Formation of the Solar System

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1 Formation of the Solar System

2

3 V.I. Ferronsky S.V. Ferronsky Formation of the Solar System A New Theory of the Creation and Decay of the Celestial Bodies 123

4 V.I. Ferronsky Water Problems Institute of the Russian Academy of Sciences Moscow Russia S.V. Ferronsky (deceased) This is a translation of the book Origin and Evolution of the Solar System (in Russian), published by Scientific World, Moscow, 2012 ISBN ISBN (ebook) DOI / Springer Dordrecht Heidelberg New York London Library of Congress Control Number: Springer Science+Business Media Dordrecht 2013 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (

5 Preface This book presents the solution of the problem of origin and evolution of the solar system based on Jacobi dynamics. The work s continuous study on the dynamics was published earlier (Ferronsky et al. 1978, 1979a, b, c, 1981a, b, 1982, 1984, 1987, 1996, 2011, Ferronsky 1983, 1984, 2005; Ferronsky and Ferronsky 2010). By analysis of orbital motion of the Earth, the Moon, other planets, and their satellites, we discovered a common dynamical effect valid for all the solar system bodies. The effect demonstrates that all the planets and satellites have been orbited by the first cosmic velocity of their protoparents. Namely, the planets move in orbits with the first cosmic velocity of the protosun, the radius of which was equal to the semimajor axis of modern orbit of each planet. The satellites of each planet have mean orbital velocity equal to the first cosmic velocity of the corresponding planet having radius equal to the semimajor axis of modern orbit of each satellite. This effect holds for all the small planets of the asteroid belt and for all the comets. We can state now that the discovered common dynamical effect of the celestial bodies orbital motion with the first cosmic velocity of their protoparents demonstrates the nature of the forces, which initiate and govern this motion. The protoparental body originates these forces in the form of an integral effect of its constituting interacted elementary particles, which is the body s inner energy. In fact, this is Newton s gravitational force, which he searched for the solution of Kepler s problem. The Kepler s laws, in particular its third law, follow from the found dynamical effect of celestial bodies orbital motion. The found dynamical effect was used as a basis for more-detailed analytical consideration of the solar system s cosmogony. We demonstrate that all the solar system bodies have been formed, separated, and orbited from the upper weightlessness shells of their protoparents during the evolutionary process. The details of the creation process like differentiation of the initial cloud into the shells, physics of the secondary body formation and first cosmic velocity orbiting, separation of the protosolar cloud itself from the protogalaxy, and other effects of the system origin and evolution are considered in the form of separate tasks solution. The following basic physical principles were accepted for the problem solution. The Sun and other stars, their planets, and satellites are considered as v

6 vi Preface self-gravitating celestial bodies, which themselves generate the energy for the motion by means of their constituent elementary particle interaction. The particle interaction is considered as a process of their collision and scattering. Because of absence of hydrostatic equilibrium of celestial bodies, found by the artificial satellite studies, the condition of dynamical equilibrium was introduced. This condition is based on the analysis of the artificial satellite orbital motion and also on the observable fact of disagreement with the virial theorem regarding the relationship between the potential and kinetic energy. The condition was accepted not as assumption but proved by derivation of the generalized virial theorem for n-interacted particles as volumetric matter values. This fundamental principle also follows from the Jacobi dynamics. In this case the energy is accepted as the measure of the particle interaction. The energy action is developed in the form of its inner pressure and accomplishes by oscillations of the moment of inertia. The resulting dynamical effect of a self-gravitating body at its dynamical equilibrium results in the periodically repeated oscillations of all the fundamental parameters like the moment of inertia, potential and kinetic energy, and their frequency and period of oscillation. In the other words, the inner energy initiates all the body s dynamical effects. In this connection, for instance, the widespread opinion that the hydrostatic equilibrium of stars (equation of state) results in the form of equality between the gaseous and gravity pressure appears to be a meaningless idea. In the case of a self-gravitating body, its gaseous pressure is the dynamical effect of interaction of the constituting particles, that is, its gravitational pressure. The measure of the body s interaction of mass particles is the energy but not the force being its first derivative. For a celestial body, the gravitational effect of its interacted masses is determined by integration of the interacted particle effects over the whole volume, that is, obtaining its energy. In contrast to the hydrostatic equilibrium where the outer forces are used for solving the problems of motion under force action, dynamical equilibrium is based on the inner energy or on the inner integral force field. Dynamical equilibrium of celestial bodies opens new possibilities for studying the nature of their motion. Their own inner and outer force field determines dynamics of a celestial body. Earlier, the inner force field was accepted to be the central symmetric field of vector forces, the sum of which is equal to zero. For dynamical equilibrium, the interacted particles form the volumetric field of pressure which cannot be equal to zero by definition. Such a field of pressure can be reduced to a resultant shell of pressure. For a sphere it will be a spherical shell and for an ellipsoid this is an ellipsoidal shell. We demonstrate that the basic mode of a body motion is its oscillation. Interaction of the uniform in density body mass realizes all its kinetic energy in the form of oscillations. For a nonuniform body, the tangential component of the potential energy appeared. This component is responsible for the body s axial rotation (tangential oscillation). It is assumed up to now that in mechanics of the macroscopic bodies the wave properties of such nature for massive particles are unessential. It is shown in this work that virial oscillations of a body masses represent the main part of kinetic energy. In the theories based on the hydrostatic equilibrium, this energy is ignored. But in this case, the potential energy of celestial bodies by two or more orders exceeds the kinetic one presented by axial inertial rotation of the masses. This effect has a simple physical explanation. In the

7 Preface vii beginning of the last century, the famous French physicist Louis de Broglie extended on the matter of the wave particle duality theory of light. Later on, his theory was fully confirmed and becomes the basis for developing the present-day wave mechanics for matter on an atomic scale. The particles of greater mass, which are the subject of classical mechanics, have mainly corpuscular properties. The relationship between oscillation of the gravity field and the Earth moment of inertia, which was proved by artificial satellite data, shows that the interaction of its masses results on the level of elementary particles. The only form of motion of the interacted mass particles is their oscillation. The continuous tremor of the Earth s gravity field fixed by changes of the gravity moments is one more conformation of the de Broglie s idea for the mass interaction of celestial bodies. Finally, the important effect of a body mass interaction is its outer force field. Its potential energy is changing according with the inverse square law (proportionally to the body s surface shell area), and the fundamental parameter of the field is its frequency of oscillation. The outer force field fills in all the space of the universe including galaxies, stars, and other bodies. And the oscillation frequency in a given point of the space indicates the energy emitted by the corresponding celestial body during its stay there and velocity of its elementary particle interaction. The outer force field is an indicator of legitimacy of the energy conservation law for the universe as a whole. Such are the main physical principles used for the solution of the solar system origin and evolution problem, which follows from our previous studies. The last chapter of the work considers some aspects of application of the obtained results to the universe problems. In particular, the results are used for interpretation of the dark matter, dark energy, and Big Bang. The conclusion is made that our universe in framework of the accepted geometry is a closed pulsating system. During its expansion (present stage of evolution), the system s decay results up to the matter, becoming like dark matter with dark energy (weightlessness discrete particle matter). During the contraction stage, the mass particles (electrons, protons, nucleus, atoms, and molecules) and bodies are created in the form of a common galaxy being in the force field ( dark energy ) of the universe. During the stage of expansion, the energy is emitted by the decaying bodies. During the stage of contraction, the dark energy is bounded into, what we say, matter, which, in fact, is a form of the compressed mass defect. V. Ferronsky References Ferronsky SV (1983) The solution for seasonal variations in the earth s rate of rotation. Celest Mech 30:71 83 Ferronsky SV (1984) Observation of coherent pulsations in the earth atmosphere with period about one and half hour. Phys Atmos Oceans 20: Ferronsky VI (2005) Virial approach to solve the problem of global dynamics of the earth. Investigated in Russia. pp

8 viii Preface Ferronsky VI, Ferronsky SV (2010) Dynamics of the Earth. Springer, Dordrecht/Heidelberg Ferronsky VI, Denisik SA, Ferronsky SV (1978) The solution of Jacobi s virial equation for celestial bodies. Celest Mech 18: Ferronsky VI, Denisik SA, Ferronsky SV (1979a) The virial-based solution for the velocity of gaseous sphere gravitational contraction. Celest Mech 19: Ferronsky VI, Denisik SA, Ferronsky SV (1979b) The asymptotic limit of the form- factor and product for celestial bodies. Celest Mech 20:69 81 Ferronsky VI, Denisik SA, Ferronsky SV (1979c) The solution of Jacobi s virial equation for nonconservative system and analysis of its dependence on parameters. Celest Mech 20: Ferronsky VI, Denisik SA, Ferronsky SV (1981a) Virial oscillations of celestial bodies: I. The effect of electromagnetic interactions. Celest Mech 23: Ferronsky VI, Denisik SA, Ferronsky SV (1981b) On the relationship between the total mass of a celestial body and the averaged mass of its constituent particles. Phys Lett 84A: Ferronsky VI, Denisik SA, Ferronsky SV (1982) Virial oscillations of celestial bodies: II General approach to the solution of perturbed oscillations problem and electromagnetic effects. Celest Mech 27: Ferronsky VI, Denisik SA, Ferronsky SV (1984) Virial approach to solution of the problem of global oscillations of the earth atmosphere. Phys Atmos Oceans 20: Ferronsky VI, Denisik SA, Ferronsky SV (1987) Jacobi dynamics. Reidel, Dordrecht Ferronsky VI, Denisik SA, Ferronsky SV (1996) Virial oscillations of celestial bodies: V. The structure of the potential and kinetic energies of a celestial body as a record of its creation history. Celest Mech Dyn Astron 64: Ferronsky VI, Denisik SA, Ferronsky SV (2011) Jacobi dynamics, 2nd edn. Springer, Dordrecht/ Heidelberg

9 Contents 1 Introduction: New Data Related to the Nature of Creation and Orbiting of the Planets and Satellites Hypotheses of Celestial Body Creation The Laws of Celestial Body Motion Based on Hydrostatics Inner Energy of Body s Interacted Masses as a Bullet Point of the Solar System s Cosmogony References Physical Meaning of Hydrostatic Equilibrium of Celestial Bodies Newton s Model of Hydrostatic Equilibrium of a Uniform Body Clairaut s Model of Hydrostatic Equilibrium of a Nonuniform Body Euler s Model of Hydrostatic Equilibrium of a Rotating Rigid Body Clausius Virial Theorem The Model of Hydrostatic Equilibrium of Elastic and Viscous-Elastic Body Evidences that the Earth and the Moon Move Being Not in Hydrostatic Equilibrium State References Physical Meaning of Dynamical Equilibrium of a Celestial Body Relationship of Gravitational Field and Moment of Inertia by Satellite Data Earthquakes Observational Data Oscillating Kinetic Energy of a Celestial Body s Interacted Masses Generalized Classical Virial Theorem as Equation of Dynamical Equilibrium of a Body Jacobi s n-body Problem ix

10 x Contents 3.6 Reduction of Inner Gravitational Field to Resultant Envelope of Pressure References Derivation of Jacobi s Virial Equation for Description of Dynamics of a Self-Gravitating Body Derivation of Jacobi s Virial Equation from Newtonian Equations of Motion Derivation of Jacobi s Virial Equation for Dissipative Systems Derivation of Jacobi s Virial Equation from Eulerian Equations Derivation of Jacobi s Virial Equation from Hamiltonian Equations Derivation of Jacobi s Virial Equation in Quantum Mechanics General Covariant Form of Jacobi s Virial Equation Relativistic Analogue of Jacobi s Virial Equation Derivation of Jacobi s Virial Equation in Statistical Mechanics Universality of Jacobi s Virial Equation for Description of Dynamics of Natural Systems References Solution of Jacobi s Virial Equation for Conservative and Dissipative Systems Solution of Kepler s Problem in Classical and Virial Approach The Classical Approach The Dynamic Approach Solution of n-body Problem in the Framework of Conservative System Solution of Jacobi s Virial Equation in Hydrodynamics The Hydrodynamic Approach The Virial Approach The Hydrogen Atom as a Quantum Mechanical Analogue of the Two-Body Problem Solution of a Virial Equation in the Theory of Relativity (Static Approach) General Approach to Solution of Virial Equation for a Dissipative System Analytical Solution of Generalized Equation of Virial Oscillations Solution of the Virial Equation for a Dissipative System Solution of the Virial Equation for a System with Friction References The Nature of the Solar System Bodies Creation The Conditions of a Body Separation and Orbiting The Structure of Potential and Kinetic Energies of a Nonuniform Body Conditions of Dynamical Equilibrium of Oscillation and Rotation of a Body

11 Contents xi 6.4 Equations of Oscillation and Rotation of a Body and Their Solution The Nature and Mechanism of Body Shell Differentiation Self-Similarity Principle and Radial Component of Nonuniform Sphere Charge-Like Motion of Nonuniformities and Tangential Component of the Force Function Physical Meaning of the Archimedes and Coriolis Forces Initial Values of Mean Density and Radius of a Body References The Body s Evolutionary Processes as Effects of Energy Emission Equilibrium Boundary Conditions for a Self-Gravitating Gaseous Sphere Velocity of Gravitational Differentiation of a Gaseous Sphere The Luminosity Mass Relationship Bifurcation of a Dissipative System Cosmochemical Effects Planets Stars Galaxies Universe Radial Distribution of Mass Density and the Body s Inner Force Field Oscillation Frequency and Angular Velocity of Shell Rotation Thickness of the Upper Earth s Rotating Shell Oscillation of the Earth s Shells Angular Velocity of Shell Rotation The Nature of Precession, Nutation, and Body s Equatorial Plane Obliquity Phenomenon of Precession Tidal Effects The Nature of Perturbations Based on Dynamic Equilibrium Rotation of the Outer Force Field and the Nature of Precession and Nutation The Nature of Possible Clockwise Rotation of the Outer Core of the Earth The Nature of the Earth s Orbit Plane Obliquity to the Sun s Equatorial Plane The Nature of Chandler s Effect of the Earth Pole Wobbling The Nature of Obliquity of the Earth s Equatorial Plane to the Ecliptic Tidal Interaction of Two Bodies

12 xii Contents Change in Climate as an Effect of Changes of the Earth s Orbit References The Nature of Electromagnetic Field of a Celestial Body and Mechanism of Its Energy Generation Electromagnetic Component of the Interacted Masses Potential Energy of the Coulomb Interaction of Mass Particles Emission of Electromagnetic Energy by a Celestial Body as an Electric Dipole Quantum Effects of Generated Electromagnetic Energy The Nature of the Star-Emitted Radiation Spectrum References Creation and Decay of a Hierarchic Body System at Expansion and Attraction of the Force Field Relationship of the Jacobi Function and Potential Energy at Simultaneous Collision of n Particles Asymptotic Limit of Simultaneous Collision of Mass Points for Conservative System Asymptotic Limit of Simultaneous Collision of Mass Points for Nonconservative System Asymptotic Limit of Simultaneous Collision of Charged Particles of a System Relationship Between the Jacobi Function and Potential Energy for a System with High Symmetry Systems with Spherical Symmetry Polytropic Gas Sphere Model System with Elliptical Symmetry System with Charged Particles Direct Derivation of the Equation of Virial Oscillation from Einstein s Equations References Conclusions References Index

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