Abstract
The virial theorem is considered for a system of randomly moving particles that are tightly bound to each other by the gravitational and electromagnetic fields, acceleration field and pressure field. The kinetic energy of the particles of this system is estimated by three methods, and the ratio of the kinetic energy to the absolute value of the energy of forces, binding the particles, is determined, which is approximately equal to 0.6 . For simple systems in classical mechanics, this ratio equals 0.5 . The difference between these ratios arises by the consideration of the pressure field and acceleration field inside the bodies, which make additional contribution to the acceleration of the particles. It is found that the total time derivative of the system's virial is not equal to zero, as is assumed in classical mechanics for systems with potential fields. This is due to the fact that although the partial time derivative of the virial for stationary systems tends to zero, but in real bodies the virial also depends on the coordinates and the convective derivative of the virial, as part of the total time derivative inside the body, is not equal to zero. It is shown that the convective derivative is also necessary for correct description of the equations of motion of particles.
Highlights
The virial theorem relates the kinetic and potential energies of a stationary system in nonrelativistic mechanics and is widely used in astrophysics for approximate evaluation of the mass of large space systems, based on their sizes and the distribution of velocities of individual objects [1]
In [3] by means of the virial theorem the kinetic energy in a tensor form is associated at the microscopic level with the stress tensor (Eshelby stress) in order to take into account the pressure effects within the framework of classical physics and in [4] the similar approach is used in variable-mass systems, where the fluxes of mass and energy are taken into consideration
In (10) we obtained the approximate dependence of the amplitude of the radial component of the particles’ velocity on the current radius, which is associated with the acceleration field acting in the system
Summary
The virial theorem relates the kinetic and potential energies of a stationary system in nonrelativistic mechanics and is widely used in astrophysics for approximate evaluation of the mass of large space systems, based on their sizes and the distribution of velocities of individual objects [1]. In [3] by means of the virial theorem the kinetic energy in a tensor form is associated at the microscopic level with the stress tensor (Eshelby stress) in order to take into account the pressure effects within the framework of classical physics and in [4] the similar approach is used in variable-mass systems, where the fluxes of mass and energy are taken into consideration In contrast to this we will analyze the virial theorem for a system of closely interacting particles, which are bound to each other by the gravitational and electromagnetic fields. If the spaces between the particles are small, as in a liquid, it can be assumed that the matter inside this sphere is distributed uniformly We studied such a physical system in [8], where the field strengths, potentials and energies of all the four fields were first defined in the framework of the relativistic uniform model. The virial theorem in a relativistic form can be written as follows:
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