**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 *electric constant*): 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 electric
constant :

.

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