**The Value of the
Gravitational Force Quantum is 1.4958 x 10 ^{-54} N.**

Tomas Kala, Pardubice, Czech Republic

Gravitation is one of the basic phenomena of the world. Tremendous number of theoretical works on
origin, nature, essentials, consequences, etc. of the gravitation and related
phenomena were published so far. The most prominent ones are based on the
Albert Einstein´s general theory of relativity. The author of this
communication based his approach to the gravitation on Isaac Newton´s law of the
universal gravitation and related quantities, i.e. gravitational forces of
mass, distance and motion. Namely on the fact, that the gravitation force is – like
as inertia – a principal feature/attribute/property of a mass. Both, inertia
and gravitational force, are additive properties. Taking into account other
positivistic quantities like mass the Earth, standard acceleration of gravity,
and a value of the atomic unit of mass, the author defined a gravitational
force of atomic unit (or “Gravitational Force Quantum”) as a gravitational
force which exerts one atomic unit of Earth´s mass on 1 kilogram of a mass on
Earth´s surface, and calculated its value GFO = 1.4958 x 10^{-54} N. This quantity can be useful for further
development of the “quantum mechanical” approach to the description and notion about
the world.

Procedure

According to the Newton´s law, a mass of m = 1 kg exerts on Earth´s surface a gravitational force F = 9.80665 N (or 1.0 kilogram-force, 1 kgf = 9.80665 N by definition).

Mass of the Earth (5.97219 x 10^{24 }kg
[1]) can be expressed as:

M = AUM x N_{UM} ,

where AUM is an atomic unit of mass, 9.10938291×10^{−31} kg
[2]),

N_{UM} is a number of atomic
units of mass contained in the Earth, i.e.:

N = M/AUM = 5.97219 x 10^{24}/_{
}9.10938291 x 10^{-31} = 0.6556 x 10^{55}. ^{ }

The value of gravitational force attributed to one atomic unit of (Earth´s) mass, i.e. a “gravitational force quantum” (GFQ) can be calculated as:

GFQ = F/N_{UM} = 9.80665/0.6556
x 10^{55} = 1.4958 x 10^{-54} N.

Results

The gravitational force quantum (GFQ), defined
by the author as a gravitational force which exerts one atomic unit of Earth´s
mass on 1 kilogram of a mass on Earth´s surface, has a value 1.4958 x 10^{-54}
N.

Limitations of validity

Verity of the result might be limited by
correctness of the following values: of the atomic unit of mass 9.10938291 x 10^{-31}
kg, of the kgf = 9.80665 N, and of the Earth´s
mass 5.97219 x 10^{24} kg, that were used in the calculation of the
gravitational force quantum.

Resources

[1] NASA, https://solarsystem.nasa.gov/planets/profile.cfm?Object=Earth&Display=Facts

[2] NIST, https://physics.nist.gov/cuu/Constants/Table/allascii.txt