**Characteristic speed** is a physical quantity characterizing the
average speed of motion of the particles inside a single body or a particle
system at rest. The ratio of the characteristic speeds of similar objects
allows us to find the coefficient of similarity in speeds between different
levels of matter in Infinite Hierarchical
Nesting of Matter. For the nucleon form of matter the
characteristic speed does not exceed the speed of light.

- 1 Definition
- 2 Connection with the escape
velocity
- 3 Application
- 4 References
- 5 External links

The characteristic speed is
estimated by the formula:

where denotes the absolute value of the total
energy of the body (particle system), is the body mass.

If we take into account that the
mass–energy equivalence is the principle of proportionality between energy and
mass, then the square of the characteristic speed is the factor that connects
these quantities in one formula: Due to its definition in terms of energy and
mass, the characteristic speed can differ from the average speed of the
system’s particles, being found in other ways and depending on the mode of
averaging.

For a sufficiently large body of
uniform density with the radius , which is spherical under the action of
gravitational force, the absolute value of the total energy, according to the
virial theorem, is equal to the half of the absolute value of gravitational
energy . It gives the following expression:

where is
the gravitational constant, for a uniform ball and increases when the
density at the center of the ball is greater than the average density.

Let us consider now the process,
in which the matter from infinity with zero initial speed is transferred into
some space region and is superimposed on each other, so that in the end the
ball under consideration is formed. Suppose is
the current radius of the ball in its growth, is the
mass of the growing ball as a function of the current radius, is
the mass density. The work done on the transfer of the layer with the
mass from infinity to the growing ball is equal to the work
of the gravitational force or to the product of mass and gravitational
potential of the ball’s surface:

Therefore, the work is
equal by its absolute value to the doubled total energy and the gravitational energy ,
so that the characteristic speed equals: On the other hand, the product of the mass
and the gravitational potential is equal to the kinetic energy of falling
of this mass on the ball with the current mass .
This gives:

In view of (1) we also obtain:

where indicates the averaged over the ball’s volume
square of the speed. We will take into account now that the speed actually is the third escape velocity, required
to remove some mass to infinity from the surface of the ball with the current
radius in the process of
the ball’s growth. Then the characteristic speed of the ball in general
represents half of the square root of the mean square of the third escape
velocity, averaged over the entire volume of the ball.

The characteristic feature of the
gravitational field inside the uniform ball is that the field is directed
radially towards the center of the ball. Besides, at the arbitrary current
radius the field depends
only on the mass inside of this radius, but not on the mass of the outer shell.
Consequently, if there were no outer shell and it did not impede the motion of
a test body, the gravitational acceleration of the test body would equal the
centripetal acceleration, so that the body would rotate around the mass under the action of gravitation:

where is
the orbital rotation speed of the test body, which is directly proportional to
the radius .

In view of (2) we find:

The speed in
its meaning is the first escape velocity as the orbital rotation speed on the
current radius inside the ball.
Then the characteristic speed of
the ball in general is the square root of the squared first escape velocity,
averaged over the volume of the ball, which is divided by .

If we take into account the
escape velocities only on the ball’s surface with ,
then we can write for them:

In the theory of Infinite Hierarchical Nesting of Matter,
the characteristic speeds of space objects’ particles fall into several
distinct groups, corresponding to different classes. This allows us to almost
definitely refer each object to one of the known classes according to the
characteristic speed of its particles.

Partitioning of space objects
into classes can be done with the help of the similarity coefficients, since
between the objects there is similarity of
matter levels, and for the stars there is discreteness of stellar parameters. If we
assume that the coefficient of similarity in velocities is equal to , then at the
stellar level we have seven characteristic speeds for different classes of
objects: ^{[1]}

- km/s.
- km/s.
- km/s.
- km/s.
- km/s.
- km/s.
- km/s.

The speed is
equal to the speed of light, and it is assumed that this is the speed of the
particles inside the proton, according to the substantial proton model, and of the
particles within the hypothetical black holes.

In the speed range from to
the neutron stars are located, the range from to
includes white dwarfs, and the speeds of
particles of the main sequence stars are greater than the stellar speed km/s, but less than the speed km/s. The characteristic speeds of planets are
not higher than km/s, otherwise such a planet should be
considered a stellar object.

For comparison, the
characteristic speed of the Earth is 4.3 km/s, the characteristic speed of
Jupiter is 23 km/s, the characteristic speed of the Sun is about 495 km/s.

The characteristic speed of a
main sequence star can be expressed in terms of the stellar speed:

where and are the mass and charge numbers, corresponding to the star from the point
of view of similarity between atoms and stars. In turn, the stellar speed is determined
through the speed of light and the coefficient of similarity in velocities: . The stellar speed is one of the stellar constants, and it determines the
characteristic speed of particles of the main sequence star with minimum mass.

Large stellar systems, such as galaxies,
consist of a number of stars, moving at quite high speeds around the common
center of inertia of one or another system. Therefore, the characteristic speed
for a galaxy is the average speed of the stars’ motion. For a large number of
galaxies, there are dependences of the speed of the stars’ motion on the
distance to the galactic center, which after averaging show the rotation of
certain parts of the galaxy. If we average the speeds of the stars’ motion over
the entire volume of the galaxy, the resulting average value will be
proportional to the characteristic speed of this galaxy. This is the
consequence of the virial theorem, according to which the absolute value of total energy of a system of particles is equal to
kinetic energy of the particles.

Quantization of parameters of cosmic systems
is manifested at all levels of matter and it is a typical property of physical
systems, which, after the exchange of energy (exchange of matter), return to
their initial state. In this case, the characteristic speed of the system’s
particles can again achieve the previous equilibrium value. Some physical
systems with degenerate relativistic objects (atoms, neutron stars) achieve a
large degree of discreteness and stability, so that their characteristic speeds
change very little. It is known, for example, that the degree of accuracy of
the best atomic clocks coincides with the accuracy of repetition of pulses,
coming from pulsars.

In the space
objects, the characteristic speed allows us to estimate the kinetic energy of
the particles’ motion and the internal temperature. From the point of view of
the Le Sage's theory of gravitation, the gravitational energy of the body and
the gravitation force are created by fluxes of gravitons, penetrating all
bodies. ^{[2]} ^{[}^{3}^{]} However, the fluxes of gravitons
create not only the gravitational pressure, but also they transfer part of
their energy to the particles, so that according to the virial theorem the
internal kinetic (thermal) energy is not less than half of the absolute value
of the body’s gravitational energy. Thus the interior of an equilibrium space body cannot get colder than a certain value,
which depends on its mass and size, while maintaining the constant
characteristic speed of the body’s particles. The same follows from the solution of the equations of the acceleration field for a relativistic uniform system, in which the
Lorentz factor, the kinetic energy and the stationary velocity distribution of
particles inside the body are determined.^{ [4]} ^{[5]}

The speeds are
boundary for the maximum rotation speeds of the stars’ surfaces, as well as for
the average motion speeds of the stars relative to those stellar systems, in
which these stars were formed (the principle of local stellar speed).

In Infinite
Hierarchical Nesting of Matter, analogs of nucleons at the level of stars are
neutron stars, and the characteristic speed of nucleons is higher than that of
stars, approximately 4.3 times. The inverse of this quantity is the coefficient
of similarity in speeds between these levels of matter. If a neutron
star consists of nucleons, then nucleons consist of similar particles of the
lowest level of matter, called praons,
and praons in turn consist of graons. Between the levels of nucleons and praons
and between the levels of praons and graons, it is also possible to estimate
the similarity coefficients for speeds, which turn out to be close to unity.
This is due to the fact that nucleons inside a neutron star have a Lorentz
factor of about 1.04, but the praons inside the nucleon and the graons inside
the praon have a Lorentz factor of about 1.9.^{[6]}

- Fedosin S.G. Fizika i filosofiia
podobiia ot preonov do metagalaktik,
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- Fedosin S.G. Model
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- Fedosin
S.G. The graviton
field as the source of mass and gravitational force in the modernized Le
Sage’s model.Physical Science International Journal, ISSN:
2348-0130, Vol. 8, Issue 4, pp. 1-18 (2015). http://dx.doi.org/10.9734/PSIJ/2015/22197
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- Fedosin S.G. The virial theorem and the
kinetic energy of particles of a macroscopic system in the general field
concept. Continuum Mechanics and Thermodynamics, Vol. 29, Issue 2, pp.
361-371 (2017). https://dx.doi.org/10.1007/s00161-016-0536-8.
- Fedosin
S.G. The
integral theorem of generalized virial in the relativistic uniform model.
Continuum Mechanics and Thermodynamics, Vol. 31, Issue 3, pp. 627-638
(2019). https://dx.doi.org/10.1007/s00161-018-0715-x.
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Relativistic Uniform Model within the Framework of the Covariant Theory of
Gravitation. International Letters of Chemistry, Physics and Astronomy,
Vol. 78, pp. 39-50 (2018). http://dx.doi.org/10.18052/www.scipress.com/ILCPA.78.39.

Source:
http://sergf.ru/hsen.htm