**Gravitational constant**

The **gravitational constant ** is a fundamental physical constant, a
gravitational interaction constant.

The gravitational
constant *G* is a key quantity in Newton's law of
universal gravitation.

**Contents**

- 1 Introduction
- 2 The history of measurement
- 3 Theoretical definition
- 4 References
- 5 See also
- 6 External links

**Introduction**

According to
the Newton's law of universal gravitation, the force of gravitational
attraction between two material points with gravitational masses *m*_{1} and *m*_{2}, which are located at the
distance *R*, is equal to:

The
proportionality coefficient *G*
in this equation is called the **gravitational
constant**. Numerically it is equal to the absolute value of the
gravitational force, acting on a point body with unit mass from another similar
body, which is located at the unit distance.

In SI units
the value recommended for the year 2014 is: ^{[1]} m^{3}·s^{−2}·kg^{ −1},
or N·м^{2}· kg^{ −2}.

The
gravitational constant is presented in most of the formulas associated with the
gravitational interaction. In particular, it is included in the equations of
the general relativity, the __gravitoelectromagnetism__
and the __covariant theory of gravitation__,
and it is also part of the formulas used to determine the __gravitational torsion
field__. The gravitational constant and its __coupling
constant__ have such values that the gravitational
interaction between the elementary particles is many orders of magnitude less
than the weak, electromagnetic, and strong interactions.

In the
theory of __Infinite Hierarchical Nesting of Matter__,
based on the __SPФ
symmetry__ the existence of __strong gravitation__
is assumed, which is acting on the level of elementary particles. The __strong
gravitational constant__ is derived from the ordinary
gravitational constant by multiplying it by the similarity coefficients, which
are found on the basis of __similarity of matter levels__.

**The history of measurement**

The
gravitational constant is used in the modern law of universal gravitation, but
it was not used in Newton’s works and in the works of other scientists until
the beginning of the 19^{ th }century. The gravitational constant
apparently was first introduced into the law of universal gravitation only
after transition to the single metric system of measurements. Possibly it was
first done by the French physicist Poisson in “Treatise on Mechanics” (1809) —
at least historians have not found any earlier works, in which the
gravitational constant was mentioned. In 1798 Henry Cavendish prepared and performed
the Cavendish experiment to determine the average density of the Earth using
the torsion balance, invented by John Michell (Philosophical Transactions
1798). Cavendish compared the pendular oscillations of the test body under the
action of gravitation of the balls with known mass and under the action of the
Earth's gravitation. The numerical value of the gravitational constant was
calculated later based on the average density of the Earth and resulted in the
value m^{3}·s^{−2}·kg^{
−1}. ^{[2]}

The accuracy
of the measured value of *G*
since the time of Cavendish’s experiment increased insignificantly.

**Theoretical definition**

In order to
calculate the gravitational constant Maurizio Michelini used the idea of
micro-quanta, filling the entire space, interacting with the bodies’ particles
and as a result pushing the bodies to each other. ^{[3]} For the matter consisting mainly of nucleons
he obtains the following:

where J/m^{3} is the energy density of the fluxes of
micro-quanta; is the nucleon
mass; is the speed of light; m^{−2}•s^{−1} is the fluence rate of the fluxes of
micro-quanta in one direction.

Sergey
Fedosin expressed the gravitational constant in the framework of Le Sage’s
theory of gravitation in terms of the parameters describing the vacuum field of
gravitons. ^{[4]} ^{[5]} ^{[6]} In the model of cubic distribution of
graviton fluxes:

Here is the momentum of gravitons interacting
with the nucleon matter; the fluence rate denotes the number of gravitons dN, that
during the time dt fell to the area
dA (perpendicular to the flux) of one
face of a certain cube, which limits the volume under consideration; m^{2} is the cross-section of
interaction of gravitons and nucleons; is the nucleon mass; J/m^{3}
is the energy density of the graviton fluxes for cubic distribution.

In the model
of spherical distribution of graviton fluxes:

where the
fluence rate denotes the number of gravitons dN, that
during the time dt fell from the unit
solid angle
inside the spherical surface dA; J/m^{3}
is the energy density of the graviton fluxes for spherical distribution.

Since the gravitational constant is expressed in terms of other variables,
it is a dynamic variable, which is constant only on the average.

The interaction cross-section can be expressed in terms of the cross-section
m² of interaction of the charged particles of
the vacuum field (praons) with
nucleons: ^{[6]}

where is the __strong gravitational
constant__. The interaction cross-section is very close in magnitude to the
geometrical cross-section of the nucleon and is used to calculate the __electric
constant__. If we substitute the expression of in terms of
into the formula for the gravitational
constant in the cubic distribution model, we will obtain a relationship between
the strong gravitational constant, the nucleon’s parameters and the energy
density of the graviton fluxes at the nucleon level of matter:

Similarly, for the gravitational constant at the stellar level of matter,
there is a relationship between the corresponding energy density of the
graviton fluxes and the parameters of the neutron star, which is an analogue of
the nucleon:

where J/m³ is
the energy density of the graviton fluxes at the stellar level for cubic
distribution; m² is the cross-section of interaction between
the gravitons and the neutron star; kg is the
neutron star’s mass. In the calculation we used the similarity coefficients
according to the __similarity of matter levels__: is the coefficient of similarity in mass, is the coefficient of similarity in sizes, is the coefficient of similarity in speeds of
same-type processes.

Thus, it is assumed that at each level of matter there is its own
gravitational constant, besides the energy density of the corresponding
graviton fluxes increases with the transition to the lower levels of matter.

The quantity can be compared with the energy density of
the gravitational wave in the GW150914 event. It is assumed that this event was
caused by a merger of two black holes with masses of 30 and 35 solar masses,
rotating near each other under the action of gravitation, during decrease in
the distance between them up to 350 km, while the maximum power of
gravitational radiation reached W. ^{[7]} If we divide this power by
the surface of the sphere with the radius of 175 km, we will obtain an estimate
of the density of the energy flux passing through the surface of the sphere.
Then this value can be divided by the speed of light, and we can estimate the
energy density in the wave: J/m³. The energy density of the wave is found
to be substantially lower than the energy density of the gravitons’ vacuum
field. Thus, the gravitational wave from the majority of powerful radiation
sources only slightly modulates the graviton fluxes in the cosmic space.

**References**

- Newtonian constant of gravitation G.
CODATA, NIST.
- Brush, Stephen G.; Holton,
Gerald James (2001), Physics, the human adventure: from Copernicus to
Einstein and beyond, New Brunswick, N.J: Rutgers University Press, p. 137,
ISBN 0-8135-2908-5.
- Maurizio Michelini.
Discussion on Fundamental Problems of Physics Hidden in Cosmology. Applied
Physics Research. Vol. 8, No. 5. pp.19-43 (2016). http://dx.doi.org/10.5539/apr.v8n5p19.
- 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, pp.
1-18 (2015). http://dx.doi.org/10.9734/PSIJ/2015/22197.
- Fedosin S.G. The Force Vacuum Field as an Alternative to the Ether
and Quantum Vacuum. WSEAS Transactions on Applied and
Theoretical Mechanics, ISSN / E-ISSN: 1991-8747 / 2224-3429, Volume 10, Art.
#3, pp. 31-38 (2015).
^{6.0}^{6.1}Fedosin S.G. The charged component of the vacuum field as the source of electric force in the modernized Le Sage’s model. Journal of Fundamental and Applied Sciences, Vol. 8, No. 3, pp. 971-1020 (2016). https://dx.doi.org/10.5281/zenodo.845357.- Abbott, B. P.;
et al. (LIGO Scientific Collaboration, Virgo Collaboration), Observation
of Gravitational Waves from a Binary Black Hole Merger. Phys. Rev. Lett.
116, 061102 (2016). https://dx.doi.org/10.1103/PhysRevLett.116.061102.

**See also**

__Strong gravitational constant____Vacuum constants____Selfconsistent gravitational constants____Coupling constant__

**External links**

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