# The Elementary Gravitational Charge and its value

Consequently to the article titled „The Gravitational Force Quantum and its Value” (see: extended the Gravitational Force Quantum concept to further Objects of the Solar Planetary System and for the Pluto (O). He calculated values of the GFQO 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 GFQO 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 GFQO values by second power of the radii of the individual objects (O), receiving values denoted as the “Elementary Gravitational Charge” (GO). 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: GMe = GV = GE = GMa = GJ = GS = GP = GSun = 6.079675463×10-41 N. The values were the same as the calculated one on the basis of the “classical” Newton´s formula: FG = 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 FEarth = 9,819962 N.

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

MEarth = AUM × NAUMEarth                        (1)

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

NAUMEarth = MEarth/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 Earths mass, i.e. a “GFQEarth (the Gravitational force quantum)” can be calculated as:

GFQEarth = FEarth/NAUM =

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

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

GEarth = GFQEarth× REarth2

= 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 (MO), Radius (RO), Gravity (FO), Number of atomic units (NAUMO), Gravitational Force Quantum (GFQO), and Elementary Gravitational Charge (GO ) of individual Objects of the Solar Planetary System and for Pluto.

 Object

MO x1024kg

RO, km

FO, ms-2

NAUMOx1055

GFQOx10-55 N

GOx10-41 N

Mercury

0,330104

2439,7

3,701428

0,036238

102,1427

6,079675463

Venus

4,86732

6051,8

8,869766

0,534319

16,60012

6,079675463

Earth

5,97219

6371

9,819962

0,655609

14,97839

6,079675463

Mars

0,641693

3389,5

3,727756

0,070443

52,91869

6,079675463

Jupiter

1898,13

69911

25,91948

208,3709

0,124391

6,079675463

Saturn

568,319

58232

11,18562

62,38831

0,17929

6,079675463

Uranus

86,8103

25362

9,007322

9,529767

0,945178

6,079675463

Neptune

102,41

24622

11,27424

11,24225

1,002845

6,079675463

Pluto

0,1309

1151

6,594478

0,01437

458,9124

6,079675463

Sun

1989100

695508

274,4377

218357,3

0,001257

6,079675463

Sources

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Own calcul.

Own calcul.

Own calcul.

Own calcul.

The value of the „Elementary Gravitational Charge” corresponding to the atomic unit of the mass GAUM was calculated by definition as a gravitational force between the atomic unit mass and a mass of m = 1 kg at a distance of 1 meter using the formula:

GAUM = ϰ × MAUM × m / R2

= 6.67408×10-11×9.10938356×10-31× 1/12

= 6,079675463 × 10-41 N.                           (5)

Conclusions

I defined the Elementary Gravitational Charge (G) as a force which exerts one atomic unit of the mass on 1 kg of the mass in the distance of 1 meter, which value was calculated as  6.079675463×10-41 N.

The parameter of the Elementary Gravitational Charge can be supposed to be analogous to the Elementary (Electric) Charge e =1.6021766208(98) x10-19 C . Namely, both of the quantities cannot be divided into smaller parts, both are additive, both can be measured on the basis of the force effects, both are well known from their apparent physical features and practical applications, however, origins and physical backgrounds of the both phenomena are hidden so far [13-15].

The quantity of the Elementary Gravitational Charge will probably be useful for the further development of the “quantum mechanical” approach to the description and to the general notion about the world.

The phenomenon of the gravitation might perhaps be connected with/caused/explained etc. by the distortion of the space around the mass objects. It could be one of the main in-born/decisive/distinguish characteristics of material objects (or a matter/mass). For further (rather philosophical) discussion, see ref. .

More details will be published soon.

References

1. Kala, T. “The Gravitational Force Quantum and its Value”, Journal of Physical Science and Application, 5 (4). 2015.

NASA. “Earth: by the Numbers.” Accessed Feb 5th, 2016:

2. https://web.archive.org/web/20150217022731/https://solarsystem.nasa.gov/planets/profile.cfm?Object=Venus&Display=Facts

3. https://web.archive.org/web/20150217142912/https://solarsystem.nasa.gov/planets/profile.cfm?Object=Earth&Display=Facts

4. https://web.archive.org/web/20150217075323/https://solarsystem.nasa.gov/planets/profile.cfm?Object=Mars&Display=Facts

5. https://web.archive.org/web/20150215072818/https://solarsystem.nasa.gov/planets/profile.cfm?Object=Jupiter&Display=Facts

6. https://web.archive.org/web/20150215075328/https://solarsystem.nasa.gov/planets/profile.cfm?Object=Saturn&Display=Facts

7. https://web.archive.org/web/20150219021122/https://solarsystem.nasa.gov/planets/profile.cfm?Object=Uranus&Display=Facts

8. https://web.archive.org/web/20150224013840/https://solarsystem.nasa.gov/planets/profile.cfm?Object=Neptune&Display=Facts

9. https://web.archive.org/web/20150206201510/https://solarsystem.nasa.gov/planets/profile.cfm?Object=Pluto

10. https://web.archive.org/web/20150207205115/https://solarsystem.nasa.gov/planets/profile.cfm?Object=Sun

11. NIST. “Fundamental Physical Constants - Complete Listing.” Accessed Feb 5th 2016.

https://physics.nist.gov/cuu/Constants/Table/allascii.txt

12. Wikipedia. “Electric Charge.” Accessed Feb 5th, 2016. https://en.wikipedia.org/wiki/Electric_charge.

13. Halliday, D. and Resnick, R. 1981. Fundamentals of Physics.” 2nd Edition, John Wiley&¨Sons, Inc. N.Y., Chichester, Brisbane, Toronto. ISBN 0-471-03363-4.

14. Kala, T. “Comments on Matter/Mass/Field Categories”, Unitary Theory of the World, Accessed Feb 5th, 2016. https://www.tomas-kala.net/.