# Реферат: Геометрия пространства двойной планетной системы: Земля - Луна

Mathematical Formulas for Calculation of Newtonian Constantof Gravitation G*Dr. Nikolay Kosinov*

** **

**ABSTRACT**

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

The group of primary constants consisting offive universal superconstants [2,4-6] is open. The researches have shown thatNewtonian constant of gravitation **G **can be expressed by means offundamental superconstants [2-9]:

**G=f (hu, lu, tu, />,/>).**

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

/>

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

As it is known, the form of Newtonian law of theworld gravitation itself v proportionality of force to masses and reciprocalproportionality to the square of the distance is checked up with much moreaccuracy than that of determination of Newtonian constant of gravitation **G**.Therefore, Newtonian constant of gravitation **G **is imposing basicrestriction on exact determination of gravitational forces. The unsufficientaccuracy of determination of Newtonian constant of gravitation **G** is thebasic interfering factor at determination of masses of heavenly bodies, theirstructure and evolution that creates problems for modern astronomy and forspace researches. From times of Newton there is open a question about a natureof gravitation and about essence of Newtonian constant of gravitation **G**.This constant is determined experimentally. It is not known whether there is ananalytical formula for determination of Newtonian constant of gravitation **G**.For this purpose it is necessary to find out: whether there is connectionbetween Newtonian constant of gravitation **G** and other fundamental physicalconstants? In theoretical physics they try using together this major constantwith Planck`s constant **h** and speed of light **c** for creation of thequantum theory of gravitation and for development of the uniform theories.Therefore, the question about primacy and independence of Newtonian constant ofgravitation **G** goes out on the foreground.

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

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

fundamental quantum of action**hu**(

**hu=7,69558071(63)•10-37 J s),**fundamental quantum of length

**lu**(

**lu=2,817940285(31)•10-15 m),**fundamental quantum of time

**tu**(

**tu=0,939963701(11)•10-23 s**)

**,**fine structure constant

**/>**(/>

**=7,297352533(27)•10-3 ),**number

**/>(/>=3,141592653589).**

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

They have succeeded to receive the value ofNewtonian constant of gravitation **G** by a calculation on the basis of useof the following physical constants: speed of light in vacuum **c**,Planck`s constant **h**, Rydberg`s constant/>**, **fine structure constant />and number/>. Thus it wasfound out that Newtonian constant of gravitation **G** is functionallydependent on other fundamental constants:

/>

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

**G=f (hu, lu, tu, />,/>).**

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

**/>**

From the given formulas it is visible thatNewtonian constant of gravitation **G** is expressed with the help of otherfundamental constants by very compact and beautiful relationships. All formulasfor 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**hu, **speed oflight **c**, fine structure constant**?,** Planck`s constant **h**,number**?**, fundamental metrics of space — time **(lu, tu)**, elementary mass **me**, elementary charge **e**,Planck temperature **Tpl**, Planck units of length **lpl**,mass **mpl**, time **tpl**, Boltzmann`s constant **k**,fundamental acceleration **b**, Rydberg`s constant/>. It indicates that there isuniform essence of electromagnetism and gravitation and also fundamental unityat all physical constants.

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

The numerical value of Newtonian constant ofgravitation **G** was determined for the first time by English physicistCavendish in 1798 on turned scales by measurement of attraction force betweentwo spheres.

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

**G=6,673(10)•10-11 m3kg-1s-2.**

From all universal physical constants theaccuracy in determination of Newtonian constant of gravitation **G** islowest.

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

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

The universal superconstants hu, lu, tu,a, Пenable to receive not only Newtonian constant of gravitation **G** but alsoother fundamental constants by calculated way. Practically complete coincidenceof calculated values of fundamental physical constants with recommendedCODATA:1998 [1] values of the same constants is a confirmation of correctnessof the received results.

The revealed compound essence of Newtonianconstant of gravitation **G** allows to understand the reasons of occurrenceof many problems in physics. In particular, it becomes clear why all attemptsof the scientists to construct the quantum theory on the basis of constantbasis received by means of addition of Planck`s constant **h** and speed oflight **c **to Newtonian constant of gravitation **G** have ended withoutresults. The reason was that Newtonian constant of gravitation **G** itselfcomprises constants Planck`s constant **h** and speed of light **c**, andthe addition them did not give any new quality to basis (**G, h, c**).

It is possible to get acquainted more in detailwith these and other results of research of fundamental physical constants onsites:

__www.sciteclibrary.com/
www.photcoef.com/236.html
www.jsup.or.jp/shiryo/PDF/0900z53.pdf
www.rusnauka.narod.ru__

www.n-t.org/tp/ng/nfk.htm

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