The BIPM measurements of the Newtonian constant of gravitation,
            <i>G</i>

Quinn, Terry; Speake, C. C.; Parks, Harold; Davis, Richard

doi:10.1098/rsta.2014.0032

Cited by 42 publications

(42 citation statements)

References 26 publications

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“…However, there is one caveat which leads to a very specific MOND correction of the static deflection G-results for a gravitational pendulum: In order to convert the measured deflection angle into a torque, from which G is determined, the restoring torque coefficient   g needs to be determined experimentally. Usually  is determined from a measurement of the pendulum frequency 0 [24]. Since the pendulum amplitude determines the MOND-related frequency increase 0 of the pendulum, the corresponding relative increase of  is given by The case of a mixed gravitational/electromagnetic restoring force is of particular interest for the socalled "time-of-swing" (ToS), which has gained popularity in recent years.…”

Section: Figs 2c and Dmentioning

confidence: 99%

“…This leads to the already mentioned nearly 100% gravitational character of the restoring torque. In fact, the values reported in [24] for the gravitational and electromagnetic components are g = 2.1810 -4 Nm/rad and em = 7.510 -6 Nm/rad, respectively, leading to  = 0.033 according to Eq. 9.…”

Section: No 4 and 5 Quinn Et Almentioning

confidence: 99%

“…7 will be further discussed in section 5. [24] and the AFA mode of the experiment by Li et al [22]. In order the visualize the BIPM results determined by the two methods, the electric servo and static deflection results are displayed with their identical an/a0 value moved to the left and right, respectively.…”

Section: No 7 Gundlach and Merkowitzmentioning

confidence: 99%

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Evidence for modified Newtonian dynamics from Cavendish-type gravitational constant experiments

Klein

2020

Class. Quantum Grav.

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Recent experimental results for the gravitational constant G from Cavendish-type experiments were analysed in the framework of Modified Newtonian Dynamics (MOND). MOND corrections were applied to the equation of motion of a pendulum, under the assumption that the magnitude of the horizontal time dependent gravitational acceleration determines the amount of MOND corrections. The large vertical component of the local gravitational field of the earth is fully compensated by the alignment of the torsion pendulum in accordance with Newton's third law and therefore not considered for MOND corrections. From the analysis of the MOND corrected equation of motion of a realistic torsion pendulum with mixed gravitational and electromagnetic restoring torque simple rules for meaningful MOND corrections of measured G values determined by different operational modes of Cavendish type G experiments were derived. Based on this analysis the reported discrepancies for G determined by "static deflection" and "electrostatic servo" methods of the "BIPM" experiment by Quinn et al. and between time-of-swing and angular acceleration feedback methods for the "HUST" experiment by Li et al. could be fully resolved by MOND corrections using one common MOND interpolation function, determined by a one parameter fit. The MOND corrected "BIPM" and "HUST" results, along with other "single method" results from G experiments by Gundlach and Merkovitz, Schlamminger et al. and Newman et al. lead to an average G value of 6.6742210 -11 m 3 kg -1 s -2 with a standard deviation of 12.5 ppm only. The applied MOND correction procedure and the fitted interpolation function employed for the G experiments were found to be consistent with the most viable MOND fits to galaxy rotation curves.

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Section: Figs 2c and Dmentioning

confidence: 99%

Section: No 4 and 5 Quinn Et Almentioning

confidence: 99%

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Evidence for modified Newtonian dynamics from Cavendish-type gravitational constant experiments

Klein

2020

Class. Quantum Grav.

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“…In the cases where these tricks are not applicable practical calculations are very computationally intensive to perform. The computational complexity often leads to the need to treat extended bodies as point masses after performing tedious case-by-case calculations to show that this assumption has negligible effect on the final result [8,9]. In this work, taking inspiration from the field of computer graphics [10], we derive a method to reduce the calculation of the force between a point mass and any arbitrary shape to a sum of one-dimensional integrals rather than a three-dimensional integral.…”

Section: Introductionmentioning

confidence: 99%

“…If the matrix is singular the no integrals need to be computed. If the matrix is non-singular then equation(8) can be evaluated with Gaussian quadrature.…”

mentioning

confidence: 99%

A vector field approach to calculating gravitational forces

Stirling¹

2017

New J. Phys.

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Calculation of gravitational forces is essential for many fundamental measurements, such as determining the gravitational constant or investigating violations of the inverse square law. These calculations, even with modern computational power, are slow and tedious. Improved calculation efficiency allows an experimentalist to easily check the effect of possible systematic biases and to ease the process of instrument design. Many gravitational measurements are expanded in terms of multipole moments for efficient calculations, however for many experimental geometries these do not converge, leaving awkward sextuple integrals. In this work we introduce a modified approach to the calculation which reduces the force between a point mass and any arbitrary object to a sum of single integrals. The force between any two objects can then be calculated as a quadruple rather than a sextuple integral.

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Progress in Precise Measurements of the Gravitational Constant

Liu

et al. 2019

Annalen der Physik

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The Newtonian gravitational constant G, which is one of the earliest fundamental constants introduced by human beings, plays an important role in cosmology, astrophysics, geophysics, metrology, and so on. In spite of the measurement of G having a relative longer history and more than 200 measurement results having been obtained during the past 200 years, G still remains the least precisely known among all fundamental physical constants up to now. Over the past three decades, many experimental physicists devoted themselves to the G measurement with various methods and resulted in a dozen precise values of G. However, the determined results are still in poor agreement with each other. A brief overview of the significance of the gravitational constant G is given herein, followed by an introduction into the history of G measurement. A summary of the five latest precise measurements performed during the past few years is presented. Finally, an outlook of the future development of G measurement is provided.

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The BIPM measurements of the Newtonian constant of gravitation, G

Cited by 42 publications

References 26 publications

Evidence for modified Newtonian dynamics from Cavendish-type gravitational constant experiments

Evidence for modified Newtonian dynamics from Cavendish-type gravitational constant experiments

A vector field approach to calculating gravitational forces

Progress in Precise Measurements of the Gravitational Constant

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