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We present a new value of the Newtonian gravitational constant G by using the time-of-swing method. Several improvements greatly reduce the uncertainties: (1) measuring the anelasticity of the fiber directly; (2) using spherical source masses minimizes the effects of density inhomogeneity and eccentricities; (3) using a quartz block pendulum simplifies its vibration modes and minimizes the uncertainty of inertial moment; (4) setting the pendulum and source masses both in a vacuum chamber reduces the error of measuring the relative positions. By two individual experiments, we obtain G = 6.673 49(18) x 10;{-11} m;{3} kg;{-1} s;{-2} with a standard uncertainty of about 2.6 parts in 10;{5}.

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... The basis of most of the experiments to measure the value of is the Newton's law of universal gravitation ( = ⁄ ) and torsion Balance [1]. In these experiments [2][3][4][5] the value of is obtained according to the Newton's law and the known values of , , and . In addition, the other various experiments with different methods have been carried out to measure the value of such as the ones using very cold atoms and atom interferometry [6][7][8][9]. ...

The value of gravitational constant has been measured after the 18th century by various methods (such as using the torsion balance, very cold atoms and atom interferometry) in the macroscopic scale, namely in the distance more than one micro meter from the matter. But its amount at the vicinity of matter (r<1Å or r < 1nm) has not yet been measured. It was not acceptable for me to use the current value of gravitation constant, which its value was derived in macroscopic scale, in the microscopic and subatomic scale. This was the idea that led to writing this article. Here we show that we are able to consider a large value for the gravitational constant, G, at the vicinity of matter (r<1Å). Here we show that there are no experimental barriers for this hypothesis. Considering a large value for G, at the vicinity of matter, the stability of atom and atomic and molecular bonds can be explained by a different method. This article seems to pave the way to remove the strong interaction by gravitation force. Maybe this is a way to unite forces. In this article, we show only the beginning of a path. Certainly, the examination of the ideas of this article needs further investigation.

... Small correlations with the 2009 TOS determination of G at HUST (Luo et al., 2009) exist because the same source masses were used in TOS-II, and the same measurement instrumentation and methods for the determination of various systematic uncertainties were used. A conservative estimate for the correlation coefficient between HUST-09 and HUST T -18 is 0.068. ...

We report the 2018 self-consistent values of constants and conversion factors of physics and chemistry recommended by the Committee on Data of the International Science Council. The recommended values can also be found at physics.nist.gov/constants. The values are based on a least-squares adjustment that takes into account all theoretical and experimental data available through 31 December 2018. A discussion of the major improvements as well as inconsistencies within the data is given. The former include a decrease in the uncertainty of the dimensionless fine-structure constant and a nearly two orders of magnitude improvement of particle masses expressed in units of kg due to the transition to the revised International System of Units (SI) with an exact value for the Planck constant. Further, because the elementary charge, Boltzmann constant, and Avogadro constant also have exact values in the revised SI, many other constants are either exact or have significantly reduced uncertainties. Inconsistencies remain for the gravitational constant and the muon magnetic-moment anomaly. The proton charge radius puzzle has been partially resolved by improved measurements of hydrogen energy levels.

... Then we can determine the value of G and the relative uncertainty via the detection of |∆ν − |. In Fig.6(a), the adopted values of G in CODATA-2014 adjustment [5,[19][20][21][22][23][24][25][26][27][28][29][30][31][32][33] are illustrated according to [2]. To visualize our result (Eq.(23)), we plot |∆ν − | as a function of G in Fig.6(b)-(c), where the parameters used are ε = 10 −2 ω r , and ω r = 2 × 10 9 Hz. ...

We develop a quantum mechanical method of measuring the Newtonian constant of gravitation, G. In this method, an optomechanical system consisting of two cavities and two membrane resonators is used. The added source mass would induce the shifts of the eigenfrequencies of the supermodes. Via detecting the shifts, we can perform our measurement of G. Furthermore, our system can features exceptional point (EP) which are branch point singularities of the spectrum and eigenfunctions. In the paper, we demonstrate that operating the system at EP can enhance our measurement of G. In addition, we derive the relationship between EP enlarged eigenfrequency shift and the Newtonian constant. This work provides a way to engineer EP-assisted optomechanical devices for applications in the field of precision measurement of G

A simple, cost-effective and high-accuracy measurement of parallelism by dual autocollimators is proposed. A differential measurement was chosen to eliminate most of the environmental noises and systematic errors. The accuracy of parallelism measurement can reach the level of 1.6 µrad (1σ). This method can be widely used for parallelism measurements of components with reflective coating, such as glass blocks in metrology laboratories and test masses in the Gravitational Reference Sensor.

We develop a quantum mechanical method of measuring the Newtonian constant of gravitation, G. In this method, an optomechanical system consisting of two cavities and two membrane resonators is used. The added source mass would induce the shifts of the eigenfrequencies of the supermodes. Via detecting the shifts, we can perform our measurement of G. Furthermore, our system can features exceptional point (EP) which are branch point singularities of the spectrum and eigenfunctions. In the paper, we demonstrate that operating the system at EP can enhance our measurement of G. In addition, we derive the relationship between EP enlarged eigenfrequency shift and the Newtonian constant. This work provides a way to engineer EP-assisted optomechanical devices for applications in the field of precision measurement of G.

First of all, the presentation material is simplified in order, on the one hand, to get more questions and criticism, on the other hand, to prevent, perhaps, the readers' possible dream of reaching an incredibly high measurement accuracy.
I can honestly say that I was not able during 40 years to answer one very obvious question: how to simplify and short the duration of research, and to reduce the cost of the project without problems and fatal errors? Now the answer is for your consideration.
I use a theoretically-proved information approach for the model's accuracy definition because, I think, it is more relevant. The second, I am going to prove that the aberration in modeling, in other words distortion of reality, is inherent before the formulation of any physical, and even more so, mathematical statement. Additional task is to calculate numerically the degree of depravity of the physical phenomena image.

This article is motivated by uncertainty in experimental determinations of the gravitational constant, G, and numerous anomalies of up to 0.5 percent in Newtonian gravitational force on bodies within the solar system. The analysis sheds new light through six natural experiments within the solar system, which draw on published reports and astrophysical databases, and involve laboratory determinations of G, orbital dynamics of the planets and the moons of Earth and Mars, and non-gravitational acceleration (NGA) of ‘Oumuamua and comets. In each case, values are known for all variables in Newton’s Law , except for the gravitational constant, G. Analyses determine the gravitational constant’s observed value, , which—across the six settings—varies with the mass of the smaller, moving body, m, so that . While further work is required, this examination shows a scale-related Newtonian gravity effect at scales from benchtop to Solar System, which contributes to the understanding of symmetry in gravity and has possible implications for Newton’s Laws, dark matter, and formation of structure in the universe.

The torsion balance, consisting of a rigid balance beam suspended by a fine thread, is an ancient scientific instrument, yet it is still a very sensitive force sensor to date. As the force sensitivity is proportional to the lengths of the beam and thread, but inversely proportional to the fourth power of the diameter of the thread, nanomaterials should be ideal building blocks for torsion balances. Here, we report a torsional balance array on a chip with the highest sensitivity level enabled by using a carbon nanotube as the thread and a monolayer graphene coated with Al nanofilms as the beam and mirror. It is demonstrated that the femtonewton force exerted by a weak laser can be easily measured. The balances on the chip should serve as an ideal platform for investigating fundamental interactions up to zeptonewton in accuracy in the near future.

An approach to determine the period of a torsion pendulum was described using correlation method. It was observed that the method can not only suppress the disturbance of white noise, but it is also insensitive to drift and damping of the torsion pendulum. It was also observed that an estimate of the frequency based on this method is an approximate minimum variance unbiased estimator. It was found that there is bigger noise other than that of the drift of temperature that makes the period of torsion pendulum unstable.

A method with scanning electron microscopy (SEM) is presented to measure the density inhomogeneity of the stainless steel (SS316) sphere prepared for measuring G using time-of-swing method. The experimental result shows that the relative density inhomogeneity of the sphere is better than 5.9 × 10−4 over the volume of 0.272 × 0.234 × 0.005 mm3. If we assume that the density inhomogeneity of the spheres used in our G measurement is the same as that of the sphere destroyed in testing, it will contribute to G value with an uncertainty of less than 0.034 ppm in our G measurement. Furthermore, the mass centre offset from the geometric centre of the sphere will be less than 4.3 × 10−4 μm due to this inhomogeneity.

The density inhomogeneity of a glass pendulum is determined by an optical interference method. The relative variations of the densities over a volume with sizes of 5 × 5 × 5 mm3 are (0.64 ± 0.97) × 10−5 and (0.99 ± 0.92) × 10−5 for the K9 glass and silica glass pendulum, respectively. These variations of densities contributing to the relative uncertainties of the Newtonian gravitational constant G are 0.20 ppm and 0.21 ppm in our experiment on measurement of G.

The Newtonian gravitational constant G is determined by means of a
high-Q torsion pendulum and the time-of-swing method, in which the
period of the pendulum is altered by the presence of two 6.25-kg
stainless steel cylinders. The nonlinear fitting method is used to
extract the frequencies from the angle-time data of the pendulum. The
resulting value of G is (6.6699+/-0.0007)×10-11
m3 kg-1 s-2.

The thermoelastic and the nonlinear properties of a torsion fiber were studied. A symmetric disk torsion pendulum was designed to measure the temperature coefficient of the torsion spring constant of a tungsten fiber at room temperature, and the result shows that the ambient temperature fluctuation with +/-1 °C would introduce a considerable uncertainty about -/+165 ppm in the torsion spring constant of the fiber. It is suggested that the thermoelasticity of the torsion fiber should be measured in a precision torsion pendulum experiment.

The numerical solution of non-linear equations shows that the abnormal mode observed in our torsion pendulum experiments is an intrinsic mode of the pendulum. Further analysis shows that the amplitude of abnormal mode increasing with of swing modes can be suppressed with a magnetic damper effectively.

Eccentricities of the mass center from the geometric center of two cylindrical source masses used in the HUST-99 measurement of the Newtonian gravitational constant $G$ are determined by means of an electronic balance. Considering a linear density distribution of source masses as well as the effect of the air buoyancy, our value of $G$ should be revised to be $6.6723(9)\ifmmode\times\else\texttimes\fi{}{10}^{$-${}11}\text{ }\text{ }{\mathrm{m}}^{3}\text{ }{\mathrm{kg}}^{$-${}1}\text{ }{\mathrm{s}}^{$-${}2}$, which is 0.036% larger than our previous published value in Phys. Rev. D 59, 042001 (1999).

In the processing of temperature and atmospheric pressure data observed in an
underground laboratory, the cross-correlation equilibrium method is proposed for
determining the phase of a signal with a particular frequency. This method
effectively suppresses the influence of white noise and reduces the phase errors
derived from higher order harmonics and any direct current component in the
experimental signal. The upper limit of phase error due to the other frequencies in
the experimental data is estimated. Theoretical analysis and the result of
computational simulation show that the signal-to-noise ratio of the phase
determined is improved significantly.

The height of the centre of mass above the base of a 1 kg artefact can be located easily within a precision of several micrometres using a simple 'weighbridge'. Analysis of the device, its realization and performance are presented. The method has applications in high-precision mass metrology and certain gravitational experiments.