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 1024 kg [1]) can be expressed as:
M = AUM x NUM ,
where AUM is an atomic unit of mass, 9.10938291×10−31 kg [2]),
NUM is a number of atomic units of mass contained in the Earth, i.e.:
N = M/AUM = 5.97219 x 1024/ 9.10938291 x 10-31 = 0.6556 x 1055.
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/NUM = 9.80665/0.6556 x 1055 = 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 1024 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