# Stellar constants

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 main-sequence 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

## Constants for the systems with main-sequence 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 main-sequence stars:

1. The coefficient of similarity in mass: .
2. 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 main-sequence 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).
3. The coefficient of similarity in size:  ,  where  .
4. 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:

1. The minimum mass of the main sequence star:  kg, where    is the proton mass,   is the mass of the Sun.
2. 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.
3. The stellar speed  km/s as the characteristic speed of the matter particles in the main-sequence star with the minimum mass.
4. The stellar Dirac constant for planetary systems of main-sequence stars:  J∙s, where   is the Dirac constant.
5. The stellar Bohr radius in the stellar hydrogen system:  m = 19.25 a.u., where   is the gravitational constant.
6. The orbital velocity of the planet – the analogue of the electron in the stellar Bohr radius in the stellar hydrogen system:  km/s.
7. 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

1. The acceleration of free fall at the surface of the main-sequence star of minimum mass:  m/s2, with the radius of the star  solar radii.
2. The stellar Boltzmann constant for planetary systems of main-sequence stars: , where   is the mass number of the star,   J/K.
3. 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.
4. The stellar gas constant for the gas from stars: , where   J/(K∙stellar mole) is the stellar gas constant for main-sequence stars of minimum mass.
5. The gyromagnetic ratio for the object – the analogue of the electron:  C/kg (or rad/(T∙s)), where   is the elementary charge.
6. The gyromagnetic relation for the stellar object – the analogue of the atomic nucleus:  C/kg (or rad/(T∙s)).
7. The stellar Stefan–Boltzmann constant:  W/(m2 ∙K4), where   is the Stefan–Boltzmann constant.
9. The absolute value of full energy of the main-sequence 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]

1. The coefficient of similarity in mass: .
2. The coefficient of similarity in speed: , where   is the characteristic speed of the matter particles in a typical neutron star.
3. The coefficient of similarity in size: .
4. 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:

1. The magnetar mass  kg.
2. The mass of the discon – the analogue of the electron:  kg or 250 Earth masses, or 0.78 Jupiter masses.
3. The stellar speed  m/s as the characteristic speed of the matter particles in a typical neutron star.
4. The stellar Dirac constant for the system with the magnetar:  J∙s.
5. The stellar Bohr radius in the stellar hydrogen system:  m.
6. The orbital velocity of the matter of the discon on the stellar Bohr radius in the stellar hydrogen system:  km/s.
7. The stellar charge:  C.
8. The stellar fine structure constant :  ,  where   is the vacuum permittivity .
9. The measure of the magnetic moment for neutron stars (stellar magneton):  J/T.
10. The magnetic moment of the magnetar:  J/T, where   is the magnetic moment of the proton.
11. The magnetic moment of the discon – the analogue of the electron:  J/T, where   is the magnetic moment of the electron.
12. The free fall acceleration at the surface of the magnetar:  m/s2, with the radius of the star  km.
13. The absolute value of full energy of the magnetar in the proper gravitational field:  J.
14. The stellar gravitational torsion flux quantum, as the velocity circulation quantum, is:  m2/s.
15. The stellar magnetic flux quantum :   J/A.

## Gravitational constants

At the level of stars the ordinary gravitation is acting with the gravitational constant  m3/(kg∙ s2). 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]

1. The cross-section of interaction of gravitons with the matter:  m².
2. The power of the energy flux of gravitons per unit area from the unit solid angle:  W/(sr∙m2), 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 .
3. 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  m3/(kg ∙s2). 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]

1. The ratio of the proton mass to the electron mass:  .
2. The ratio of the Bohr radius to the radius of the proton  : ,  where the approximate equality for the Planck constant is used  .
3. 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 main-sequence 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:

1. The ratio of the mass of the magnetar to the mass of the discon:  .
2. The ratio of the stellar Bohr radius to the radius of the magnetar: ,  where the approximate equality for stellar Planck constant is used:  .
3. 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. 1.0 1.1 1.2 1.3 Fedosin S.G. Fizika i filosofiia podobiia: ot preonov do metagalaktik, Perm: Style-MG, 1999, ISBN 5-8131-0012-1. 544 pages, Tabl.66, Ill.93, Bibl. 377 refs.
2. 2.0 2.1 Comments to the book: Fedosin S.G. Fizicheskie teorii i beskonechnaia vlozhennostmaterii. – Perm, 2009, 844 pages. ISBN 978-5-9901951-1-0. (in Russian).
3. Sergey Fedosin, The physical theories and infinite hierarchical nesting of matter, Volume 1, LAP LAMBERT Academic Publishing, pages: 580, ISBN-13: 978-3-659-57301-9.
4. Fedosin S.G. Model of Gravitational Interaction in the Concept of Gravitons. Journal of Vectorial Relativity, Vol. 4, No. 1, March 2009, P.1-24.
5. 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).