**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). http://dx.doi.org/10.4314/jfas.v8i3.18, 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