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# Determination of the Newtonian gravitational constant G with time-of-swing method.

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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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... After realizing the seriousness of measuring G, scientists made much more effort finding and solving systematic errors when improving previous experimental methods. Several precise values of G were published between 2000 and 2010 [31][32][33][34][35][36][37][38][39]. According to the addition of these values of G, the CODATA 2002, CODATA 2006 and CODATA 2010 recommended values are (6.6742 ...
... These new results did not resolve the considerable disagreements that have existed among the measurements of G for the past 20 years. The weighted mean of the fourteen values of G [21,25,26,[31][32][33][34][35][36][37][38][39]41,42,44] are adopted in the CODATA 2014 recommended value, which is (6.674 08 ± 0.000 31) × 10 −11 m 3 kg −1 s −2 with a relative uncertainty of 47 ppm [4]. Compared with the uncertainties of previous recommended values, it is improved by a factor of 2. But this value remains the least precisely known among all of the fundamental constants. ...
... In 2018, G values measured with two independent methods, the time-of-swing (ToS) method and angular acceleration feedback (AAF) method, were obtained with the smallest uncertainty reported to date and both agreed with the CODATA 2014 recommended value to within two standard deviations [50]. The thirteen values of the Newtonian gravitational constant [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44]50,51] measured after 2000 are listed in Table 3 and shown in Fig. 2. Further experimental details are given in the next section. ...
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The Newtonian gravitational constant G, which is one of the most important fundamental physical constants in nature, plays a significant role in the fields of the theoretical physics, geophysics, astrophysics, and astronomy. Although G was the first physical constant to be introduced in the history of science, it is considered to be one of the most difficult to measure accurately so far. Over the past two decades, eleven precision measurements of gravitational constant have been performed, and the latest recommended value for G published by the Committee on Data for Science and Technology (CODATA) is (6.67408 ± 0.00031) × 10−11 m3kg−1s−2 with a relative uncertainty of 47 parts per million (ppm). This uncertainty is the smallest one compared with the previous CODATA recommended values of G, however, it remains a relatively large uncertainty among other fundamental physical constants. This paper briefly reviews the history of G measurement, and also introduces eleven values of G adopted in the CODATA-2014 after the year 2000 and our latest two values published in 2018 using two independent methods.
... 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. ...
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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
... Most of the experiments performed so far, including recent ones [121,122,123,124,125], were based on the torsion pendulum or torsion balance scheme as in the experiment by Cavendish. Some experiments were based on different schemes: a beam-balance system [126], a laser interferometry measurement of the acceleration of a freely falling test mass [127], experiments based on Fabry-Perot or microwave cavities [128,129,130]. ...
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Article
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.
Presentation
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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.
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