**Self-consistent gravitational constants** are complete sets of fundamental constants, which are self-consistent and
define various physical quantities associated with gravitation. These constants
are calculated in the same way as electromagnetic constants in electrodynamics.
This is possible because in the weak field equations of general relativity are
simplified into equations of gravitoelectromagnetism,
similar in form to Maxwell's Equations. Similarly, in the weak field
approximation equations of covariant theory
of gravitation ^{[1]} turn into equations of Lorentz-invariant theory of gravitation
(LITG). LITG equations are Maxwell-like
gravitational equations, which are similar to equations of gravitoelectromagnetism. If these equations are written
with the help of self-consistent gravitational constants, there is the best
similarity of equations of gravitational and electromagnetic fields. Since in 19-th century there was no International System of Units, the first mention of
gravitational constants was possibly due to Forward (1961).^{[2]}

- 1 Definition
- 2
Connection with Planck mass and Stoney mass
- 3 Connection with fine-structure constant
- 4
Strong gravitational torsion flux quantum
- 5 See also
- 6 References
- 7 External links

Primary set of *gravitational constants*
is:

1. *First gravitational constant*: , which is the speed of gravitational
waves in vacuum; ^{[3]}

2. *Second gravitational constant*: , which is the *gravitational
characteristic impedance of free space*.

Secondary set of *gravitational
constants* is:

1. Gravitoelectric gravitational constant
(like *vacuum permittivity*): where is the gravitational constant.

2. Gravitomagnetic gravitational constant
(like *vacuum permeability*): If the speed of gravitation is
equal to the speed of light, then ^{[4]}

Both, primary and secondary sets of
gravitational constants are selfconsistent, because they are connected by the
following relationships:

If then gravitational characteristic impedance
of free space be equal to: ^{[5]} ^{[6]}

In Lorentz-invariant
theory of gravitation the constant
is contained in formula
for vector energy flux density of gravitational field (Heaviside vector): ^{[3]}

where:

§
** **** ** is gravitational
field strength or gravitational acceleration,

§
is gravitational torsion field or simply torsion field.

For
plane transverse uniform gravitational wave, in which for amplitudes of field
strengths holds , may be written:

A
similar relation in electrodynamics for amplitude of flux density of
electromagnetic energy of a plane electromagnetic wave in vacuum, in which , is as follows: ^{[7]}

where
– Poynting
vector, – electric field strength, – magnetic flux density,

– vacuum permeability, – impedance of free space.

Gravitational impedance of free space was used in paper ^{[8]} to evaluate the
interaction section of gravitons with the matter.

**Connection with Planck mass
and Stoney mass**

Since gravitational constant and speed of
light are included in Planck mass , where –
reduced Planck constant or Dirac constant, then gravitational characteristic
impedance of free space can be represented as:

,

where –
Planck constant.

There is Stoney mass, related to elementary charge and vacuum permittivity :

.

Stoney mass can be expressed through the
Planck mass:

,

where
is the electric fine-structure constant.

This implies another expression for
gravitational characteristic impedance of free space:

.

Newton law for gravitational force between
two Stoney masses can be written as:

Coulomb's law for electric force between two
elementary charges is:

Equality of and leads to equation for the Stoney mass that was stated above. Hence the Stony mass may be determined from the
condition that two such masses interact via gravitation with the same force as
if these masses had the charges equal to the elementary charge and only
interact through electromagnetic forces.

**Connection with fine structure
constant**

The electric fine structure constant is:

We can determine the same value for
gravitation so: with the equality of the fine structure
constants for both fields.

On the other hand, the gravitational fine
structure constant for hydrogen system
at the atomic level and at the level of star is also equal to fine structure
constant:

,

where – strong
gravitational constant, and – the mass of proton and electron, and – mass of the star-analogue of proton and the planet-analogue of electron,
respectively, – stellar Dirac constant, – characteristic speed of stars
matter.

**Strong
gravitational torsion flux quantum**

The magnetic force between two fictitious elementary
magnetic charges is:

where is the magnetic charge, is the magnetic coupling constant for fictitious magnetic charges.^{
[9]}

The force of gravitational
torsion field between two fictitious elementary torsion masses is:

where is the gravitational
torsion coupling constant for the gravitational torsion mass .

In the case of equality of the
above forces, we shall get the equality of the coupling constants for magnetic
field and gravitational torsion field:

from which the Stoney mass and the gravitational torsion mass could be derived:

Instead of fictitious magnetic
charge the single magnetic flux
quantum Φ_{0} = *h*/(2*e*)
≈2.067833758(46)×10^{−15}

Wb ^{[10]} has the real meaning
in quantum mechanics. On the other hand at the level of atoms the strong
gravitation operates and we must use the strong gravitational constant. So we believe
that the strong gravitational torsion flux quantum there should be important:

m^{2}/s,

which is related
to proton with its mass
and to its velocity circulation quantum.

- Lorentz-invariant
theory of gravitation
- Gravitoelectromagnetism
- Speed of gravitation
- Maxwell-like
gravitational equations
- Gravitational
induction
- Gravitational characteristic impedance of free space
- Selfconsistent electromagnetic constants
- Velocity circulation quantum
- Quantum Gravitational Resonator
- Classical electromagnetism
- Gravitational wave

- Fedosin S.G. Fizicheskie teorii i beskonechnaia
vlozhennost’ materii.
– Perm, 2009, 844 pages, Tabl. 21, Pic. 41, Ref.
289. ISBN 978-5-9901951-1-0. (in Russian).
- R.
L. Forward, Proc. IRE 49, 892 (1961).
^{3.0}^{3.1}Fedosin S.G. (1999), written at Perm, pages 544,*Fizika**i filosofiia podobiia ot preonov do metagalaktik*, ISBN 5-8131-0012-1.- Kiefer, C.; Weber, C. On
the interaction of mesoscopic quantum systems with gravity. Annalen der Physik, 2005,
Vol. 14, Issue 4, Pages 253 – 278.
- J. D. Kraus, IEEE Antennas and
Propagation. Magazine 33, 21 (1991).
- Raymond Y. Chiao.
"New directions for gravitational wave physics via
“Millikan oil drops”, arXiv:gr-qc/0610146v16
(2007).PDF
- Иродов И.Е. Основные законы электромагнетизма. Учебное пособие для
студентов вузов. 2- издание. М.: Высшая школа, 1991.
- 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.
- Yakymakha O.L.(1989).
*High Temperature Quantum Galvanomagnetic Effects in the Two- Dimensional Inversion Layers of MOSFET's*(In Russian). Kiev: Vyscha Shkola. p.91. ISBN 5-11-002309-3. djvu. - "Magnetic flux quantum Φ0". 2010 CODATA recommended values. Retrieved 10 January 2012.

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