**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. 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 total energy of a
system of particles is equal to the absolute value of the kinetic energy of the
particles.

In the theory of Infinite
Hierarchical Nesting of Matter it is assumed that the matter, which protons and
neutrons consist of, can move faster than light. The analogues of nucleons at
the stellar level are neutron stars, and the characteristic speed of nucleons
is higher than that of the stars approximately 4.3 times. Similarly, at the
level of the nucleon the particles, that the nucleons are made up of, should
have their own characteristic speed which is 4.3 times greater than the speed
of light, which is the characteristic speed of nucleons.

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 the 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 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).

- Fedosin S.G. Fizika i filosofiia
podobiia ot preonov do metagalaktik,
Perm, pages 544, 1999. ISBN 5-8131-0012-1.
- Fedosin S.G. Model
of Gravitational Interaction in the Concept of Gravitons. Journal of
Vectorial Relativity, March 2009, Vol. 4, No. 1, P.1–24.
- 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, P. 1-18
(2015). http://dx.doi.org/10.9734/PSIJ/2015/22197
.

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