MATHEMATICAL FORMULAS FOR CALCULATION OF NEWTONIAN CONSTANT OF GRAVITATION G

© Ph.D. Nikolay Kosinov

E-mail: kosinov@unitron.com.ua

ABSTRACT

The global connection existing between fundamental physical constants is open [2-9]. On this basis Newtonian constant of gravitation G is explored. It is established that this constant is a compound constant and is comprising Planck`s constant h, speed of light c and other constants.

The group of primary constants consisting of five universal superconstants [2,4-6] is open. The researches have  shown that Newtonian constant of gravitation G can be expressed by means of fundamental superconstants [2-9]: 

G=f (h_{u ,} l_u , t_u , α , π). 

The universal superconstants have allowed to receive 10 equivalent formulas for calculation of Newtonian constant of gravitation G [2,3,5,6]. The new exact value of Newtonian constant of gravitation G found on this formulas is equal to:

The new value of Newtonian constant of gravitation G contains 9 digits [2,3,6] instead of four digits.  

1. THE PROBLEM OF PRIMACY AND INDEPENDENCE OF NEWTONIAN CONSTANT OF GRAVITATION G 

 As it is known, the form of Newtonian law of the world gravitation itself – proportionality of force to masses and reciprocal proportionality to the square of the distance is checked up with much more accuracy than that of determination of Newtonian constant of gravitation G. Therefore, Newtonian constant of gravitation G is imposing basic restriction on exact determination of gravitational forces. The unsufficient accuracy of determination of Newtonian constant of gravitation G is the basic interfering factor at determination of masses of heavenly bodies, their structure and evolution that creates problems for modern astronomy and for space researches. From times of Newton there is open a question about a nature of gravitation and about essence of Newtonian constant of gravitation G. This constant is determined experimentally. It is not known whether there is an analytical formula for determination of Newtonian constant of gravitation G. For this purpose it is necessary to find out: whether there is connection between Newtonian constant of gravitation G and other fundamental physical constants? In theoretical physics they try using together this major constant with Planck`s constant h and speed of light c for creation of the quantum theory of gravitation and for development of the uniform theories. Therefore, the question about primacy and independence of Newtonian constant of gravitation G goes out on the foreground.

When there was no so much fundamental physical constants proceeding from idea of independence of constants G, h, c, M.Planck has received on their basis new constants of length, mass, time. They have been called Planck units. Since the attempts to apply these constants for creation of the quantum theory of gravitation do not stop. Now, when the quantity of fundamental physical constants has reached already hundreds [1], it was arising a serious problem - what of them can really pretend on the status to be fundamental?  

2. CONSTANT G - COMPOUND CONSTANT 

In [5-12] the researches of fundamental physical constants are carried out. The task to reveal criteria of fundamentality was set and thus to reduce number of the pretenders on a title "it is true fundamental " constants. As a result, the group of primary constants, of which the fundamental constants [2-9] consist was open: 

• fundamental quantum of action h_u (h_u=7,69558071(63)•10^-37 J s),

• fundamental quantum of length l_u (l_u=2,817940285(31)•10^-15 m),

• fundamental quantum of time t_u (t_u=0,939963701(11)•10^-23 s),

• fine structure constant α (α =7,297352533(27)•10^-3 ),

• number π (π=3,141592653589).

The found group consisting of five primary superconstants [2,8] has allowed for the first time to reveal major feature of Newtonian constant of gravitation G. It turns out, that Newtonian constant of gravitation G is a compound constant and comprises Planck`s constant h and speed of light c.

They have succeeded to receive the value of Newtonian constant of gravitation G by a calculation on the basis of use of the following physical constants: speed of light in vacuum c, Planck`s constant h, Rydberg`s constant R_∞, fine structure constant α and number π . Thus it was found out that Newtonian constant of gravitation G is functionally dependent on other fundamental constants:

G=f (h , c, R_∞, α, π). 

The further researches have shown, that that Newtonian constant of gravitation G can be expressed by means of fundamental superconstants [2-9]: 

G=f (h_{u ,} l_u , t_u , α , π). 

3. TEN EQUIVALENT FORMULAS FOR CALCULATION OF NEWTONIAN CONSTANT OF GRAVITATION G. 

Opened group of universal superconstants and revealed global connection of fundamental constants have allowed to receive the mathematical formulas for calculation of Newtonian constant of gravitation G [2,3.5]. It turned out, there are several formulas. As confirmation to this, 10 equivalent formulas for calculation of that Newtonian constant of gravitation G below are given:

G = l_pl² bα/m_e,               G = 2πc³l_u²/αhD_o,          G = l_u³/t_u² m_e D_o,

G = l_u⁵/t_u³h_uD_o,               G = c³l_pl²α/h_u,               G = h_uα²/4πt_u m_pl²R_∞,

G = t_pl²c²bα/m_e,             G = c⁵t_pl²α/h_u,               G = h_u c⁵/T_pl² k²α,

G = l_u⁴10⁷/e²t_u²D_o,

From the given formulas it is visible that Newtonian constant of gravitation G is expressed with the help of other fundamental constants by very compact and beautiful relationships. All formulas for Newtonian constant of gravitation G keep coherence. Among constants, with the help of which Newtonian constant of gravitation G is presented, there are such constants: fundamental quantum h_u, speed of light c, fine structure constant α, Planck`s constant h, number π, fundamental metrics of space - time (l<sub>u</sub> , t<sub>u</sub> ), elementary mass m<sub>e</sub>, elementary charge e, Planck temperature Tpl, Planck units of length l<sub>pl</sub>, mass m<sub>pl</sub>, time t<sub>pl</sub>, Boltzmann`s constant k, fundamental acceleration b, Rydberg`s constant R_∞. It indicates that there is uniform essence of electromagnetism and gravitation and also fundamental unity at all physical constants. 

4. NEW VALUE OF NEWTONIAN CONSTANT OF GRAVITATION G. 

 Of much importance is that Newtonian constant of gravitation G can be expressed by means of electromagnetic constants. The values of electromagnetic constants are known with high accuracy. It allows to receive new exact value of Newtonian constant of gravitation G.

The numerical value of Newtonian constant of gravitation G was determined for the first time by English physicist Cavendish in 1798 on turned scales by measurement of attraction force between two spheres.

Modern value of Newtonian constant of gravitation G being recommended CODATA: 1998 [1]: 

G=6,673(10)•10^-11 m³kg^-1s^-2 .   

 From all universal physical constants the accuracy in determination of Newtonian constant of gravitation G is lowest.

As the accuracy in determination of constants of electromagnetism is high the calculated value of gravitational constant which on accuracy comes nearer to accuracy of electromagnetic constants is received on the basis of the formulas found by us. All above mentioned formulas give new value of Newtonian constant of gravitation G, which on accuracy almost on five orders is exacter than value known on today. The new value of Newtonian constant of gravitation G instead of four digits contains already 9 digits [2]: 

G=6,67286742(94)•10^-11 m³ kg^-1s^-2. 

The universal superconstants hu, lu, tu,a, ð enable to receive not only Newtonian constant of gravitation G but also other fundamental constants by calculated way. Practically complete coincidence of calculated values of fundamental physical constants with recommended CODATA:1998 [1] values of the same constants is a confirmation of correctness of the received results.            

The revealed compound essence of Newtonian constant of gravitation G allows to understand the reasons of occurrence of many problems in physics. In particular, it becomes clear why all attempts of the scientists to construct the quantum theory on the basis of constant basis received by means of addition of Planck`s constant h and speed of light c to Newtonian constant of gravitation G have ended without results. The reason was that Newtonian constant of gravitation G itself comprises constants Planck`s constant h and speed of light c, and the addition them did not give any new quality to basis (G, h, c).

It is possible to get acquainted more in detail with these and other results of research of fundamental physical constants on sites:

• http://www.sciteclibrary.ru

• www.photcoef.com/236.html

• www.jsup.or.jp/shiryo/PDF/0900z53.pdf

• http://www.rusnauka.narod.ru

• http://www.n-t.org/tp/ng/nfk.htm

REFERENCE

1. Peter J. Mohr and Barry N.Taylor. CODATA Recommended Values of the Fundamental Physical Constants: 1998; Physics.nist.gov/constants. Constants in the category "All constants"; Reviews of Modern Physics, Vol 72, No. 2, 2000.

2. Nikolay Kosinov, Physical vacuum and gravitation. Physical vacuum and nature, N4, 2000.

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4. Nikolay Kosinov, Five universal superconstants underlying all fundamental constants, laws and formulas of physics and cosmology. Topical problems of natural sciences of a beginning of century. Materials of the international conference August 21- 25, 2000, St.-Petersburg, Russia, publishing house: "Anatoliya", 2001, p.p. 176 - 179.

5. Nikolay Kosinov, Universal physical superconstants. http://piramyd.express.ru

6. Nikolay Kosinov, Electrodynamics of physical vacuum. Physical vacuum and nature, N1, 1999.

7. Nikolay Kosinov, The laws of unitron theory of physical vacuum and new fundamental physical constants. Physical vacuum and nature, N3, 2000.

8. Nikolay Kosinov, Vacuum - hypothesis and basic theorems of unitron theory of physical vacuum. Physical vacuum and nature, N2, 1999.

9. Nikolay Kosinov, Problems of an origin - the latest direction of physical researches. Physical vacuum and nature, N4, 2000.

10. Nikolay Kosinov, The solving problems of an origin - basic task of unitron theory of physical vacuum. Physical vacuum and nature, N3, 2000.

11. Nikolay Kosinov, A problem of vacuum in a context of unsolved problems of physics. Physical vacuum and nature, N3, 2000.

12. Nikolay V. Kosinov, Shanna N. Kosinova “GENERAL CORRELATION AMONG FUNDAMENTAL PHYSICAL CONSTANTS.” Journal of New Energy , 2000 , Vol. 5, no. 1, pages 134 -135.

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