Gravitation, Inertia and Weightlessness : Centrifugal and Gyroscopic Effects of the N-Body System's Interaction Energy

This work discusses the problem of physical meaning of the three main dynamical properties of matter motion, namely gravitation, inertia and weightlessness. It considers that Newtonian gravitation and Galileoℓ́ℓs inertia are the centrifugal effects of interaction energy of a self-gravitating n-body system and its potential field. A self-gravitating celestial body appears to be an excellent natural centrifuge that is rotated by the energy of interacting elementary particles. Weightlessness is a consequence of the centrifugal effect of elementary particles interaction that appears at differentiation of a body matter with respect to density. The author analyzes the problem of creation of mass particles and elements from the elementary particles of ℓ́ℓdark matterℓ́ℓ, and discusses the basic physics of the Jacobi dynamics from the viewpoint of quantum gravitation. Chapters assert that the fundamentals of Jacobi dynamics completely correspond to conditions of natural centrifuges. The centrifuge is an excellent experimental model for the study of dynamical effects in solving the many body problem. In this book, readers may follow the demonstration of some of those studies and follow derivations, solutions and conclusions that provide a solid basis for further research in celestial mechanics, geophysics, astrophysics, geo- and planetary sciences Preface 6 Contents 10 1 Introduction: Phenomenon of Gravitation, Inertia and Weightlessness 14 Abstract 14 1.1 Newton’s Law of Universal Gravitation 15 1.2 Einstein’s Gravitation 31 1.3 Other Theories on Gravitation 33 1.4 Inertia Forces and Reference Systems 34 1.5 Effect of Weightlessness 36 2 Gravitation, Inertia and Weightlessness as the Centrifugal Effects of Interaction Energy of the n–Body System 38 Abstract 38 2.1 The Centrifuge as a Model of Dynamical Effects of the n–Body’s Interaction Energy and Its Potential Field 39 2.2 Illusion of Two-Body Mutual Attraction at Their Gravitational Interaction 41 2.3 Relationship Between a Body’s Moment of Inertia and Outer Gravitational Field by Satellite Data 47 2.4 Observation of Moment of Inertia and Inner Gravitational Field Oscillation During Earthquakes 56 2.5 Kinetic Energy of a Body at Gravitational Interaction of Its Elementary Particles 57 2.6 Generalized Classical Virial Theorem as Equation of Dynamical Equilibrium of a п–Body’s Mass Point System 58 2.7 Jacobi’s п–Mass Point Problem and Centrifugal Effects of the Reduced Inner Gravitational Field of a Body 66 References 73 3 Derivation of Unified Jacobi’s Equation for Different Types of Physical Interactions 74 Abstract 74 3.1 Derivation of Jacobi’s Virial Equation from Newtonian Equations of Motion 75 3.2 Derivation of Jacobi’s Virial Equation for Dissipative Systems 83 3.3 Derivation of Jacobi’s Virial Equation from Eulerian Equations 86 3.4 Derivation of Jacobi’s Virial Equation from Hamiltonian Equations 94 3.5 Derivation of Jacobi’s Virial Equation in Quantum Mechanics 95 3.6 General Covariant Form of Jacobi’s Virial Equation 103 3.7 Relativistic Analogue of Jacobi’s Virial Equation 106 3.8 Direct Derivation of the Equation of Virial Oscillation from Einstein’s Equations 109 3.9 Derivation of Jacobi’s Virial Equation in Statistical Mechanics 113 3.10 Universality of Jacobi’s Virial Equation for Description of Dynamics of Natural Systems 116 References 117 4 Solution of Jacobi’s Virial Equation for Self-gravitating Systems 118 Abstract 118 4.1 Solution of Kepler’s Problem in Classical and Virial Approach 119 4.1.1 The Classical Approach 120 4.1.2 The Dynamic Approach 123 4.2 Solution of n-Body Problem in the Framework of Conservative System 126 4.3 Solution of Jacobi’s Virial Equation in Hydrodynamics 131 4.3.1 The Hydrodynamic Approach 131 4.3.2 The Virial Approach 135 4.4 The Hydrogen Atom as a Quantum Mechanical Analogue of the Two-Body Problem 137 4.5 Solution of a Virial Equation in the Theory of Relativity (Static Approach) 145 4.6 General Approach to Solution of Virial Equation for a Dissipative System 147 4.7 Analytical Solution of Generalized Equation of Virial Oscillations 149 4.8 Solution of the Virial Equation for a Dissipative System 157 4.9 Solution of the Virial Equation for a System with Friction 160 References 162 5 Centrifugal Effects as the Mechanism of the Solar System Creation from a Common Gaseous Cloud 163 Abstract 163 5.1 The Conditions for a Body Separation and Orbiting 164 5.2 The Structure of Potential and Kinetic Energies of a Non-uniform Body 167 5.3 Equations of Oscillation and Rotation of a Body and Their Solution 170 5.4 The Nature and Mechanism of Body’s Shell Differentiation by Action of the Centrifugal Roche’s Dynamics 174 5.5 Self-similarity Principle and Radial Component of Non-uniform Sphere 176 5.6 Charges-like Motion of Non-uniformities and Tangential Component of the Force Function 177 5.7 Centrifugal Nature of the Archimedes and Coriolis Forces 179 5.8 Initial Values of Mean Density and Radius of a Secondary Body 180 References 182 6 The Body’s Evolutionary Processes as Сentrifugal and Gyroscopic Effects of Interaction Energy Emission 183 Abstract 183 6.1 Equilibrium Boundary Conditions for a Self-gravitating Gaseous Sphere 184 6.2 Velocity of Centrifugal Differentiation of a Gaseous Sphere 187 6.3 The Luminosity–Mass Relationship 193 6.4 Bifurcation of a Dissipative System 195 6.5 Cosmochemical Effects 198 6.5.1 Planets 199 6.5.2 Stars 200 6.5.3 Galaxies 200 6.5.4 Universe 201 6.6 Radial Distribution of Mass Density and the Body’s Inner Force Field 201 6.7 Oscillation Frequency and Angular Velocity of a Body Shell Rotation 210 6.7.1 Thickness of the Upper Earth’s Rotating Shell 211 6.7.2 Oscillation of the Earth’s Shells 212 6.7.3 Angular Velocity of Shell Rotation 213 6.8 The Nature of Precession, Nutation and Body’s Equatorial Plane Obliquity 214 6.8.1 Phenomenon of Precession 214 6.8.2 Tidal Effects 216 6.8.3 The Nature of Perturbations Based on Dynamic Equilibrium 217 6.8.4 Rotation of the Outer Force Field and the Nature of Precession and Nutation 220 6.8.5 The Nature of Possible Clockwise Rotation of the Outer Core of the Earth 224 6.8.6 The Nature of the Earth’s Orbit Plane Obliquity to the Sun’s Equatorial Plane 225 6.8.7 The Nature of Chandler’s Effect of the Earth Pole Wobbling 227 6.8.8 The Nature of Obliquity of the Earth’s Equatorial Plane to the Ecliptic 228 6.8.9 Tidal Interaction of Two Bodies 228 6.8.10 Change in Climate as an Effect of Changes of the Earth’s Orbit 229 References 230 7 The Unity of Electromagnetic and Gravitational Field of a Celestial Body and Centrifugal Mechanism of Its Energy Generation 232 Abstract 232 7.1 Electromagnetic Component of the Interacting Masses 233 7.2 Potential Energy of the Coulomb Interaction of Mass Particles 235 7.3 Emission of Electromagnetic Energy by a Celestial Body as an Electric Dipole 241 7.4 Centrifugal and Quantum Effects of Generated Electromagnetic Energy 246 7.5 The Nature of the Star-Emitted Radiation Spectrum 247 References 248 8 Creation and Decay of a Hierarchic Body System by Centrifugal Effects of the Potential Field Energy Interaction 250 Abstract 250 8.1 Relationship of the Jacobi Function and Potential Energy at Simultaneous Collision of n Particles 253 8.2 Asymptotic Limit of Simultaneous Collision of Mass Particles for a Conservative System 254 8.3 Asymptotic Limit of Simultaneous Collision of Mass Particles for a Non-conservative System 256 8.4 Asymptotic Limit of Simultaneous Collision of Charged Particles of a System 271 8.5 Relationship Between the Jacobi Function and Potential Energy for a System with High Symmetry 276 8.5.1 Systems with Spherical Symmetry 276 8.5.2 Poytropic Gas Sphere Model 280 8.5.3 A System with Elliptical Symmetry 285 8.5.4 System with Charged Particles 290 References 291 9 Conclusions 292 References 300 Index 301 This work discusses the problem of physical meaning of the three main dynamical properties of matter motion, namely gravitation, inertia and weightlessness. It considers that Newtonian gravitation and Galileoĺls inertia are the centrifugal effects of interaction energy of a self-gravitating n-body system and its potential field. A self-gravitating celestial body appears to be an excellent natural centrifuge that is rotated by the energy of interacting elementary particles. Weightlessness is a consequence of the centrifugal effect of elementary particles interaction that appears at differentiation of a body matter with respect to density. The author analyzes the problem of creation of mass particles and elements from the elementary particles of ĺldark matterĺl, and discusses the basic physics of the Jacobi dynamics from the viewpoint of quantum gravitation. Chapters assert that the fundamentals of Jacobi dynamics completely correspond to conditions of natural centrifuges. The centrifuge is an excellent experimental model for the study of dynamical effects in solving the many body problem. In this book, readers may follow the demonstration of some of those studies and follow derivations, solutions and conclusions that provide a solid basis for further research in celestial mechanics, geophysics, astrophysics, geo- and planetary sciences Front Matter....Pages i-xiv Introduction: Phenomenon of Gravitation, Inertia and Weightlessness....Pages 1-24 Gravitation, Inertia and Weightlessness as the Centrifugal Effects of Interaction Energy of the n–Body System....Pages 25-60 Derivation of Unified Jacobi’s Equation for Different Types of Physical Interactions....Pages 61-104 Solution of Jacobi’s Virial Equation for Self-gravitating Systems....Pages 105-149 Centrifugal Effects as the Mechanism of the Solar System Creation from a Common Gaseous Cloud....Pages 151-170 The Body’s Evolutionary Processes as Сentrifugal and Gyroscopic Effects of Interaction Energy Emission....Pages 171-219 The Unity of Electromagnetic and Gravitational Field of a Celestial Body and Centrifugal Mechanism of Its Energy Generation....Pages 221-238 Creation and Decay of a Hierarchic Body System by Centrifugal Effects of the Potential Field Energy Interaction....Pages 239-280 Conclusions....Pages 281-289 Back Matter....Pages 291-297