Stellar
constants characterize the
stellar level of matter, describing the typical physical quantities inherent in
stars and planetary systems of stars. In some cases stellar constants are the natural
units, in which physical quantities can be measured at the level of stars.
A considerable part of stellar constants was introduced by Sergey Fedosin in
1999. ^{[1]}
Contents
 1
Constants for the systems with mainsequence stars
 1.1 Constants of the hydrogen system
 1.2 Other constants
 2
Constants for the systems with neutron stars
 2.1 The hydrogen system with a magnetar
 3 Gravitational constants
 4 Dimensionless constants
 5 References
 6 See also
 7 External links

Constants for the systems with mainsequence stars
According
to the similarity of matter levels and SPФ symmetry between the corresponding
objects and phenomena we can establish similarity relations and predict the
physical quantities, characterizing them. This allows us to connect different
levels of matter in the framework of the Theory of Infinite Hierarchical Nesting of Matter.
At the
level of stars the following similarity coefficients are used between atoms and
mainsequence stars:
 The coefficient of similarity in mass: .
 The coefficient of similarity in speed: ,
where is the coefficient of similarity in
speed for the hydrogen system, is
the characteristic speed of the matter particles in the mainsequence star
with the minimum mass , is the speed of light as the
characteristic speed of the matter in the proton, and
are
the mass and charge numbers of the star, found from the correspondence
between stars and chemical elements (more on this in the article Discreteness of stellar parameters).
 The coefficient of similarity in size:
,
where .
 The coefficient of similarity in time:
, where
.
In
determining the stellar constants the constants for the level of atoms and
elementary particles are commonly used, which are multiplied by the
coefficients of similarity according to the dimension of physical quantities.
Some stellar constants can also be calculated through other stellar constants.
Constants of the hydrogen system
The
stellar hydrogen system consists of the
star – the analogue of the proton and the planet – the analogue of the
electron. The constants, describing these objects and their interaction, equal:
 The minimum mass of the main sequence star: kg, where is the
proton mass, is
the mass of the Sun.
 The mass of the planet, which is the analogue of the electron: kg or 10.1 Earth masses, where is the mass of the electron.
 The stellar speed km/s as the characteristic speed of the matter
particles in the mainsequence star with the minimum mass.
 The stellar Dirac constant for
planetary systems of mainsequence stars: J∙s, where is the Dirac constant.
 The stellar Bohr radius in the stellar hydrogen system: m = 19.25 a.u., where is
the gravitational constant.
 The orbital velocity of the planet – the analogue of the electron in
the stellar Bohr radius in the stellar hydrogen system: km/s.
 The stellar fine structure
constant: .
In the stellar
hydrogen system the balance of forces acting on the planet, and the condition
for the orbital angular momentum are as follows:
,
,
which
implies that:
,
.
With the orbit of the planet corresponds to the
Bohr radius in the hydrogen atom, and the velocity and the orbital radius of
the planet become equal to and .
Other constants
 The acceleration of free fall at the surface of the mainsequence star
of minimum mass: m/s^{2}, with the
radius of the star solar radii.
 The stellar Boltzmann constant for planetary systems of mainsequence
stars: , where is the mass number of the
star, J/K.
 The stellar mole is defined as the amount of matter, consisting of
stars, the number of which is (stellar mole)^{–1}, where the
number is
the Avogadro constant.
 The stellar gas constant for the gas from stars: ,
where J/(K∙stellar
mole) is the stellar gas constant for mainsequence stars of minimum mass.
 The gyromagnetic ratio for the object – the analogue of the electron: C/kg (or rad/(T∙s)), where is the elementary charge.
 The gyromagnetic relation for the stellar object – the analogue of the
atomic nucleus: C/kg (or rad/(T∙s)).
 The stellar Stefan–Boltzmann constant: W/(m^{2} ∙K^{4}),
where is
the Stefan–Boltzmann constant.
 The stellar radiation constant: J/(m^{3}∙K^{4}), where is the radiation constant.
 The
absolute value of full energy of the mainsequence star with the
minimum mass in its proper gravitational field: J.
The summary dependence "magnetic
moment – spin" for planets, stars and the Galaxy. ^{[1]}
By definition,
the gyromagnetic ratio (magnetomechanical ratio) is
the ratio of the dipole magnetic moment of the object to its proper angular
momentum. For the electron the value of the spin as the characteristic angular
momentum is assumed to be equal to , and the magnetic moment is equal to the
Bohr magneton:
.
The
measure of the magnetic moment of atomic nuclei is the nuclear magneton:
.
From
this it follows that the gyromagnetic ratio for the Bohr magneton and the
nuclear magneton is equal to the ratio of the charge to the corresponding mass.
If on the coordinate plane with the coordinate axes, equal to the magnetic
moment and the proper angular momentum, we draw straight lines corresponding to
the gyromagnetic ratios for the object – the analogue of the electron and for
the stellar object – the analogue of the atomic nucleus, it turns out that the
magnetic moments of cosmic objects, from the planets’ moons to galaxies, fall
into the space between these straight lines (see the figure). ^{[1]}
Constants for the systems with neutron stars
The
coefficients of similarity between atoms and neutron stars: ^{[2]}
 The coefficient of similarity in mass: .
 The coefficient of similarity in speed: , where is the characteristic speed of
the matter particles in a typical neutron star.
 The coefficient of similarity in size: .
 The coefficient of similarity in time: .
The hydrogen system with a magnetar
For
degenerate stellar objects the stellar hydrogen system consists of the magnetar –
the analogue of the proton and the disc (discon) – the analogue of the
electron. These objects are characterized by the following constants:
 The magnetar mass kg.
 The mass of the discon – the analogue of the electron: kg or 250 Earth masses, or 0.78 Jupiter
masses.
 The stellar speed m/s as the characteristic speed of the matter
particles in a typical neutron star.
 The stellar Dirac constant for the
system with the magnetar: J∙s.
 The stellar Bohr radius in the stellar hydrogen system: m.
 The orbital velocity of the matter of the discon on the stellar Bohr
radius in the stellar hydrogen system: km/s.
 The stellar charge: C.
 The stellar fine structure
constant : , where is
the vacuum permittivity .
 The measure of the magnetic moment for neutron stars (stellar
magneton): J/T.
 The magnetic moment of the magnetar: J/T, where is
the magnetic moment of the proton.
 The magnetic moment of the discon – the analogue of the electron: J/T, where is the magnetic moment of the
electron.
 The free fall acceleration at the surface of the magnetar: m/s^{2}, with the
radius of the star km.
 The
absolute value of full energy of the magnetar in the proper
gravitational field: J.
 The stellar gravitational torsion flux quantum, as the velocity circulation quantum,
is: m^{2}/s.
 The stellar magnetic flux quantum : J/A.
Gravitational constants
At the
level of stars the ordinary gravitation is acting with the gravitational constant m^{3}/(kg∙
s^{2}). In the framework of Le Sage's theory of gravitation the
gravitational constant is associated with other physical quantities,
characterizing the fluxes of gravitons: ^{[3]} ^{[4] [5]}
 The crosssection of interaction of gravitons with the matter: m².
 The power of the energy flux of gravitons per unit area from the unit
solid angle: W/(sr∙m^{2}), where is
the momentum of the graviton, moving at the speed of light , is
the flux of gravitons, crossing per unit time the unit area perpendicular
to the flux from the unit solid angle, is the mass of the nucleon .
 The maximum gravitational pressure from gravitons: Pa, which is approximately equal to the
density of gravitational energy of the fluxes of gravitons.
The gravitational
characteristic impedance of free space is:
It is
assumed that strong gravitation is
responsible for the integrity of objects with the sizes of elementary
particles, and the strong gravitational
constant is m^{3}/(kg ∙s^{2}).
In the gravitational model of strong
interaction the strong gravitation, the gravitational
torsion fields, emerging during the rotation and the motion of elementary
particles, and the electromagnetic forces are responsible for the strong
interaction.
Dimensionless constants
In the hydrogen system we can determine the
dimensionless constants associated with the mass, sizes and speeds: ^{[1]}
 The ratio of the proton mass to the electron mass: .
 The ratio of the Bohr radius to the radius of the proton : , where the approximate
equality for the Planck constant is used
.
 The ratio of the electron velocity on the first Bohr orbit to the
speed of light (the fine structure
constant): .
For
these coefficients we obtain the relation:
.
In the
hydrogen system, including the mainsequence star and the planet (or the
magnetar and the discon around it), after substituting in the formulas for the
dimensionless constants of the constants atomic quantities with the
corresponding stellar quantities, the values of these constants remain the
same, as a result the above relation between the dimensionless constants does
not change. In particular, for the system with the magnetar and the discon we
obtain:
 The ratio of the mass of the magnetar to the mass of the discon: .
 The ratio of the stellar Bohr radius to the radius of the magnetar: , where the approximate equality for stellar Planck constant is used: .
 The ratio of the velocity of the discon matter on the stellar Bohr
radius to the stellar speed (the stellar fine structure constant):
Then
again .
Another
type of the dimensionless constant is the constant of gravitational interaction,
which shows the relative force of the interaction between two magnetars. This
constant is calculated as the ratio of the gravitational interaction energy of
two magnetars to the energy, associated with the stellar Dirac constant and with the stellar speed :
,
where
the coefficient for the interaction of two neutron stars as
the consequence of the exponential decay of the flux of gravitons in the matter according to the
Le Sage's theory of gravitation, and for the less dense bodies tends to unity. ^{[2]}
The
obtained value of the dimensionless constant is
of the same order of magnitude as the coupling
constant of interaction for two protons in the field of strong gravitation,
which follows from SPФ symmetry and the
similarity of matter levels of atoms
and stars.
References
 ^{1.0} ^{1.1} ^{1.2} ^{1.3} Fedosin S.G. Fizika i filosofiia podobiia: ot preonov do metagalaktik,
Perm: StyleMG, 1999, ISBN 5813100121. 544 pages, Tabl.66, Ill.93,
Bibl. 377 refs.
 ^{2.0} ^{2.1} Comments to the
book: Fedosin S.G. Fizicheskie teorii i beskonechnaia
vlozhennost’ materii.
– Perm, 2009, 844 pages. ISBN 9785990195110. (in Russian).
 Sergey Fedosin, The physical theories and infinite hierarchical
nesting of matter,
Volume 1, LAP LAMBERT Academic Publishing, pages: 580, ISBN13:
9783659573019.
 Fedosin
S.G. Model of Gravitational Interaction
in the Concept of Gravitons. Journal of Vectorial Relativity, Vol. 4,
No. 1, March 2009, P.124.
 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: 23480130, Vol. 8, Issue 4, P. 118 (2015). http://dx.doi.org/10.9734/PSIJ/2015/22197.
See also