scholarly journals Equations of state of iron sulfide and constraints on the sulfur content of the Earth

1988 ◽  
pp. 427-440
Author(s):  
Thomas J. Ahrens
Keyword(s):  
Sulfur Content ◽  
Iron Sulfide ◽  
Equations Of State ◽  
The Earth

Constraints on core composition from shock-waves data

1982 ◽  
Vol 306 (1492) ◽  
pp. 37-47 ◽  
Keyword(s):  
Equations Of State ◽  
Liquid Core ◽  
Light Element ◽  
Outer Core ◽  
Atomic Ratio ◽  
Core Material ◽  
Solar Photosphere ◽  
The Core ◽  
The Earth ◽  
Core Composition

Seismic data demonstrate that the density of the liquid core is some 8-10 % less than pure iron. Equations of state of Fe-Si, C, FeS 2 , FeS, KFeS 2 and FeO, over the pressure interval 133-364 GPa and a range of possible core temperatures (3500- 5000 K), can be used to place constraints on the cosmochemically plausible light element constituents of the core (Si, C, S, K and O ). The seismically derived density profile allows from 14 to 20 % Si (by mass) in the outer core. The inclusion of Si, or possibly G (up to 11 %), in the core is possible if the Earth accreted inhomogeneously within a region of the solar nebulae in which a C :0 (atomic) ratio of about 1 existed, compared with a G : O ratio of 0.6 for the present solar photosphere. In contrast, homogeneous accretion permits Si, but not C, to enter the core by means of reduction of silicates to metallic Fe-Si core material during the late stages of the accumulation of the Earth. The data from the equation of state for the iron sulphides allow up to 9-13 % S in the core. This composition would provide the entire Earth with a S:Si ratio in the range 0.14-0.3, comparable with meteoritic and cosmic abundances. Shock-wave data for KFeS 2 give little evidence for an electronic phase change from 4s to 3d orbitals, which has been suggested to occur in K, and allow the Earth to store a cosmic abundance of K in the metallic core.

scholarly journals Equations of state of the Earth

1975 ◽  
Vol 13 (3) ◽  
pp. 335 ◽  
Author(s):  
Thomas J. Ahrens
Keyword(s):  
Equations Of State ◽  
The Earth

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.

VOLUME DEPENDENCE OF GRÜNEISEN RATIO FOR LOWER MANTLE AND CORE OF THE EARTH

2011 ◽  
Vol 25 (18) ◽  
pp. 1549-1556 ◽  
Author(s):  
S. K. SRIVASTAVA
Keyword(s):  
Free Volume ◽  
Lower Mantle ◽  
Recent Literature ◽  
Equations Of State ◽  
Earth Planet ◽  
Free Volume Theory ◽  
The Earth ◽  
Volume Dependence ◽  
Earth’S Interior ◽  
Relationship Of

In this study, we have examined the various formulations for volume dependence of the Grüneisen ratio, γ. The thermodynamic constraints for γ∞, q∞ and λ∞ have been used to discuss the validity of various relationships. The volume dependence of γ and its derivatives, reported by Stacey and Davis [F. D. Stacey and P. M. Davis, Phys. Earth Planet. Inter.142 (2004) 137–184], are analyzed. The Al'tshuler et al.'s relationship of γ(V), widely used in recent literature, has been found to be inadequate on the variation of λ with compression. The estimates of γ, q and λ are obtained with the combination of generalized free volume theory and reciprocal K-prime equations of state for the Earth's interior.

The motion of a lunar orbiter

1966 ◽  
Vol 25 ◽  
pp. 373
Author(s):  
Y. Kozai
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Artificial Satellite ◽  
Equations Of Motion ◽  
Triaxial Ellipsoid ◽  
The Moon ◽  
Secular Motion ◽  
The Earth ◽  
Close Satellite ◽  
The Mean

The motion of an artificial satellite around the Moon is much more complicated than that around the Earth, since the shape of the Moon is a triaxial ellipsoid and the effect of the Earth on the motion is very important even for a very close satellite.The differential equations of motion of the satellite are written in canonical form of three degrees of freedom with time depending Hamiltonian. By eliminating short-periodic terms depending on the mean longitude of the satellite and by assuming that the Earth is moving on the lunar equator, however, the equations are reduced to those of two degrees of freedom with an energy integral.Since the mean motion of the Earth around the Moon is more rapid than the secular motion of the argument of pericentre of the satellite by a factor of one order, the terms depending on the longitude of the Earth can be eliminated, and the degree of freedom is reduced to one.Then the motion can be discussed by drawing equi-energy curves in two-dimensional space. According to these figures satellites with high inclination have large possibilities of falling down to the lunar surface even if the initial eccentricities are very small.The principal properties of the motion are not changed even if plausible values ofJ3andJ4of the Moon are included.This paper has been published in Publ. astr. Soc.Japan15, 301, 1963.

Formation of Lunar Craters and Bright Rays as a Result of Meteorite Impacts

1962 ◽  
Vol 14 ◽  
pp. 415-418
Author(s):  
K. P. Stanyukovich ◽  
V. A. Bronshten
Keyword(s):  
Explosive Charge ◽  
The Moon ◽  
Meteorite Impacts ◽  
The Earth ◽  
Lunar Craters ◽  
The Impact

The phenomena accompanying the impact of large meteorites on the surface of the Moon or of the Earth can be examined on the basis of the theory of explosive phenomena if we assume that, instead of an exploding meteorite moving inside the rock, we have an explosive charge (equivalent in energy), situated at a certain distance under the surface.

The Origin of the Moon

1962 ◽  
Vol 14 ◽  
pp. 149-155 ◽  
Author(s):  
E. L. Ruskol
Keyword(s):  
Chemical Composition ◽  
Solar System ◽  
The Moon ◽  
The Earth ◽  
The Difference ◽  
Origin Of The Moon

The difference between average densities of the Moon and Earth was interpreted in the preceding report by Professor H. Urey as indicating a difference in their chemical composition. Therefore, Urey assumes the Moon's formation to have taken place far away from the Earth, under conditions differing substantially from the conditions of Earth's formation. In such a case, the Earth should have captured the Moon. As is admitted by Professor Urey himself, such a capture is a very improbable event. In addition, an assumption that the “lunar” dimensions were representative of protoplanetary bodies in the entire solar system encounters great difficulties.

The Origin of the Moon and its Relationship to the Origin of the Solar System

1962 ◽  
Vol 14 ◽  
pp. 133-148 ◽  
Author(s):  
Harold C. Urey
Keyword(s):  
Solar System ◽  
The Moon ◽  
The Past ◽  
The Earth ◽  
Short Period ◽  
Origin Of The Moon

During the last 10 years, the writer has presented evidence indicating that the Moon was captured by the Earth and that the large collisions with its surface occurred within a surprisingly short period of time. These observations have been a continuous preoccupation during the past years and some explanation that seemed physically possible and reasonably probable has been sought.

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