; Rochester, 1973; Smith, 1974; Shen and Mansinha, 1976). This report summarizes the application of the perturbation method of celestial mechanics to calculate the rotation of the Earth (Takagi, 1978). In this solution the Earth is assumed to consist of three components: a mantle, liquid outer core, and a solid inner core, each having a separate rotational velocity vector. Hamiltonian equations of motion were constructed to solve the rotational motion of the Earth.

scholarly journals Space astrometry prospects and limitations

1986 ◽  
Vol 114 ◽  
pp. 369-382
Author(s):  
J. Kovalevsky ◽  
F. Mignard ◽  
M. Froeschlé
Keyword(s):  
Relativistic Effects ◽  
Second Order ◽  
Point Of View ◽  
Wide Field ◽  
Theoretical Point ◽  
Small Field ◽  
Light Deflection ◽  
Celestial Bodies ◽  
Space Astrometry ◽  
Magnitude Improvement

Among the few parameters that describe the generalized space time metrics, astrometric techniques are essentially sensitive to the displacement of the apparent positions of celestial bodies. This includes the relativistic light deflection and aberration. The possibilities of small field and wide field astrometry in measuring these effects are described. The case of the second order aberration terms is considered with some detail from the theoretical point of view, both for stellar and planetary aberration. New results are presented in the latter case.A section is devoted to a description of the existing space astrometry projects among which Space Telescope and HIPPARCOS are approved but will not contribute significantly to relativistic studies. Several “second generation” projects exist that aim at 2 or 3 orders of magnitude improvement in precision. They would yield results on second order relativistic effects and may be used to determine masses of some single stars. However, the present state of engineering of space astrometric missions has permitted to identify several limitations of the present and future missions. They will not all be readily suppressed and one should be very careful in assessing now their potentialities. It seems however that interferometric techniques have more chance to reach the 10−4 and 10−5 arc second precision than the imaging methods.

scholarly journals ACTION BASED APPROACH TO THE DYNAMICS OF EXTENDED BODIES IN GENERAL RELATIVITY

2003 ◽  
Vol 12 (09) ◽  
pp. 1651-1655 ◽  
Author(s):  
JEEVA ANANDAN ◽  
NARESH DADHICH ◽  
PARAMPREET SINGH
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Equations Of Motion ◽  
Weak Field ◽  
Multipole Moments ◽  
Field Limit ◽  
Extended Body ◽  
Weak Field Limit ◽  
Extended Object ◽  
First Time

We present, for the first time, an action principle that gives the equations of motion of an extended body possessing multipole moments in an external gravitational field, in the weak field limit. From the action, the experimentally observable quantum phase shifts in the wavefunction of an extended object due to the coupling of its multipole moments with the gravitational field are obtained. Also, since the theory may be quantized using the action, the present approach is useful in the interface between general relativity and quantum mechanics.

scholarly journals Reference Frame/Coordinate System in General Relativity

1986 ◽  
Vol 7 ◽  
pp. 113-116
Author(s):  
Toshio Fukushima
Keyword(s):  
General Relativity ◽  
Coordinate System ◽  
Reference Frame ◽  
Relativistic Effects ◽  
Speed Of Light ◽  
The Earth ◽  
Order Of Magnitude

The order of magnitude of relativistic effects is expressed as the power of v/c where v is a typical speed of objects and c is the speed of light in vacuum. In the neighbourhood of the Earth, v ≅ 30 km/s. Then the magnitudes of the relativistic effects are ordered as follows:

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