Dynamics of the Earth (eBook)

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