The Elementary Gravitational Charge and its value

Consequently to the article titled „The Gravitational Force Quantum and its Value” (see: https://www.davidpublisher.org/Public/uploads/Contribute/563c64d6451b6.pdf),  I extended the Gravitational Force Quantum concept to further Objects of the Solar Planetary System and for the Pluto (O). He calculated values of the GFQ_O on the analogous basis, i.e. of the mass and the standard acceleration of the gravity of individual objects and of the atomic unit of the mass. I  received GFQ_O values for:  the Mercury 102.1427×10^-55 N, the Venus 16,60012×10^-55 N, the Earth 14.97839×10^-55 N, the Mars 52.91869×10^-55 N, the Jupiter 0.124391×10^-55 N, the Saturn 0.17929 ×10^-55 N, the Uranus 0.945178×10^-55 N, the Neptune 1.002845×10^-55 N, for the Pluto 458.9124×10^-55 N, and for the Sun 0.001257×10^-55 N, respectively. I multiplied the GFQ_O values by second power of the radii of the individual objects (O), receiving values denoted as the “Elementary Gravitational Charge” (G_O). The Elementary Gravitational Charge represented a gravitational force of one atomic unit of mass in the (radius) distance of 1 meter. They were found of the same value: G_Me = G_V = G_E = G_Ma = G_J = G_S = G_P = G_Sun = 6.079675463×10^-41 N. The values were the same as the calculated one on the basis of the “classical” Newton´s formula: F_G = ϰ × M × m / R², for the gravitational force between the atomic unit mass and a mass of 1 kg at a distance of 1 meter, which value was calculated as G=6.079675463×10^-41 N. The quantity of the Elementary Gravitational Charge can be supposed to be analogous to the Elementary (Electric) Charge (e =1.6021766208(98) x10^-19 C) quantity.

Methodology

I used the following procedure:

According to the Newton´s law, a mass of m = 1 kg exerts on the Earth´s surface a gravitational force F_Earth = 9,819962 N.

The mass of the Earth (5.97219×10²⁴ kg [4]) can be expressed as:    

      M_Earth = AUM × N_AUMEarth                        (1)

where, the AUM is the atomic unit of the mass, 9.10938356×10^-31 kg [12]),  the N_AUMEarth is a number of atomic units of the mass contained in the Earth, i.e.:

N_AUMEarth = M_Earth/AUM =

5.97219×10²⁴/9.10938356×10^-31=

0,655609 ×10⁵⁵                                                                 (2)        

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

      GFQ_Earth = F_Earth/N_AUM =

9,819962/0,655609×10⁵⁵ = 1.497839×10^-54 N.  (3)

   The value of the “Elementary Gravitational Charge” (G_O) of the Earth was calculated as:

      G_Earth = GFQ_Earth× R_Earth²

         = 1.497839×10^-54 × (6.371×10⁶)²

               = 6,079675463 ×10^-41 N                                    (4)

The same procedures were followed with data for the planets of the solar system and Pluto given in the Table 1. 

TABLE 1  Values of Mass (M_O), Radius (R_O), Gravity (F_O), Number of atomic units (N_AUMO), Gravitational Force Quantum (GFQ_O), and Elementary Gravitational Charge (G_O ) of individual Objects of the Solar Planetary System and for Pluto.