_{1}

^{*}

In this paper, we are going to rely on the first law in physics through which we can obtain a precise ideal value of the universal gravitational constant, a thing which has not happened so far. The significance of this law lies in the fact that, besides determining a precise ideal value of the gravitational constant, it connects three different physical disciplines together, which are mechanics, electromagnetism and thermodynamics. It is what distinguishes this from other law. Through this law, we have created the theoretical value of the gravitational constant
G_{i} and we found it equivalent to 6.674010551359 × 10
^{-11} m
^{3}
·kg
^{-1}
·s
^{-2}. In the discussion, the table of measurements of the gravitational constant was divided into three groups, and the average value of the first group
G
_{1} which is the best precision, equals the following sum 6.67401×10
^{-11} m
^{3}
·kg
^{-1}
·s
^{-2}, and it’s the same equal value to the ideal value
G_{i} that results from the law, as shown through our research that any other experimental values
must not exceed the relative standard uncertainty which has a certain amount that is equivalent to a value of 5.325×10
^{-5}
and that’s a square value of the fine-structure constant.

Although 3 centuries have elapsed since Newton set forth his gravitational law, physiology has been unable so far to create an exact theoretical value for the universal gravitational constant with no available values of the gravitational constant values except those values concluded by scientific experiments, especially conducted for obtaining the most accurate values of this constant.

We are going, in this research, to surmount this problem by way of setting forth a universal gravitational constant sole theory value, to be calculated through an index of a law known in the Khromatic theory as “The Law of Gravitational Constant” [

To overcome this problem, we put forth a supposition that a certain marginal velocity can be a basis for calculating a gravitational greater value acceptable as an ideal value within a certain error rate. And to ascertain the validity of the hypothesis we compared, through discussion, the values we obtained with those on the gravitation

The law of gravitational constant looks like this:

as,

We are not going in our discussion, to deal with the method of the inference of this law, because of that it will be through another search that will be published completely, but we will content ourselves by reviewing the law and finds the precise ideal value of gravity through it.

Taking the values of the constants above from an abbreviated list of the 2014 CODATA recommended values of the fundamental constants of physics and chemistry, we get

So, using substitution in the value of constants we get the precise value of the gravitation constant equaling:

Perhaps the ideal precise value of the gravitation constant is suitable for the static large blocks or those having negligible velocity-induced increment.

As for small masses moving at high speeds, it is more suitable to deal with relativity when calculated, however, we can handle expected values of the gravitational constant for experiments in which the body's velocity is so limited that the block's increment may be overlooked.

And to find such values, we can suppose that the block’s laboratory speed limit should not exceed the orbital speed of electron in an atom of hydrogen and consequently the maximum expected gravitational value should not exceed a maximum value of the gravitational constant that is calculable using the equation.

And on calculation of this value we get the following:

Hence we can deduce the ideal standard uncertainty vale

And the ideal value of the relative standard uncertainty is

which is a somewhat an acceptable value.

Since

Thus

and

In this discussion we are going to compare the ideal values we had got by theoretical means and the documented experimental values in CODATA gravitational tables, and we will show that the values are close in both cases.

In this table there are three groups of measurements [

・ The first such group consists of six measurements with the average value of

Standard uncertainty

・ The second one consists of four measurements with the average value of

Standard uncertainty

・ The third one consists of one measurement with the value of

Standard uncertainty

Therefore, we conclude that the ideal value of the gravitational constant equals the sum

Source | Identification^{a} | Method | 10^{−11} m^{3}∙kg^{−1}∙s^{−2} | Rel.stand. uncert. ur |
---|---|---|---|---|

Luther and Towler (1982) | NIST-82 | Fiber torsion balance, dynamic mode | 6.67248 (43) | 6.4 × 10^{−5} |

Karagioz and Izmailov (1996) | TR&D-96 | Fiber torsion balance, dynamic mode | 6.6729 (5) | 7.5 × 10^{−5} |

Bagley and Luther (1997) | LANL-97 | Fiber torsion balance, dynamic mode | 6.67398 (70) | 1.0 × 10^{−4} |

Gundlach and Merkowitz (2000, 2002) | UWash-00 | Fiber torsion balance, Dynamic compensation | 6.674255 (92) | 1.4 × 10^{−5} |

Quinn et al. (2001) | BIPM-01 | Strip torsion balance, Compensation mode, static deflection | 6.67559 (27) | 4.0 × 10^{−5} |

Kleinevoß (2002) and Kleinvoß et al. (2002) | UWup-02 | Suspended body, displacement | 6.67422 (98) | 1.5 × 10^{−4} |

Armstrong and Fitzgerald (2003) | MSL-03 | Strip torsion balance, compensation mode | 6.67387 (27) | 4.0 × 10^{−5} |

Hu, Guo, and Luo (2005) | HUST-05 | Fiber torsion balance, dynamic mode | 6.67222 (87) | 1.3 × 10^{−4} |

Schlamminger et al. (2006) | UZur-06 | Stationary body, weight change | 6.67425 (12) | 1.9 × 10^{−5} |

Luo et al. (2009) and Tu et al. (2010) | HUST-09 | Fiber torsion balance, dynamic mode | 6.67349 (18) | 2.7 × 10^{−5} |

Parks and Faller (2010) | JILA-10 | Suspended body, displacement | 6.67234 (14) | 2.1 × 10^{−5} |

which is extremely close to the average value G_{1}, that equals the following sum

So we can choice the first group of G measurements as the best precision group of all others.

We learn from

That is, based upon the above table, the experimental value of the gravitational constant should range from a maximum value of

which is extremely close to the gravitational experimental value, that equals the following sum

When comparing the ideal quantity of standard uncertainty, which equals

To its counterpart mentioned in

we find great similarity in values.

Likewise, when comparing the ideal value of the relative standard uncertainty, which equals:

To its counterpart contained in

Newtonian constant of gravitation G | |
---|---|

Value | 6.67408 × 10^{−11} m^{3}∙kg^{−1}∙s^{−2} |

Standard uncertainty ∆G | 0.00031 × 10^{−11} m^{3}∙kg^{−1}∙s^{−2} |

Relative standard uncertainty u_{r} | 4.7 × 10^{−5} |

Concise form | 6.67408(31) × 10^{−11} m^{3}∙kg^{−1}∙s^{−2} |

ideal Newtonian constant of gravitation G_{i} | |
---|---|

Value | 6.6740105 × 10^{−11} m^{3}∙kg^{−1}∙s^{−2} |

fine-structure constant α | 7.2973525664 × 10^{−3} |

Standard uncertainty ∆G | 0.000 3554 × 10^{−11} m^{3}∙kg^{−1}∙s^{−2} |

Relative standard uncertainty | 5.325 × 10^{−5} α^{2} |

Concise form | 6.6740105 (3554) × 10^{−11} m^{3}∙kg^{−1}∙s^{−2} |

we also find great similarity in values.

Therefore, we conclude that all ideal values we have obtained through the theoretical equations are extremely close to their experimental counterparts which we had got from

There is a precise ideal value of the universal gravitational constant which equals 6.674010551359 × 10^{−11}.

That may be calculated through a theoretically concluded equation of its own, and the cause of discrepancy of the gravitation value is attributable to the circumstances of the experiment as well as the sophistication of the nature and speed of particles used to measure the gravitational constant in such experiments.

Abou Layla, A.E.K.S. (2017) Precise Ideal Value of the Universal Gravitational Constant G. Journal of High Energy Physics, Gravitation and Cosmology, 3, 248-253. https://doi.org/10.4236/jhepgc.2017.32020