This book develops the statistical mechanics of the formation of gravitating cosmogonical bodies in the investigation of our solar system and other exoplanetary systems. The first part of the text acquaints the reader with the developing statistical theory of gravitating cosmogonical body formation. Within the framework of this theory, the models and evolution equations of the statistical mechanics are proposed, while well-known problems of gravitational condensation of infinite distributed cosmic substances are solved on the basis of the proposed statistical model of spheroidal bodies.

• Table of Contents
• Introduction
• Part I: A Statistical Mechanics of the Formation of Gravitating Cosmogonical Bodies
  • Chapter One
    • 1.1. On Newton’s Universal Gravitation Law and theproblem of finding the mass center of a spread cosmicmatter under its initial gravitational condensation
    • 1.2. The virial theorem
    • 1.3. On the gravitational instability of Jeans and the rotational instability of Rayleigh in a gravitating molecular cloud
    • 1.4. Poincaré’s general theorem and Roche’s model apropos the equilibrium figure for rotating and gravitating continuous medium
    • 1.5. On the fundamental difficulties of the theory of gravitational instability and the theory of gravitational condensation of an infinitely spread media
    • 1.6. Fundamental principles and main problems of the statistical mechanics of a molecular cloud
    • Conclusion and comments
  • Chapter Two
    • 2.1. The derivation of a function of particle distribution in space based on the statistical model of a molecular cloud
    • 2.2. The distribution of mass density as a result of the initial gravitational interaction of particles in a molecular cloud
    • 2.3. The critical (threshold) value of mass density and gravitational condensation parameter
    • 2.4. The strength and potential of the gravitational field of a sphere-like gaseous body formed by a collection of interacting particles
    • 2.5. The potential energy of a gravitating sphere-like gaseous body
    • 2.6. The probability interpretation of physical values describing the gravitational interaction of particles in a sphere-like gaseous body
    • 2.7. The statistical model of gravitation treated from the point of view of Einstein’s general relativity
    • 2.8. The pressure in a gravitating sphere-like gaseous body formed by a collection of interacting particles
    • 2.9. The internal energy of a gravitating sphere-like gaseous body
    • 2.10. The Jeans mass and the number of particles needed for gravitational binding of a sphere-like gaseous body
    • Conclusion and comments
  • Chapter Three
    • 3.1. Poincaré’s general theorem and Roche’s model in statistical interpretation for a slowly rotating and gravitating cosmogonical body
    • 3.2. The nonequilibrium particle distribution function for spatial coordinates in a sphere-like gaseous body during its initial rotation
    • 3.3. Derivation of the equilibrium distribution function of liquid particles in space and mass density functions based on the statistical model of a uniformly rotating and gravitating spheroidal body with a small angular velocity
    • 3.4. Derivation of the distribution function of the specific angular momentum value and angular momentum density for a uniformly rotating spheroidal body in a state of relative mechanical equilibrium
    • 3.5. The distribution function of particles in space for a rotating and gravitating spheroidal body from the point of view of the general relativity theory
    • 3.6. The strength and potential of the gravitational field of a uniformly rotating spheroidal body
    • 3.7. The potential energy of a uniformly rotating and gravitating spheroidal body
    • Conclusion and comments
  • Chapter Four
    • 4.1. The main anti-diffusion equation of initial gravitational condensation of a spheroidal body with a centrally symmetric distribution of masses from an infinitely spread matter
    • 4.2. General differential equations for physical values describing the anti-diffusion process of an initial gravitational condensation of a centrally symmetric spheroidal body near mechanical equilibrium
    • 4.3. Special cases of the basic equation of slow-flowing initial gravitational condensation and its solution near the state of mechanical equilibrium of a centrally symmetric spheroidal body
    • 4.4. The gravity–thermodynamic relationship for a centrally symmetric gravitating spheroidal body
    • 4.5. The mass density and internal energy flows for slow-flowing and initial gravitational condensation of a centrally symmetric spheroidal body
    • 4.6. Dynamical states of a forming centrally symmetric spheroidal body near the points of mechanical equilibrium
    • 4.7. The derivation of the general anti-diffusion equation for a slowly evolving process of gravitational condensation of a rotating axially symmetric spheroidal body
    • Conclusion and comments
  • Chapter Five
    • 5.1. The density of anti-diffusion mass flow and the anti-diffusion velocity into a gravitational compressible spheroidal body
    • 5.2. The initial potential of an arising gravitational field, the initial gravitational strength induced by the anti diffusionvelocity, and the characterizing number K as a control parameter of dynamical states of a formingspheroidal body
    • 5.3. The equilibrium dynamical states after the origin of a gravitational field inside a forming spheroidal body
    • 5.4. The dynamical states after the decay of a rotating spheroidal body and the formation of protoplanetary shells
    • 5.5. Interconnections of the proposed statistical theory of gravitating spheroidal bodies with Nelson’s statistical mechanics and Nottale’s scale relativistic theory
    • 5.6. The derivation of the generalized nonlinear Schrödinger-like equation in the statistical theory of gravitating spheroidal bodies
    • 5.7. Some particular cases of the generalized nonlinear Schrödinger-like equation describing different dynamical states of a gravitating spheroidal body
    • 5.8. Derivation of the reduced model in the state-space of a nonlinear dynamical system describing the behavior of the cubic generalized Schrödinger-like equation
    • Conclusion and comments
• Part II: The Statistical Theory of Gravity in Solar and Extrasolar System Applications
  • Chapter Six
    • 6.1. Evolution equations of the distribution of the specific angular momentum in the protoplanetary cloud and the laws on planetary distances
    • 6.2. The thermal emission model of protoplanetary cloud formation
    • Conclusion and comments
  • Chapter Seven
    • 7.1. 􀉋alculation of the gravitational potential in a remote zone of a uniformly rotating spheroidal body
    • 7.2. The calculation of the orbits of planets and bodies of the Solar system in a centrally symmetric gravitational field of a rotating spheroidal body based on Binet’s differential equation
    • 7.3. Calculation of the orbit of the planet Mercury and estimation of the angular displacement of Mercury’s perihelion based on the statistical theory of gravitating spheroidal bodies
    • Conclusion and Comments
  • Chapter Eight
    • 8.1. On the potential and potential energy of the gravitational field of a spheroidal body
    • 8.2. Derivation of the universal stellar law
    • 8.3. Estimation of mean relative molecular weight of a highly ionized stellar substance and verification of the universal stellar law
    • 8.4. Estimation of the temperature of the stellar corona
    • 8.5. Comparison with estimations of temperatures based on regression dependences for multi-planet extrasolar systems
    • 8.6. Derivation of Hertzsprung–Russell’s dependence based on the USL
    • Conclusion and comments
  • Chapter Nine
    • 9.1. The derivation of the combination of Kepler’s 3rd law with the universal stellar law (3KL-USL) and an explanation of the stability of planetary orbits through 3KL-USL
    • 9.2. On the Alfvén–Arrhenius specific additional periodic force modifying circular orbits of bodies
    • 9.3. Newtonian prediction of the Alfvén–Arrhenius specific additional periodic force
    • 9.4. The regular and wave gravitational potentials arising under the orbital motion of a gravitating body in the theory of retarded gravitational potentials
    • 9.5. Oscillations of gravitational field strength acting on planets: toward the nature of Alfvén–Arrhenius oscillations from the point of view of the statistical theo
    • 9.6. Axial and radial oscillations of the orbital motion in the gravitational field of a rotating and gravitating ellipsoid-like central body
    • Conclusion and comments
• References