Dynamical theory of the rotation of the Earth

1986 ◽  
Vol 408 (1835) ◽  
pp. 267-275 ◽  
Keyword(s):  
Average Rate ◽  
Liquid Core ◽  
Angular Acceleration ◽  
Dynamical Theory ◽  
Rate Of Change ◽  
Moment Of Inertia ◽  
Iron Core ◽  
The Past ◽  
The Earth ◽  
The Moment

From recent values of improved accuracy of the apparent secular accelerations v and v' of the Moon and Sun, the lunar and solar tidal couples N and N' can be found. The appropriate dynamical theory shows that the moment of inertia of the Earth, C , has been diminishing at an average rate of -1.67 x 10 27 cm 2 g s -1 during the past 3300 years, giving rise to a non-tidal angular acceleration ω ∙ i = 1.52 x 10 -22 s -2 in addition to the retardations of ω resulting from the lunar and solar couples. The intrinsic couple associated with Ċ , the time-rate of change of C , is considerably greater than the solar tidal couple on all values of v and v' so far determined. For an initially all-solid Earth, use of known seismic data shows that the moment of inertia has decreased during the past 3 Ga at an average rate of -1.72 x 10 27 cm 2 g s -1 since a liquid core first began to form, a figure in close agreement with the value based on ancienteclipse data. On the time-honoured hypothesis that the core has resulted from iron separating downwards in an originally homogeneous Earth, the rate of decrease of C is -0.873 x 10 27 cm 2 g s -1 , only about one-half of that based on ancient-eclipse data, while if applied to these data the ratio N / N' = 11.35, which is more than twice the theoretical ratio on any tidal hypothesis. These results show that the iron-core theory is physically unacceptable.

On the dynamical theory of the rotation of the earth. II. The effect of precession on the motion of the liquid core

1953 ◽  
Vol 49 (3) ◽  
pp. 498-515 ◽  
Author(s):  
H. Bondi ◽  
R. A. Lyttleton
Keyword(s):  
Angular Velocity ◽  
Liquid Core ◽  
Rotation Period ◽  
Steady Motion ◽  
Dynamical Theory ◽  
Rate Of Change ◽  
Body Motion ◽  
Angular Velocity Vector ◽  
The Core ◽  
The Earth

In an earlier paper of the same general title (1) the possibility that the core of the Earth, in view of its supposed liquid nature, does not partake of the rigid-body motion of the outer shell was discussed with particular reference to the secular diminution of the angular velocity. In addition to this small rate of change of the magnitude of the angular velocity vector of the shell there occur changes in its direction consisting of the precession and nutation, but all the rates of change therein involved are small. The secular retardation takes place with extreme slowness, the nutations involve deviations of the axis with small angular amplitudes, while the precession, though of large angular amplitude, is of very long period compared with the rotation period of the Earth. Accordingly, it may be supposed that the effects of these various changes in the angular velocity can be considered separately in their relation to the motion within the core, and it is the object of this paper to give an account of our investigation into what may be termed for brevity the precession problem. It should perhaps be stated at the outset that the work does not constitute a solution of the problem, which our studies have led us to believe is one of the utmost mathematical difficulty presenting features of an exceptional character in hydro-dynamic theory. After first obtaining the equations of steady motion applicable to the interior, and those applicable to the boundary layer, the solution of the latter equations has been obtained; but in respect of the former equations we have been able to carry the question of the interior motion only as far as showing that no motion representable everywhere by analytic functions and consistent with the boundary conditions is possible. The investigation strongly suggests that no steady-state motion of a permanent character is possible for the interior, though the precise nature of the motion that actually occurs poses a problem of special interest from a hydrodynamic standpoint, but it is one to which we are not able to arrive at any definite answer at present. Without making any progress with the problem thus produced, the paper nevertheless makes clear the inherent difficulties of the problem and also serves to emphasize the inadequacy of any simplified mode of attack assuming classical fluid and resembling, for example, Poincaré's method for the nutation problem adopted by Lamb (3). Thus despite its incompleteness it seemed worth while to publish some account of such progress with these highly interesting questions as we have been able to make.

scholarly journals Modelling of spacecraft spin period during eclipse

2011 ◽  
Vol 29 (5) ◽  
pp. 875-882 ◽  
Author(s):  
E. Georgescu ◽  
F. Plaschke ◽  
U. Auster ◽  
K.-H. Fornaçon ◽  
H. U. Frey
Keyword(s):  
Magnetic Field ◽  
Heat Dissipation ◽  
Spin Model ◽  
Moment Of Inertia ◽  
Magnetic Field Direction ◽  
Spin Period ◽  
The Earth ◽  
Spacecraft Spin ◽  
The Moment ◽  
The Magnetic Field

Abstract. The majority of scientific satellites investigating the Earth magnetosphere are spin stabilized. The attitude information comes usually from a sun sensor and is missing in the umbra; hence, the accurate experimental determination of vector quantities is not possible during eclipses. The spin period of the spacecraft is generally not constant during these times because the moment of inertia changes due to heat dissipation. The temperature dependence of the moment of inertia for each spacecraft has a specific signature determined by its design and distribution of mass. We developed an "eclipse-spin" model for the spacecraft spin period behaviour using magnetic field vector measurements close to the Earth, where the magnetic field is dominated by the dipole field, and in the magnetospheric lobes, where the magnetic field direction is mostly constant. The modelled spin periods give us extraordinarily good results with accumulated phase deviations over one hour of less than 10 degrees. Using the eclipse spin model satellite experiments depending on correct spin phase information can deliver science data even during eclipses. Two applications for THEMIS B, one in the lobe and the other in the lunar wake, are presented.

Effect of a Changing G on the Moment of Inertia of the Earth

1978 ◽  
Vol 221 ◽  
pp. 412 ◽  
Author(s):  
R. A. Lyttleton ◽  
J. P. Fitch
Keyword(s):  
Moment Of Inertia ◽  
The Earth ◽  
The Moment

On the Internal Constitutions of the Planets

1967 ◽  
Vol 1 (1) ◽  
pp. 2-3 ◽  
Author(s):  
K. E. Bullen
Keyword(s):  
Temperature Dependence ◽  
Stress Tensor ◽  
Equations Of State ◽  
Moment Of Inertia ◽  
Terrestrial Planets ◽  
Use Of Data ◽  
The Earth ◽  
The Moment ◽  
Full Stress Tensor ◽  
Secondary Consequence

The internal constitutions of the terrestrial planets Mars, Venus and Mercury are investigated through the use of ‘equations of state’ empirically derived for particular internal zones of the Earth. The equations usually take the form of tabular relations between the pressure p and density p, temperature dependence being treated as of secondary consequence. In using p rather the full stress tensor in solid zones, i.e. in using a hydrostatic theory, the effects of strength and deviatoric stress are also treated as of secondary consequence. Except for the use of data on the ellipticity ∊ of figure of a planet to provide evidence on the moment of inertia I, the planets are treated as spherically symmetrical.

scholarly journals Relativity effects in the rotation of the Earth and the motion of atmospheric masses

1986 ◽  
Vol 114 ◽  
pp. 289-292
Author(s):  
V. G. Shkodrov ◽  
V. G. Ivanova
Keyword(s):  
Angular Velocity ◽  
Observational Data ◽  
Atmospheric Pressure ◽  
Earth Rotation ◽  
Numerical Results ◽  
Moment Of Inertia ◽  
The Earth ◽  
Rotation Of The Earth ◽  
The Moment

On the basis of observational data on atmospheric pressure (1963–1967), the variation of the moment of inertia, and, with certain restrictions, the changes in the angular velocity of the Earth are obtained. The numerical results derived are compared to the relativity effects in Earth rotation. The comparison shows that both effects are equal in periods and very close in amplitudes.

On the phase-change hypothesis of the structure of the Earth

1965 ◽  
Vol 287 (1411) ◽  
pp. 471-493 ◽  
Keyword(s):  
Phase Change ◽  
Average Rate ◽  
Liquid Core ◽  
Rotation Period ◽  
Crystal Form ◽  
Outer Radius ◽  
Gravitational Energy ◽  
The Earth ◽  
Slow Expansion ◽  
Central Regions

The hypothesis that the liquid core of the Earth represents a phase-change at high pressure (and suitable temperature) of the mantle material is further investigated. A more accurate series of two-zone models have been computed, and also a new series of three-zone models. The change of overall radius as between an original all-solid Earth and the present size is shown to be at least 370 km. In the outer regions, greater pressure may be needed with rising temperature to effect the transition to denser crystal form (associated with the 20°-discontinuity), and from this cause acting alone slight expansion of the Earth would result but to an extent less than one-tenth the overall contraction. Epochs of rapid contraction (mountain-building eras) could thus be separated by longer intervals of very slow expansion. The initial liquefaction of the central regions brings about pressure increase at the boundary of the core that renders the Earth unstable in that about 6 per cent of the entire mass liquefies extremely rapidly to cause a sudden collapse of the planet as a whole. The accompanying decrease of outer radius is about 70 km. Thereafter the planet remains thoroughly stable and contracts only slowly. The total contraction to date would have reduced the moment of inertia by a factor about 4/5, and the corresponding reduction in rotation period (through conservation of angular momentum) would be an effect comparable with tidal friction. The contraction also leads to release of gravitational energy at an average rate comparable with that from radioactive sources. An important consequence of the phase-change hypothesis is that the melting-point gradient changes sign after sufficient depth, thereby permitting melting of the central regions to occur at moderate temperatures explicable by a reasonable content of radioactive elements.

scholarly journals An analysis of equity share price movement of selected companies listed in nse

2012 ◽  
Vol 1 (3) ◽  
pp. 246-252
Author(s):  
CHITRA R ◽  
SATHYA M
Keyword(s):  
Average Rate ◽  
Moving Average ◽  
Secondary Data ◽  
Relative Strength ◽  
Rate Of Change ◽  
Share Price ◽  
Price Movement ◽  
Share Prices ◽  
The Past ◽  
Data Collections

The stock market has an important role in the allocation of resources, both directly as a source of funds and as a determinant of firm’s value and borrowing capacity. This study we made a study and analysis on Equity share price behaviour of selected companies listed in NSE India. The Purpose of the study is, attempted to test the equity price movements of IT,Pharmaceuticals, Banking and Automobiles sectors. These are taken as sample sectors. The objective of the study is to analyze the Equity share price movement of selected companies listed in NSE, India and to analyze the movements of the high pricedequity shares of four sectors for the past 3 years. Data collections are to be used in the study is secondary data. The study usestools such as Simple Moving Average, Rate of Change, Relative Strength Index, Stochastic oscillator and Trend analysis. TheMonthly share prices of above mentioned companies were taken for a period of three years from January 2009 to Dec 2011. Theclosing prices of share prices were taken. All four sectors registered tremendous growth in the past 3 years, and as per theanalysis all these sectors companies were predicted as best to invest for better rate of return for the investors.

scholarly journals A Novel Moment of Inertia Identification Strategy for Permanent Magnet Motor System Based on Integral Chain Differentiator and Kalman Filter

Energies ◽  
2020 ◽  
Vol 14 (1) ◽  
pp. 166
Author(s):  
Chenchen Jing ◽  
Yan Yan ◽  
Shiyu Lin ◽  
Le Gao ◽  
Zhixin Wang ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Permanent Magnet ◽  
Motor System ◽  
Error Function ◽  
Angular Acceleration ◽  
Moment Of Inertia ◽  
Calculation Error ◽  
Acceleration Process ◽  
Permanent Magnet Motor ◽  
The Moment

In a motor control system, the parameters tuning of speed and position controller depend on the value of the moment of inertia. A new moment of inertia identification scheme for permanent magnet motor system was proposed in this paper. This is an extension of the existing acceleration deceleration methods, which solves the large moment of inertia identification error caused by variable angular acceleration, large calculation error of inertia torque, and large measurement noise in the acceleration process. Based on the fact that the angular acceleration is not constant and the sampling signal is noisy, the integral chain differentiator was used to calculate the instantaneous angular acceleration at any time and suppress the sampling signal noise at the same time. The error function with instantaneous angular acceleration and inertia torque as parameters was designed to estimate the moment of inertia. In order to calculate the inertia torque accurately, viscous friction torque was considered in the calculation of inertia torque, and Kalman filter was used to estimate the total load torque to solve the problem of under rank of motor motion equation. Simulation and experimental results showed that the proposed method could effectively identify the moment of inertia in both noisy and noiseless environments.

scholarly journals Optically stimulated luminescence techniques applied to the dating of the fall of meteorites in Morasko

2018 ◽  
Vol 45 (1) ◽  
pp. 74-81
Author(s):  
Piotr Moska ◽  
Wojciech Stankowski ◽  
Grzegorz Poręba
Keyword(s):  
Iron Meteorite ◽  
Optically Stimulated Luminescence ◽  
Luminescence Dating ◽  
Luminescence Signal ◽  
Geological Materials ◽  
The Past ◽  
The Earth ◽  
Materials Used ◽  
The Moment

Abstract Geological materials used for luminescence dating and associated with the fall of meteorites on the Earth’s surface are extremely rare. The Morasko region has gained fame over the past 100 years because of a cosmic catastrophe which took place there. After thousands of years, the remains of a large metal meteorite which fell in this area have been found. In this article, we would like to state whether it is possible, using luminescence methods, to determine the moment when the iron meteorite fell on the surface of the Earth. The material which was analysed consisted of meteorite crust layers – melt/fusion and “semi melt/fusion”, including sintered ones, along with the sediments surrounding the meteorite. The final results are connected with four objects of different sizes (large ones and small shrapnel – 261 kg, 34 kg, 970 g and 690 g). The obtained results show a large discrepancy, which is most likely associated with the problem of resetting the luminescence signal of the tested materials.

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