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Journal articles on the topic 'Newtonian gravitational constant'

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Published: 10 March 2023

Last updated: 11 March 2023

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1

UV, Satya Seshavatharam, and Lakshminarayana S. "Final unification with three gravitational constants associated with nuclear, electromagnetic and gravitational interactions." International Journal of Advanced Astronomy 4, no. 2 (November 17, 2016): 105. http://dx.doi.org/10.14419/ijaa.v4i2.6799.

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By introducing two large pseudo gravitational constants assumed to be associated with strong and electromagnetic interactions, we make an attempt to combine the old Abdus Salam’s ‘strong gravity’ concept with ‘Newtonian gravity’ and try to understand the constructional features of nuclei, atoms and neutron stars in a unified approach. From the known elementary atomic and nuclear physical constants, estimated magnitude of the Newtonian gravitational constant is (6.66 to 6.70) x10-11 m3/kg/sec2. Finally, by eliminating the proposed two pseudo gravitational constants, we inter-related the Newtonian gravitational constant, Fermi’s weak coupling constant and Strong coupling constant, in a generalized approach.

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2

UV, Satya Seshavatharam, and Lakshminarayana S. "To fit Fermi’s weak coupling constant with three gravitational constants." International Journal of Physical Research 6, no. 1 (December 28, 2017): 8. http://dx.doi.org/10.14419/ijpr.v6i1.8781.

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By considering three virtual gravitational constants assumed to be associated with gravitational, electromagnetic and strong interactions, Fermi’s weak coupling constant can be shown to be a natural manifestation of microscopic quantum gravity. As our approach is heuristic and completely different from the current methods of estimating the Newtonian gravitational constant, concerning the call of ‘Ideas lab 2016’ organized by NSF, we appeal for inclusion of this theoretical work as a project under the unification scheme. Estimated magnitudes of Fermi’s weak coupling constant and Newtonian gravitational constant are 1.44021X10(-62) J.m3 and 6.679856X10(-11) m3/kg/sec2 respectively.

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3

Ognean, Teodor. "Some considerations on the Newtonian gravitational constant G measurements." Physics Essays 32, no. 3 (September 12, 2019): 292–97. http://dx.doi.org/10.4006/0836-1398-32.3.292.

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Certain relationships between the Newtonian gravitational constant, the Planck constant, and the square of the fine structure constant, established by dimensional analysis, are presented. Here we show that, based on these relationships, a more exact value for the Newtonian gravitational constant G equal to 6.67409076 × 10−11 m3 kg−1 s−2 can be calculated. In this way, these relationships could be used as a nonconventional tool for establishing a G gravitational constant value very close to the real one. It is considered that the difference between this calculated value and the values provided by the most accurate measurements of this constant is very important, whereas such difference could reflect certain, subtle and unknown “links” existing between the natural phenomena. This article also highlights a very interesting relationship between the Newtonian gravitational constant G, the square of the fine structure constant (α−1)2, and the Planck constant h, having the following form: 2XG = π (10Xα/2Xh)2, where XG, 10Xα, and Xh are the normalized values (dimensionless) of these constants.

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4

Xue, Chao, Jian-Ping Liu, Qing Li, Jun-Fei Wu, Shan-Qing Yang, Qi Liu, Cheng-Gang Shao, Liang-Cheng Tu, Zhong-Kun Hu, and Jun Luo. "Precision measurement of the Newtonian gravitational constant." National Science Review 7, no. 12 (July 22, 2020): 1803–17. http://dx.doi.org/10.1093/nsr/nwaa165.

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Abstract 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 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 the gravitational constant have been performed, and the latest recommended value for G published by the Committee on Data for Science and Technology (CODATA) is (6.674 08 ± 0.000 31) × 10−11 m3 kg−1 s−2 with a relative uncertainty of 47 parts per million. This uncertainty is the smallest compared with previous CODATA recommended values of G; however, it remains a relatively large uncertainty among other fundamental physical constants. In this paper we briefly review the history of the G measurement, and introduce eleven values of G adopted in CODATA 2014 after 2000 and our latest two values published in 2018 using two independent methods.

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5

FALKENBERG, SVEN, and SERGEI D. ODINTSOV. "GAUGE DEPENDENCE OF THE EFFECTIVE AVERAGE ACTION IN EINSTEIN GRAVITY." International Journal of Modern Physics A 13, no. 04 (February 10, 1998): 607–23. http://dx.doi.org/10.1142/s0217751x98000263.

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We study the gauge dependence of the effective average action Γk and Newtonian gravitational constant using the RG equation for Γk. Then we truncate the space of action functionals to get a solution of this equation. We solve the truncated evolution equation for the Einstein gravity in the De Sitter background for a general gauge parameter α and obtain a system of equatons for the cosmological and Newtonian constants. Analyaing the running of the gravitational constant we find that the Newtonian constant depends strongly on the gauge parameter. This leads to the appearance of antiscreening and screening behavior of the quantum gravity. The resolution of the gauge dependence problem is suggested. For physical gauges like the Landau–DeWitt gauge the Newtonian constant shows an antiscreening.

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6

Seshavatharam, UVS, and S. Lakshminarayana. "Is Newtonian gravitational constant a quantized constant of microscopic quantum gravity?" International Journal of Advanced Astronomy 8, no. 2 (September 2, 2020): 29. http://dx.doi.org/10.14419/ijaa.v8i2.30976.

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Considering the Newtonian gravitational constant as a quantized constant of microscopic quantum gravity, an attempt is made to fit its value in a verifiable approach with reference to three large atomic gravitational constants pertaining to weak, strong and electromagnetic interactions linked with a quantum relation. Estimated value seems to be 865 ppm higher than the recommended value.

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7

Wood, Barry M. "Recommending a value for the Newtonian gravitational constant." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 372, no. 2026 (October 13, 2014): 20140029. http://dx.doi.org/10.1098/rsta.2014.0029.

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The primary objective of the CODATA Task Group on Fundamental Constants is ‘to periodically provide the scientific and technological communities with a self-consistent set of internationally recommended values of the basic constants and conversion factors of physics and chemistry based on all of the relevant data available at a given point in time’. I discuss why the availability of these recommended values is important and how it simplifies and improves science. I outline the process of determining the recommended values and introduce the principles that are used to deal with discrepant results. In particular, I discuss the specific challenges posed by the present situation of gravitational constant experimental results and how these principles were applied to the most recent 2010 recommended value. Finally, I speculate about what may be expected for the next recommended value of the gravitational constant scheduled for evaluation in 2014.

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8

Zumberge, Mark A., John A. Hildebrand, J. Mark Stevenson, Robert L. Parker, Alan D. Chave, Mark E. Ander, and Fred N. Spiess. "Submarine measurement of the Newtonian gravitational constant." Physical Review Letters 67, no. 22 (November 25, 1991): 3051–54. http://dx.doi.org/10.1103/physrevlett.67.3051.

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9

HSUI, A. T. "Borehole Measurement of the Newtonian Gravitational Constant." Science 237, no. 4817 (August 21, 1987): 881–83. http://dx.doi.org/10.1126/science.237.4817.881.

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10

Milyukov, V. K., Chen Tao, and A. P. Mironov. "Problems of measurement of the Newtonian gravitational constant." Gravitation and Cosmology 15, no. 1 (January 2009): 65–68. http://dx.doi.org/10.1134/s0202289309010162.

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11

Gillies, George T. "The Newtonian Gravitational Constant: An index of measurements." Metrologia 24, S (January 1, 1987): 1–56. http://dx.doi.org/10.1088/0026-1394/24/s/001.

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12

Tian, Yong, Chung-Ming Ko, and Mu-Chen Chiu. "Hubble constant, lensing, and time delay in Te Ve S." Proceedings of the International Astronomical Union 8, S289 (August 2012): 344–47. http://dx.doi.org/10.1017/s1743921312021692.

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AbstractThe Hubble constant can be determined from the time delay of gravitationally lensed systems. We adopt Te Ve S as the relativistic version of Modified Newtonian Dynamics to study gravitational lensing phenomena and evaluate the Hubble constant from the derived time-delay formula. We test our method on observed quasar lensing published in the literature. Three candidates are suitable for our study, HE 2149-2745, FBQ J0951+2635, and SBS 0909+532.

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13

Parks, Harold V., and James E. Faller. "A simple pendulum laser interferometer for determining the gravitational constant." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 372, no. 2026 (October 13, 2014): 20140024. http://dx.doi.org/10.1098/rsta.2014.0024.

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We present a detailed account of our 2004 experiment to measure the Newtonian constant of gravitation with a suspended laser interferometer. The apparatus consists of two simple pendulums hanging from a common support. Each pendulum has a length of 72 cm and their separation is 34 cm. A mirror is embedded in each pendulum bob, which then in combination form a Fabry–Perot cavity. A laser locked to the cavity measures the change in pendulum separation as the gravitational field is modulated due to the displacement of four 120 kg tungsten masses.

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14

Cooper, A. P. R., and M. R. Gorman. "Investigating variations in the gravitational constant." Polar Record 25, no. 152 (January 1989): 55–58. http://dx.doi.org/10.1017/s0032247400009992.

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AbstractIn August–September 1987 a group of geophysicists, led by M. Ander of the Los Alamos National Laboratory and M. Zumberge of Scripps Institution of Oceanography, performed a geophysical experiment to determine the value of the gravitational constant, G. Using the DYE-3 borehole on the Greenland ice cap, the experiment was intended to provide evidence concerning possible scale variations in G, and thus for non-Newtonian gravity. This report describes the background to the experiment and the radio echo-sounding survey carried out to provide terrain corrections for the gravity model. The experiment showed values of G differing from laboratory determinations by margins which considerably exceed experimental error.

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15

Casadio, Roberto, and Andrea Giusti. "Bootstrapped Newtonian Cosmology and the Cosmological Constant Problem." Symmetry 13, no. 2 (February 22, 2021): 358. http://dx.doi.org/10.3390/sym13020358.

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Bootstrapped Newtonian gravity was developed with the purpose of estimating the impact of quantum physics in the nonlinear regime of the gravitational interaction, akin to corpuscular models of black holes and inflation. In this work, we set the ground for extending the bootstrapped Newtonian picture to cosmological spaces. We further discuss how such models of quantum cosmology can lead to a natural solution to the cosmological constant problem.

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16

ROSSI, M., and L. ZANINETTI. "LINEAR AND NONLINEAR EFFECTS ON THE NEWTONIAN GRAVITATIONAL CONSTANT AS DEDUCED FROM THE TORSION BALANCE." International Journal of Modern Physics A 22, no. 29 (November 20, 2007): 5391–400. http://dx.doi.org/10.1142/s0217751x07037329.

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The Newtonian gravitational constant has still 150 parts per million of uncertainty. This paper examines the linear and nonlinear equations governing the rotational dynamics of the torsion gravitational balance. A nonlinear effect modifying the oscillation period of the torsion gravitational balance is carefully explored.

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17

Gillies, George T. "The Newtonian gravitational constant: recent measurements and related studies." Reports on Progress in Physics 60, no. 2 (February 1, 1997): 151–225. http://dx.doi.org/10.1088/0034-4885/60/2/001.

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18

Luo, Jun, and Zhong-Kun Hu. "Status of measurement of the Newtonian gravitational constant G." Classical and Quantum Gravity 17, no. 12 (June 8, 2000): 2351–63. http://dx.doi.org/10.1088/0264-9381/17/12/307.

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19

ONOFRIO, ROBERTO. "HIGH-ENERGY DENSITY IMPLICATIONS OF A GRAVITOWEAK UNIFICATION SCENARIO." Modern Physics Letters A 29, no. 01 (January 7, 2014): 1350187. http://dx.doi.org/10.1142/s0217732313501873.

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We discuss how a scenario recently proposed for the morphing of macroscopic gravitation into weak interactions at the attometer scale affects our current understanding of high-energy density phenomena. We find that the Yukawa couplings of the fundamental fermions are directly related to their event horizons, setting an upper bound [Formula: see text] for their observability through gauge interactions. Particles with larger Yukawa couplings are not precluded, but should interact only gravitationally, providing a natural candidate for dark matter. Furthermore, the quantum vacuum contribution to the cosmological constant is reduced by several orders of magnitude with respect to the current estimates. The expected running of the Newtonian gravitational constant could provide a viable alternative scenario to the inflationary stage of the Universe.

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20

SAVICKAS, D. "A DERIVATION OF THE SCHWARZSCHILD EQUATIONS BY THE USE OF NEWTONIAN MECHANICS." International Journal of Modern Physics A 09, no. 20 (August 10, 1994): 3555–69. http://dx.doi.org/10.1142/s0217751x94001424.

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An exact derivation of both the Schwarzschild metric of general relativity and its equations of motion is made by the use of Newtonian mechanics. Although the form of Newtonian mechanics itself is not modified, the concepts of length and time on which it is based are modified in a manner that allows Newton’s laws to be expressed in a non-Euclidean space-time geometry. The lengths used in the laws are defined in terms of local-scale-measured distances, rather than the usual coordinate distances. Particle velocities are then defined in terms of these differential scale lengths. The Newtonian law of gravitation is also defined in terms of the gradient of the usual Newtonian potential with respect to these same scale lengths. It is shown that non-Euclidean geometry is imposed by the requirement that a photon in a gravitational field should maintain a constant total energy that is expressed in terms of its frequency, while also having a potential energy that is independent of the geometry of space. These conditions and modifications make it possible to derive equations of motion which are Newtonian, but which can also be reduced to forms that are identical to the Schwarzschild equations of motion for an orbiting particle or a gravitationally deflected photon.

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21

Coleman, Les. "Additional Solar System Gravitational Anomalies." Symmetry 13, no. 9 (September 14, 2021): 1696. http://dx.doi.org/10.3390/sym13091696.

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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.

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22

Haug, Espen Gaarder. "Progress in the Composite View of the Newton Gravitational Constant and Its Link to the Planck Scale." Universe 8, no. 9 (August 30, 2022): 454. http://dx.doi.org/10.3390/universe8090454.

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The Newtonian gravity constant G plays a central role in gravitational theory. Researchers have, since at least the 1980s, tried to see if the Newton gravitational constant can be expressed or replaced with more fundamental units, such as the Planck units. However, it was already pointed out in 1987 that this led to a circular problem; namely, that one must know G to find the Planck units, and that it is therefore of little or no use to express G through the Planck units. This is a view repeated in the literature in recent years, and is held by the physics’ community. However, we will claim that the circular problem was solved a few years ago. In addition, when one expresses the mass from the Compton wavelength formula, this leads to the conclusion that the three universal constants of G, h, and c now can be replaced with only lp and c to predict observable gravitational phenomena. While there have been several review papers on the Newton gravitational constant, for example, about how to measure it, we have not found a single review paper on the composite view of the gravitational constant. This paper will review the history of, as well as recent progress in, the composite view of the gravitational constant. This should hopefully be a useful supplement in the ongoing research for understanding and discussion of Newton’s gravitational constant.

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23

ONOFRIO, ROBERTO. "ON WEAK INTERACTIONS AS SHORT-DISTANCE MANIFESTATIONS OF GRAVITY." Modern Physics Letters A 28, no. 07 (March 6, 2013): 1350022. http://dx.doi.org/10.1142/s0217732313500223.

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We conjecture that weak interactions are peculiar manifestations of quantum gravity at the Fermi scale, and that the Fermi constant is related to the Newtonian constant of gravitation. In this framework one may understand the violations of fundamental symmetries by the weak interactions, in particular parity violations, as due to fluctuations of the spacetime geometry at a Planck scale coinciding with the Fermi scale. As a consequence, gravitational phenomena should play a more important role in the microworld, and experimental settings are suggested to test this hypothesis.

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24

Wilkins, D. "Gravitational fields and the cosmological constant in multidimensional Newtonian universes." American Journal of Physics 54, no. 8 (August 1986): 726–31. http://dx.doi.org/10.1119/1.14482.

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25

Rosi, G., F. Sorrentino, L. Cacciapuoti, M. Prevedelli, and G. M. Tino. "Precision measurement of the Newtonian gravitational constant using cold atoms." Nature 510, no. 7506 (June 2014): 518–21. http://dx.doi.org/10.1038/nature13433.

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26

Fattori, M., G. Lamporesi, T. Petelski, J. Stuhler, and G. M. Tino. "Towards an atom interferometric determination of the Newtonian gravitational constant." Physics Letters A 318, no. 3 (November 2003): 184–91. http://dx.doi.org/10.1016/j.physleta.2003.07.011.

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27

Stuhler, J., M. Fattori, T. Petelski, and G. M. Tino. "MAGIA using atom interferometry to determine the Newtonian gravitational constant." Journal of Optics B: Quantum and Semiclassical Optics 5, no. 2 (April 1, 2003): S75—S81. http://dx.doi.org/10.1088/1464-4266/5/2/361.

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28

STUCHLÍK, ZDENĚK, and JIŘÍ KOVÁŘ. "PSEUDO-NEWTONIAN GRAVITATIONAL POTENTIAL FOR SCHWARZSCHILD–DE SITTER SPACE–TIMES." International Journal of Modern Physics D 17, no. 11 (October 2008): 2089–105. http://dx.doi.org/10.1142/s021827180801373x.

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Pseudo-Newtonian gravitational potential describing the gravitational field of static and spherically symmetric black holes in the universe with a repulsive cosmological constant is introduced. In order to demonstrate the accuracy of the pseudo-Newtonian approach, the related effective potential for test particle motion is constructed and compared with its general-relativistic counterpart given by the Schwarzschild–de Sitter geometry. The results indicate that such an approach could be useful in applications of developed Newtonian theories of accretion disks in astrophysically interesting situations in large galactic structures for the Schwarzschild–de Sitter space–times with the cosmological parameter y = Λ M2/3 ≤ 10-6.

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29

Rivera, Paul Cadelina. "The Theoretical Value of the Hubble Constant Ho and Unification of the Fundamental Forces of Nature." European Journal of Applied Physics 3, no. 4 (July 21, 2021): 17–24. http://dx.doi.org/10.24018/ejphysics.2021.3.4.88.

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The Hubble constant Ho represents the speed of expansion of the universe and various cosmological observations and modeling methods were utilized by astronomers for a century to pin down its exact value. Determining Ho from cosmological observations is a long and tedious process requiring highly accurate datasets. To circumvent this need, a simple theoretical approach is introduced in this study which uses the concept of gravitational weakening and seismic-induced recession. As tremors occur among celestial objects, their gravitational fields would also change. This resulted in a fundamental relation of Ho and the computed rate of recession that gives a theoretical value for Ho=69.921 Km/s/Mpc. Using the newly discovered seismic-induced gravitational weakening and time dilation, it is possible that various astrophysical methods using different measurement methods would converge to this theoretical Ho value when cosmological distances and time delay measurements are corrected with the simple formulas we derived. The new model assumes that, as quakes occur in celestial objects, luminosity-induced acceleration and high-energy collision of protons and electrons may produce a massive number of neutrinos, quarks and other subatomic particles. Furthermore, the fine structure constant was found to be inversely proportional to Ho-squared and that the fine-structure constant obtained in this study gives a new physical interpretation of α. New relations for the speed of light, orbital velocity, gravitational force and the Hubble constant were further derived from the new recession constant using approximate relations for the Newtonian and electric force constant. This resulted in a modified gravitational law that is both repulsive and attractive and a theoretical explanation of the phenomenon of light-induced gravitation analogous to the electromagnetic force where photon is the force-carrier. Finally, the fundamental forces of gravitation, electromagnetism and strong nuclear force are now unified.

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30

Xue, Chao, Li-Di Quan, Shan-Qing Yang, Bing-Peng Wang, Jun-Fei Wu, Cheng-Gang Shao, Liang-Cheng Tu, Vadim Milyukov, and Jun Luo. "Preliminary determination of Newtonian gravitational constant with angular acceleration feedback method." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 372, no. 2026 (October 13, 2014): 20140031. http://dx.doi.org/10.1098/rsta.2014.0031.

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This paper describes the preliminary measurement of the Newtonian gravitational constant G with the angular acceleration feedback method at HUST. The apparatus has been built, and preliminary measurement performed, to test all aspects of the experimental design, particularly the feedback function, which was recently discussed in detail by Quan et al . The experimental results show that the residual twist angle of the torsion pendulum at the signal frequency introduces 0.4 ppm to the value of G . The relative uncertainty of the angular acceleration of the turntable is approximately 100 ppm, which is mainly limited by the stability of the apparatus. Therefore, the experiment has been modified with three features: (i) the height of the apparatus is reduced almost by half, (ii) the aluminium shelves were replaced with shelves made from ultra-low expansion material and (iii) a perfect compensation of the laboratory-fixed gravitational background will be carried out. With these improvements, the angular acceleration is expected to be determined with an uncertainty of better than 10 ppm, and a reliable value of G with 20 ppm or below will be obtained in the near future.

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31

Milyukov, V. K., Jun Luo, Chen Tao, and A. P. Mironov. "Status of the experiments on measurement of the Newtonian gravitational constant." Gravitation and Cosmology 14, no. 4 (October 2008): 368–75. http://dx.doi.org/10.1134/s0202289308040130.

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32

Liu Jian-Ping, Wu Jun-Fei, Li Qing, Xue Chao, Mao De-Kai, Yang Shan-Qing, Shao Cheng-Gang, Tu Liang-Cheng, Hu Zhong-Kun, and Luo Jun. "Progress on the precision measurement of the Newtonian gravitational constant G." Acta Physica Sinica 67, no. 16 (2018): 160603. http://dx.doi.org/10.7498/aps.67.20181381.

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33

Klein, Norbert. "Evidence for modified Newtonian dynamics from Cavendish-type gravitational constant experiments." Classical and Quantum Gravity 37, no. 6 (February 18, 2020): 065002. http://dx.doi.org/10.1088/1361-6382/ab6cab.

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34

Gillies, G. T. "Some background on the measurement of the Newtonian gravitational constant,G." Measurement Science and Technology 10, no. 6 (January 1, 1999): 421–25. http://dx.doi.org/10.1088/0957-0233/10/6/301.

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35

Dousse, J. ‐Cl, and Ch Rhême. "A student experiment for accurate measurements of the Newtonian gravitational constant." American Journal of Physics 55, no. 8 (August 1987): 706–11. http://dx.doi.org/10.1119/1.15061.

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36

Hildebrand, John A., Alan D. Chave, Fred N. Speiss, Robert L. Parker, Mark E. Ander, and Mark A. Zumberge. "The Newtonian gravitational constant on the feasibility of an oceanic measurement." Eos, Transactions American Geophysical Union 69, no. 32 (1988): 769. http://dx.doi.org/10.1029/88eo01045.

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37

Boer, H. de, H. Haars, and W. Michaelis. "A New Experiment for the Determination of the Newtonian Gravitational Constant." Metrologia 24, no. 4 (January 1, 1987): 171–74. http://dx.doi.org/10.1088/0026-1394/24/4/003.

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38

Quinn, T. J., C. C. Speake, and R. S. Davis. "Novel torsion balance for the measurement of the Newtonian gravitational constant." Metrologia 34, no. 3 (June 1997): 245–49. http://dx.doi.org/10.1088/0026-1394/34/3/6.

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39

KOKUBUN, FERNANDO. "RESTRICTED PROBLEM OF THREE BODIES WITH NEWTONIAN + YUKAWA POTENTIAL." International Journal of Modern Physics D 13, no. 05 (May 2004): 783–806. http://dx.doi.org/10.1142/s021827180400492x.

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Trajectories of the third body in the Restricted Problem of Three Bodies including a Yukawa term to the Newtonian gravitational potential are analyzed. It is shown that this modified gravitational potential changes some important aspects of the Restricted Problem of Three Bodies. Depending of coupling constant α, motions obtained in the pure Newtonian case are qualitatively different when Yukawa term is included. Depending of coupling parameters α, the nature of dynamics change from regular to chaotic (α<0) or from chaotic to regular (α>0) and in both cases using the same length scales λ.

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40

Ziefle, Reiner Georg. "Newtonian quantum gravity and the derivation of the gravitational constant G and its fluctuations." Physics Essays 33, no. 4 (December 25, 2020): 387–94. http://dx.doi.org/10.4006/0836-1398-33.4.387.

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The theory of gravity “Newtonian quantum gravity” (NQG) is an ingeniously simple theory, because it precisely predicts so-called “general relativistic phenomena,” as, for example, that observed at the binary pulsar PSR B1913 + 16, by just applying Kepler’s second law on quantized gravitational fields. It is an irony of fate that the unsuspecting relativistic physicists still have to effort with the tensor calculations of an imaginary four-dimensional space-time. Everybody can understand that a mass that moves through space must meet more “gravitational quanta” emitted by a certain mass, if it moves faster than if it moves slower or rests against a certain mass, which must cause additional gravitational effects that must be added to the results of Newton's theory of gravity. However, today's physicists cannot recognize this because they are caught in Einstein's relativistic thinking and as general relativity can coincidentally also predict these quantum effects by a mathematically defined four-dimensional curvature of space-time. Advanced NQG is also able to derive the gravitational constant G and explains why G must fluctuate. The “string theory” tries to unify quantum physics with general relativity, but as the so-called “general relativistic” phenomena are quantum physical effects, it cannot be a realistic theory. The “energy wave theory” is lead to absurdity by the author.

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41

Alfedeel, Alnadhief, Amare Abebe, and Hussam Gubara. "A Generalized Solution of Bianchi Type-V Models with Time-Dependent G and Λ." Universe 4, no. 8 (July 27, 2018): 83. http://dx.doi.org/10.3390/universe4080083.

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We study the homogeneous but anisotropic Bianchi type-V cosmological model with time-dependent gravitational and cosmological “constants”. Exact solutions of the Einstein field equations (EFEs) are presented in terms of adjustable parameters of quantum field theory in a spatially curved and expanding background. It has been found that the general solution of the average scale factor a as a function of time involved the hypergeometric function. Two cosmological models are obtained from the general solution of the hypergeometric function and the Emden–Fowler equation. The analysis of the models shows that, for a particular choice of parameters in our first model, the cosmological “constant” decreases whereas the Newtonian gravitational “constant” increases with time, and for another choice of parameters, the opposite behaviour is observed. The models become isotropic at late times for all parameter choices of the first model. In the second model of the general solution, both the cosmological and gravitational “constants” decrease while the model becomes more anisotropic over time. The exact dynamical and kinematical quantities have been calculated analytically for each model.

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UV, Satya Seshavatharam, and Lakshminarayana S. "Quantum gravitational applications of nuclear, atomic and astrophysical phenomena." International Journal of Advanced Astronomy 4, no. 1 (March 11, 2016): 20. http://dx.doi.org/10.14419/ijaa.v4i1.5841.

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<p>By following the old concept of “gravity is having a strong coupling at nuclear scale” and considering the ‘reduced Planck’s constant’ as a characteristic quantum gravitational constant, in this letter we suggest that: 1) There exists a gravitational constant associated with strong interaction, G<sub>s</sub>~3.328x10<sup>28</sup> m<sup>3</sup>/kg/sec<sup>2</sup>. 2) There also exists a gravitational constant associated with electromagnetic interaction, G<sub>e</sub>~2.376x10<sup>37 </sup>m<sup>3</sup>/kg/sec<sup>2</sup>.Based on these two assumptions, in a quantum gravitational approach, an attempt is made to understand the basics of final unification with various semi empirical applications like melting points of elementary particles, strong coupling constant, proton-electron mass ratio, proton-neutron stability, nuclear binding energy, neutron star’s mass and radius, Newtonian gravitational constant, Avogadro number and molar mass unit. With further research and investigation, a practical model of ‘quantum gravitational string theory’ can be developed.</p>

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Haug, Espen Gaarder. "Measurements of the Planck Length from a Ball Clock without Knowledge of Newton’s Gravitational Constant G or the Planck Constant." European Journal of Applied Physics 3, no. 6 (December 2, 2021): 15–20. http://dx.doi.org/10.24018/ejphysics.2021.3.6.133.

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We demonstrate how one can extract the Planck length from ball with a built-in stopwatch without knowledge of the Newtonian gravitational constant or the Planck constant. This could be of great importance since until recently it has been assumed the Planck length not can be found without knowledge of Newton’s gravitational constant. This method of measuring the Planck length should also be of great interest to not only physics researchers but also to physics teachers and students as it conveniently demonstrates that the Plank length is directly linked to gravitational phenomena, not only theoretically, but practically. To demonstrate that this is more than a theory we report 100 measurements of the Planck length using this simple approach. We will claim that, despite the mathematical and experimental simplicity, our findings could be of great importance in better understanding the Planck scale, as our findings strongly support the idea that to detect gravity is to detect the effects from the Planck scale indirectly.

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BALAGUERA-ANTOLÍNEZ, ANDRÉS, MAREK NOWAKOWSKI, and CHRISTIAN G. BÖHMER. "ON ASTROPHYSICAL BOUNDS OF THE COSMOLOGICAL CONSTANT." International Journal of Modern Physics D 14, no. 09 (September 2005): 1507–25. http://dx.doi.org/10.1142/s0218271805007383.

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Astrophysical bounds on the cosmological constant are examined for spherically symmetric bodies. Similar limits emerge from the hydrostatical and gravitational equilibrium and the validity of the Newtonian limit. The methods in use seem to be disjoint from the basic principles, however they have the same implication regarding the upper bounds. Therefore we will compare different inequalities and comment on the possible relationship between them. These inequalities are of relevance for the so-called coincidence problem and for the bound of the cosmological constant which comes surprisingly close to the "experimental" value.

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Shalaby, Asmaa G. "Impact of the running gravitational constant on the extensive thermodynamics of galaxies." International Journal of Modern Physics A 34, no. 02 (January 20, 2019): 1950014. http://dx.doi.org/10.1142/s0217751x19500143.

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We study the effect of the running gravitational constant on a system of particles (galaxies) interact via gravitational potential. The gravitational potential is derived based on the entropic modified Newtonian force by logarithmic and power correction terms. We derive the partition function for many-body system and the exact equations of state including the thermodynamic properties. A modified parameter B emerged from the thermodynamics derivation. Moreover, an extension of the study is done to determine the distribution function for point mass and extended mass structure galaxies. In particular, the rotation velocity of some galaxies is studied, and the results confronted the observed data which fit well only for short distance with considering the logarithmic correction effect. This leads us to conclude that the logarithmic correction effect explains the rotation velocity data for short and long distances at least qualitatively.

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KLINKHAMER, F. R., and M. KOPP. "ENTROPIC GRAVITY, MINIMUM TEMPERATURE, AND MODIFIED NEWTONIAN DYNAMICS." Modern Physics Letters A 26, no. 37 (December 7, 2011): 2783–91. http://dx.doi.org/10.1142/s021773231103711x.

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Verlinde's heuristic argument for the interpretation of the standard Newtonian gravitational force as an entropic force is generalized by the introduction of a minimum temperature (or maximum wave length) for the microscopic degrees of freedom on the holographic screen. With the simplest possible setup, the resulting gravitational acceleration felt by a test mass m from a point mass M at a distance R is found to be of the form of the modified Newtonian dynamics (MOND) as suggested by Milgrom. The corresponding MOND-type acceleration constant is proportional to the minimum temperature, which can be interpreted as the Unruh temperature of an emerging de Sitter space. This provides a possible explanation of the connection between local MOND-type two-body systems and cosmology.

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Dannenberg, Rand. "Excluded Volume for Flat Galaxy Rotation Curves in Newtonian Gravity and General Relativity." Symmetry 12, no. 3 (March 4, 2020): 398. http://dx.doi.org/10.3390/sym12030398.

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Using the classical vacuum solutions of Newtonian gravity that do not explicitly involve matter, dark matter, or the gravitational constant, subject to an averaging process, a form of gravity relevant to the flattening of galaxy rotation curves results. The latter resembles the solution found if the vacuum is simply assigned a gravitational field density, and a volume of the vacuum is then excluded, with no averaging process. A rationale then follows for why these terms would become important on the galactic scale. Then, a modification of General Relativity, motivated by the Newtonian solutions, that are equivalent to a charge void, is partially defined and discussed in terms of a least action principle.

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Hanımeli, Ekim Taylan, Isaac Tutusaus, Brahim Lamine, and Alain Blanchard. "Low-redshift tests of Newtonian cosmologies with a time-varying gravitational constant." Monthly Notices of the Royal Astronomical Society 497, no. 4 (August 8, 2020): 4407–15. http://dx.doi.org/10.1093/mnras/staa2310.

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ABSTRACT In this work, we investigate Newtonian cosmologies with a time-varying gravitational constant, G(t). We examine whether such models can reproduce the low-redshift cosmological observations without a cosmological constant, or any other sort of explicit dark energy fluid. Starting with a modified Newton’s second law, where G is taken as a function of time, we derive the first Friedmann–Lemaître equation, where a second parameter, G*, appears as the gravitational constant. This parameter is related to the original G from the second law, which remains in the acceleration equation. We use this approach to reproduce various cosmological scenarios that are studied in the literature, and we test these models with low-redshift probes: type-Ia supernovae (SNIa), baryon acoustic oscillations, and cosmic chronometers, taking also into account a possible change in the supernovae intrinsic luminosity with redshift. As a result, we obtain several models with similar χ2 values as the standard ΛCDM cosmology. When we allow for a redshift-dependence of the SNIa intrinsic luminosity, a model with a G exponentially decreasing to zero while remaining positive (model 4) can explain the observations without acceleration. When we assume no redshift-dependence of SNIa, the observations favour a negative G at large scales, while G* remains positive for most of these models. We conclude that these models offer interesting interpretations to the low-redshift cosmological observations, without needing a dark energy term.

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Friedman, Yaakov, Tzvi Scarr, and Joseph Steiner. "A geometric relativistic dynamics under any conservative force." International Journal of Geometric Methods in Modern Physics 16, no. 01 (January 2019): 1950015. http://dx.doi.org/10.1142/s0219887819500154.

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Riemann’s principle “force equals geometry” provided the basis for Einstein’s General Relativity — the geometric theory of gravitation. In this paper, we follow this principle to derive the dynamics for any static, conservative force. The geometry of spacetime of a moving object is described by a metric obtained from the potential of the force field acting on it. We introduce a generalization of Newton’s First Law — the Generalized Principle of Inertia stating that: An inanimate object moves inertially, that is, with constant velocity, in its own spacetime whose geometry is determined by the forces affecting it. Classical Newtonian dynamics is treated within this framework, using a properly defined Newtonian metric with respect to an inertial lab frame. We reveal a physical deficiency of this metric (responsible for the inability of Newtonian dynamics to account for relativistic behavior), and remove it. The dynamics defined by the corrected Newtonian metric leads to a new Relativistic Newtonian Dynamics for both massive objects and massless particles moving in any static, conservative force field, not necessarily gravitational. This dynamics reduces in the weak field, low velocity limit to classical Newtonian dynamics and also exactly reproduces the classical tests of General Relativity, as well as the post-Keplerian precession of binaries.

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He, G., C. Jiang, and W. Lin. "Second post-Minkowskian metric for a moving Kerr black hole." International Journal of Modern Physics D 23, no. 09 (August 2014): 1450079. http://dx.doi.org/10.1142/s0218271814500795.

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In this paper, the harmonic metric for a moving Kerr black hole is presented in the second post-Minkowskian approximation. It is further demonstrated that the obtained metric is consistent with the Liénard–Wiechert gravitational potential for a moving and spinning source with an arbitrary constant velocity. Based on the metric, we also give the post-Newtonian equations of motion for photon and massive test particle in the time-dependent gravitational field.

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