Ferronsky Dynamics of the Earth

Theory of the Planet's Motion Based on Dynamic Equilibrium
1. Auflage 2010
ISBN: 978-90-481-8723-2
Verlag: Springer Netherlands
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 299 Seiten

In their search for solutions to problems concerning the dynamics of the Earth as a self-gravitating body, the authors have applied the fundamentals found in their book 'Jacobi Dynamics' (1987, Reidel). First, satellite observations have shown that the Earth does not remain in hydrostatic equilibrium, which forms the physical basis of modern geodynamics. Secondly, satellite data have established a relationship between the planet's polar moment of inertia and the potential of the Earth's outer force field, which proves the most basic point of Jacobi dynamics. This allowed the authors to revise their derivation of the classical virial theorem, introducing the concept of a volumetric force and volumetric moment, and so to obtain a generalized virial theorem in the form of Jacobi's equation.
The main dynamical effects are: the kinetic energy of oscillation of the interacting particles, which explains the physical meaning and nature of gravitational forces; separation of shells of a self-gravitating body with respect to its mass density; differences in angular velocities of the shell's rotation; continuity in variance of the potential of the outer gravitational force field, together with reductions in the envelope of the interacting masses (volumetric center of gravity); the nature of Earth, Moon and satellite precession; the nature and generating mechanism of the planet's electromagnetic field; the common nature of gravitational and electromagnetic energy, and other related issues.
The work is a logical continuation of the book 'Jacobi Dynamics' and is intended for researchers, teachers and students engaged in theoretical and experimental research in various branches of astronomy, geophysics, planetology and cosmogony, and for students of celestial, statistical, quantum and relativistic mechanics and hydrodynamics.

Autoren/Hrsg.

Ferronsky, V. I.

Inhaltsverzeichnis

1;Contents;6
2;Preface;10
3;Chapter 1 Introduction;15
3.1;1.1 Copernican Heliocentric World System;16
3.2;1.2 Galilean Laws of Inertia and Free Fall;16
3.3;1.3 Kepler’s Laws of Planets’ Orbital Motion;17
3.4;1.4 Huygens Laws of Clock Pendulum Motion;20
3.5;1.5 Hooke’s Law of Elasticity;22
3.6;1.6 Newton’s Model of Hydrostatic Equilibrium of a Uniform Earth;23
3.7;1.7 Clairaut’s Model of Hydrostatic Equilibrium of a Non-uniform Earth;35
3.8;1.8 Euler’s Model of the Rigid Earth Rotation;37
3.9;1.9 Jacobi’s n Body Problem;39
3.10;1.10 The Clausius Virial Theorem;41
3.11;1.11 De Broglie’s Wave Theory;41
3.12;1.12 Other Approaches to Dynamics of the Planet Based on Hydrostatics;42
3.13;1.13 The Observation Results;45
4;Chapter 2 Irrelevance of the Hydrostatics Modeland the Earth’s Dynamic Equilibrium;51
4.1;2.1 Hydrostatic Equilibrium Conditions;51
4.2;2.2 Relationship Between Moment of Inertia and Gravitational Force Field According to Satellite Data;54
4.3;2.3 Oscillation of the Moment of Inertia and the Inner Gravitational Field Observed During Earthquakes;58
4.4;2.4 Imbalance Between the Earth’s Potential and Kinetic Energies;59
4.5;2.5 Equation of Dynamical Equilibrium;60
4.6;2.6 Reduction of Inner Gravitation Field to the Resultant Envelope of Pressure;67
5;Chapter 3 Fundamentals of the Theory of DynamicEquilibrium;73
5.1;3.1 The Generalized Virial Theorem As the Equation of Dynamic Equilibrium of the Earth’s Oscillating Motion;73
5.1.1;3.1.1 The Averaged Virial Theorem;74
5.1.2;3.1.2 The Generalized Virial Theorem;76
5.2;3.2 Derivation of Jacobi’s Virial Equation from Newtonian Equations of Motion;77
5.3;3.3 Derivation of a Generalized Jacobi’s Virial Equation for Dissipative Systems;84
5.4;3.4 Derivation of Jacobi’s Virial Equation from Eulerian Equations;87
5.5;3.5 Derivation of Jacobi’s Virial Equation from Hamiltonian Equations;94
5.6;3.6 Derivation of Jacobi’s Virial Equation in Quantum Mechanics;95
5.7;3.7 General Covariant Form of Jacobi’s Virial Equation;103
5.8;3.8 Relativistic Analogue of Jacobi’s Virial Equation;105
5.9;3.9 Universality of Jacobi’s Virial Equation for Description of the Dynamics of Natural Systems;108
6;Chapter 4 Solution of Jacobi’s Virial Equationfor Conservative Systems;110
6.1;4.1 Solution of Jacobi’s Virial Equation in Classical Mechanics;111
6.1.1;4.1.1 The Classical Approach;111
6.1.2;4.1.2 The Dynamic (Virial) Approach;115
6.2;4.2 Solution of the n-Body Problem in the Framework of a Conservative System;117
6.3;4.3 Solution of Jacobi’s Virial Equation in Hydrodynamics;122
6.3.1;4.3.1 The Hydrodynamic Approach;122
6.3.2;4.3.2 The Virial Approach;126
6.4;4.4 The Hydrogen Atom as a Quantum Mechanical Analogue of the Two-Body Problem;128
6.5;4.5 Solution of a Virial Equation in the Theory of Relativity (Static Approach);135
7;Chapter 5 Perturbed Virial Oscillations of a System;138
7.1;5.1 Analytical Solution of a Generalized Equation of Virial Oscillations;140
7.2;5.2 Solution of the Virial Equation for a Dissipative System;147
7.3;5.3 Solution of the Virial Equation for a System with Friction;150
8;Chapter 6 The Nature of Oscillation and Rotationof the Earth;153
8.1;6.1 The Problem of the Earth’s Eigenoscillations;154
8.1.1;6.1.1 The Differential Approach;155
8.1.2;6.1.2 The Dynamic Approach;159
8.2;6.2 Separation of Potential and Kinetic Energies of the Non-uniform Earth;164
8.3;6.3 Conditions of Dynamical Equilibrium of Oscillation and Rotation of the Earth;167
8.4;6.4 Equations of Oscillation and Rotation of the Earth and Their Solution;168
8.5;6.5 Application of Roche’s Tidal Approach for Separation of the Earth’s Shells;171
8.6;6.6 Physical Meaning of Archimedes and Coriolis Forces and Separation of the Earth’s Shells;172
8.7;6.7 Self-similarity Principle and the Radial Component of a Non-uniform Sphere;173
8.8;6.8 Charges-like Motion of Non-uniformities and Tangential Component of the Force Function;175
8.9;6.9 Radial Distribution of Mass Density and the Earth’s Inner Force Field;176
8.10;6.10 Oscillation Frequency and Angular Velocity of the Earth’s Shell Rotation;185
8.10.1;6.10.1 Thickness of the Upper Earth’s Rotating Shell;186
8.10.2;6.10.2 Oscillation of the Earth’s Shells;186
8.10.3;6.10.3 Angular Velocity of Shell Rotation;187
8.11;6.11 Perturbation Effects in Dynamics of the Earth;188
8.11.1;6.11.1 The Nature of Perturbations in the Framework of Hydrostatic Equilibrium;189
8.11.2;6.11.2 The Nature of Perturbations Based on Dynamic Equilibrium;191
8.11.3;6.11.3 Change of the Outer Force Field and the Nature of Precession and Nutation;194
8.11.4;6.11.4 Observed Picture of a Body Precession;196
8.11.5;6.11.5 The Nature of Precession and Nutation Based on Dynamical Equilibrium;196
8.11.6;6.11.6 The Nature of Possible Clockwise Rotation of the Outer Core of the Earth;197
8.11.7;6.11.7 The Nature of the Force Field Potential Change;198
8.11.8;6.11.8 The Nature of the Earth’s Orbit Plane Obliquity;199
8.11.9;6.11.9 The Nature of Chandler’s Effect of the Earth Pole Wobbling;199
8.11.10;6.11.10 Change in Climate as an Effect of Rotation of the Earth’s Shells;199
8.11.11;6.11.11 The Nature of Obliquity of the Earth’s Equatorial Plane to the Ecliptic;200
8.11.12;6.11.12 Tidal Interaction of Two Bodies;201
8.12;6.12 Earthquakes, Orogenesis and Volcanism;202
8.12.1;6.12.1 Earth Crust Tremor and Earthquakes;203
8.12.2;6.12.2 Orogenesis;204
8.12.3;6.12.3 Volcanism;204
8.13;6.13 Earth’s Mass in its Own Force Field;205
9;Chapter 7 Dynamics of the Earth’s Atmosphereand Oceans;208
9.1;7.1 Derivation of the Virial Equation for the Earth’s Atmosphere;209
9.2;7.2 Non-perturbed Oscillation of the Atmosphere;213
9.3;7.3 Perturbed Oscillations;216
9.4;7.4 Resonance Oscillation;220
9.5;7.5 Observation of the Virial Eigenoscillations of the Earth’s Atmosphere;223
9.5.1;7.5.1 Oscillation of the Temperature;224
9.5.2;7.5.2 Oscillation of the Pressure;227
9.6;7.6 The Nature of the Oceans;230
9.7;7.7 The Nature of the Weather and Climate Changes;232
10;Chapter 8 The Nature of the Earth’s Electromagnetic Fieldand Mechanism of its Energy Generation;233
10.1;8.1 Electromagnetic Component of Interacting Masses;234
10.2;8.2 Potential Energy of the Coulomb Interaction of Mass Particles;235
10.3;8.3 Emission of Electromagnetic Energy by a Celestial Body as an Electric Dipole;239
10.4;8.4 Quantum Effects of Generated Electromagnetic Energy;244
10.5;8.5 Equilibrium Conditions on the Body’s Boundary Surface;245
10.6;8.6 Solution of the Chandrasekhar-Fermi Equation;247
10.7;8.7 The Nature of the Star Emitted Radiation Spectrum;248
11;Chapter 9 Observable Facts Related to Creationand Evolution of the Earth;250
11.1;9.1 A Selection of Existing Approaches to Solution of the Problem;250
11.2;9.2 Separation of Hydrogen and Oxygen Isotopes in Natural Objects;253
11.3;9.3 Evidence from Carbon and Sulfur Isotopes;264
11.4;9.4 Chemical Differentiation of Proto-planetary Substance;273
11.5;9.5 Differentiation of the Substances with Respect to Density and Conditions for the Planet and Satellite Separation;285
11.6;9.6 Conclusion;293
12;References;295
13;Subject Index;303