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Analysis of the orbital motion of the Earth, the Moon and other
planets and their satellites led to the discovery that all bodies
in the Solar System are moving with the first cosmic velocity of
their proto parents. The mean orbital velocity of each planet is
equal to the first cosmic velocity of the Protosun, the radius of
which is equal to the semi-major axis of the planet's orbit. The
same applies for the planets' satellites. All the small planets,
comets, other bodies and the Sun itself follow this law, a finding
that has also been proven by astronomical observations. The
theoretical solutions based on the Jacobi dynamics explain the
process of the system creation and decay, as well as the nature of
Kepler's laws.
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.
In their approach to Earth dynamics the authors consider the
fundamentals of "Jacobi Dynamics" (1987, Reidel) for two reasons.
First, because satellite observations have proved that the Earth
does not stay in hydrostatic equilibrium, which is the physical
basis of today's treatment of geodynamics. And secondly, because
satellite data have revealed a relationship between gravitational
moments and the potential of the Earth's outer force field
(potential energy), which is the basis of "Jacobi Dynamics." This
has also enabled the authors to come back to the derivation of the
classical virial theorem and, after introducing the volumetric
forces and moments, to obtain a generalized virial theorem in the
form of Jacobi's equation. Thus a physical explanation and rigorous
solution was found for the famous Jacobi's equation, where the
measure of the matter interaction is the energy.
The main dynamical effects which become understandable by that
solution can be summarized as follows:
" "the kinetic energy of oscillation of the interacting particles
which explains the physical meaning and nature of the gravitation
forces;
" "separation of the shell's rotation of a self-gravitating body
with respect to the mass density;
difference in angular velocities of the shell rotation;
" "continuity in changing the potential of the outer gravitational
force field together withchanges in density distributionof the
interacting masses (volumetric center of masses);
" "the nature of the precession of the Earth, the Moon and
satellites; the nature of the rotating body's magnetic field and
the generation of the planet's electromagnetic field.As a final
result, the creation of the bodies in the Solar System having
different orbits was discussed. This result is based on the
discovery that all the averaged orbital velocities of the bodies in
the Solar System and the Sun itself are equal to the first cosmic
velocities of their proto-parents during the evolution of their
redistributed mass density.
Audience
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 (astrophysics, celestial mechanics and stellar dynamics
and radiophysics), geophysics (physics and dynamics of the Earth's
body, atmosphere and oceans), planetology and cosmogony, and for
students of celestial, statistical, quantum and relativistic
mechanics and hydrodynamics.
Analysis of the orbital motion of the Earth, the Moon and other
planets and their satellites led to the discovery that all bodies
in the Solar System are moving with the first cosmic velocity of
their proto parents. The mean orbital velocity of each planet is
equal to the first cosmic velocity of the Protosun, the radius of
which is equal to the semi-major axis of the planet s orbit. The
same applies for the planets satellites. All the small planets,
comets, other bodies and the Sun itself follow this law, a finding
that has also been proven by astronomical observations. The
theoretical solutions based on the Jacobi dynamics explain the
process of the system creation and decay, as well as the nature of
Kepler s laws.
This book sets forth and builds upon the fundamentals of the
dynamics of natural systems in formulating the problem presented by
Jacobi in his famous lecture series "Vorlesungen tiber Dynamik"
(Jacobi, 1884). In the dynamics of systems described by models of
discrete and continuous media, the many-body problem is usually
solved in some approximation, or the behaviour of the medium is
studied at each point of the space it occupies. Such an approach
requires the system of equations of motion to be written in terms
of space co-ordinates and velocities, in which case the
requirements of an internal observer for a detailed description of
the processes are satisfied. In the dynamics discussed here we
study the time behaviour of the fundamental integral
characteristics of the physical system, i. e. the Jacobi function
(moment of inertia) and energy (potential, kinetic and total),
which are functions of mass density distribution, and the structure
of a system. This approach satisfies the requirements of an
external observer. It is designed to solve the problem of global
dynamics and the evolution of natural systems in which the motion
of the system's individual elements written in space co-ordinates
and velocities is of no interest. It is important to note that an
integral approach is made to internal and external interactions of
a system which results in radiation and absorption of energy. This
effect constitutes the basic physical content of global dynamics
and the evolution of natural systems.
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.
This book sets forth and builds upon the fundamentals of the
dynamics of natural systems in formulating the problem presented by
Jacobi in his famous lecture series "Vorlesungen tiber Dynamik"
(Jacobi, 1884). In the dynamics of systems described by models of
discrete and continuous media, the many-body problem is usually
solved in some approximation, or the behaviour of the medium is
studied at each point of the space it occupies. Such an approach
requires the system of equations of motion to be written in terms
of space co-ordinates and velocities, in which case the
requirements of an internal observer for a detailed description of
the processes are satisfied. In the dynamics discussed here we
study the time behaviour of the fundamental integral
characteristics of the physical system, i. e. the Jacobi function
(moment of inertia) and energy (potential, kinetic and total),
which are functions of mass density distribution, and the structure
of a system. This approach satisfies the requirements of an
external observer. It is designed to solve the problem of global
dynamics and the evolution of natural systems in which the motion
of the system's individual elements written in space co-ordinates
and velocities is of no interest. It is important to note that an
integral approach is made to internal and external interactions of
a system which results in radiation and absorption of energy. This
effect constitutes the basic physical content of global dynamics
and the evolution of natural systems.
In their approach to Earth dynamics the authors consider the
fundamentals of Jacobi Dynamics (1987, Reidel) for two reasons.
First, because satellite observations have proved that the Earth
does not stay in hydrostatic equilibrium, which is the physical
basis of today's treatment of geodynamics. And secondly, because
satellite data have revealed a relationship between gravitational
moments and the potential of the Earth's outer force field
(potential energy), which is the basis of Jacobi Dynamics. This has
also enabled the authors to come back to the derivation of the
classical virial theorem and, after introducing the volumetric
forces and moments, to obtain a generalized virial theorem in the
form of Jacobi's equation. Thus a physical explanation and rigorous
solution was found for the famous Jacobi's equation, where the
measure of the matter interaction is the energy. The main dynamical
effects which become understandable by that solution can be
summarized as follows: * the kinetic energy of oscillation of the
interacting particles which explains the physical meaning and
nature of the gravitation forces; * separation of the shell's
rotation of a self-gravitating body with respect to the mass
density; difference in angular velocities of the shell rotation; *
continuity in changing the potential of the outer gravitational
force field together with changes in density distribution of the
interacting masses (volumetric center of masses); * the nature of
the precession of the Earth, the Moon and satellites; the nature of
the rotating body's magnetic field and the generation of the
planet's electromagnetic field. As a final result, the creation of
the bodies in the Solar System having different orbits was
discussed. This result is based on the discovery that all the
averaged orbital velocities of the bodies in the Solar System and
the Sun itself are equal to the first cosmic velocities of their
proto-parents during the evolution of their redistributed mass
density. Audience 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 (astrophysics, celestial mechanics
and stellar dynamics and radiophysics), geophysics (physics and
dynamics of the Earth's body, atmosphere and oceans), planetology
and cosmogony, and for students of celestial, statistical, quantum
and relativistic mechanics and hydrodynamics.
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