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Journal articles on the topic 'Newtonian gravitational constant'

Author: Grafiati

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 (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 Newtoni

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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 (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 gravi

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3

Ognean, Teodor. "Some considerations on the Newtonian gravitational constant G measurements." Physics Essays 32, no. 3 (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

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4

Xue, Chao, Jian-Ping Liu, Qing Li, et al. "Precision measurement of the Newtonian gravitational constant." National Science Review 7, no. 12 (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 Technol

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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 (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

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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 (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 (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 resul

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8

Zumberge, Mark A., John A. Hildebrand, J. Mark Stevenson, et al. "Submarine measurement of the Newtonian gravitational constant." Physical Review Letters 67, no. 22 (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 (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 (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 (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 (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 (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 (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 e

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15

Casadio, Roberto, and Andrea Giusti. "Bootstrapped Newtonian Cosmology and the Cosmological Constant Problem." Symmetry 13, no. 2 (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 (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 (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 (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 (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

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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 (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

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21

Coleman, Les. "Additional Solar System Gravitational Anomalies." Symmetry 13, no. 9 (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

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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 (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 th

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23

ONOFRIO, ROBERTO. "ON WEAK INTERACTIONS AS SHORT-DISTANCE MANIFESTATIONS OF GRAVITY." Modern Physics Letters A 28, no. 07 (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 (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 (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 (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 (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 (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 situ

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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 (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 r

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30

Xue, Chao, Li-Di Quan, Shan-Qing Yang, et al. "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 (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, whi

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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 (2008): 368–75. http://dx.doi.org/10.1134/s0202289308040130.

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32

Liu Jian-Ping, Wu Jun-Fei, Li Qing, et al. "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 (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 (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 (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 (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 (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 (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 (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

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41

Alfedeel, Alnadhief, Amare Abebe та Hussam Gubara. "A Generalized Solution of Bianchi Type-V Models with Time-Dependent G and Λ". Universe 4, № 8 (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

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42

UV, Satya Seshavatharam, and Lakshminarayana S. "Quantum gravitational applications of nuclear, atomic and astrophysical phenomena." International Journal of Advanced Astronomy 4, no. 1 (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>/

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43

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 (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 phen

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44

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 (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 clos

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45

Shalaby, Asmaa G. "Impact of the running gravitational constant on the extensive thermodynamics of galaxies." International Journal of Modern Physics A 34, no. 02 (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 partic

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46

KLINKHAMER, F. R., and M. KOPP. "ENTROPIC GRAVITY, MINIMUM TEMPERATURE, AND MODIFIED NEWTONIAN DYNAMICS." Modern Physics Letters A 26, no. 37 (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 ca

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47

Dannenberg, Rand. "Excluded Volume for Flat Galaxy Rotation Curves in Newtonian Gravity and General Relativity." Symmetry 12, no. 3 (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 solution

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48

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 (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

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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 (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 f

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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 (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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