Cited by 60Scientific Measurement and Uncertainty EvaluationRelativity and Gravitational TheoryAdvanced Measurement and Metrology Techniques

Precision measurement of the Newtonian gravitational constant

Open access
Xue, Chao, Liu, Jian-Ping, Li, Qing, Wu, Jun-Fei, Yang, Shan-Qing, Liu, Qi, Shao, Cheng-Gang, Tu, Liang-Cheng, Hu, Zhong-Kun, Luo, Jun·2020·National Science Review

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.

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1093/nsr/nwaa165

Cites

Statistics

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • Gobs has only been accurately measured to a relative precision of ε = 10^-15.

    “Whereas G obs has only been accurately measured to a relative precision of ε = 10 -15 [39]”

    From Is cosmological tuning fine or coarse? (2021) · cites this paper as [39]

    The History of the G Measurement (Table 3) lists the smallest reported relative uncertainty as 12 ppm, or 1.2 × 10^-5—not 10^-15. The Conclusion and Outlook also reports a roughly 550 ppm discrepancy among measured values of G. (LLM, conf=0.93)

    Checked by a reasoning model — may be wrong.

    Experimental — accuracy not yet measured

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Cites

No references could be resolved yet.

Research works printed but not linked: 98

  1. Newton, 1687, Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), 10.5479/sil.52126.39088015628399 · DOI
  2. Herrick, 1971, Astrodynamics: Orbit Determination, Space Navigation, Celestial Mechanics
  3. Gillies, 1987, The Newtonian gravitational constant: an index of measurements, Metrologia, 24, 1, 10.1088/0026-1394/24/S/001 · DOI
  4. Mohr, 2016, CODATA recommended values of the fundamental physical constants: 2014, Rev Mod Phys, 88, 035009, 10.1103/RevModPhys.88.035009 · DOI
  5. Mohr, 2012, CODATA recommended values of the fundamental physical constants: 2010, Rev Mod Phys, 84, 1527, 10.1103/RevModPhys.84.1527 · DOI
  6. Cavendish, 1798, Experiments to determine the density of the Earth, Philos Trans R Soc Lond, 88
  7. Mackenzie, 1900, The Laws of Gravitation: Memoirs by Newton, Bouguer and Cavendish, Together with Abstracts of Other Important Memoirs
  8. Rothleitner, 2017, Measurements of the Newtonian constant of gravitation, G, Rev Sci Instrum, 88, 111101, 10.1063/1.4994619 · DOI
  9. Milyukov, 2012, The Newtonian gravitational constant: modern status of measurement and the new CODATA value, Gravit Cosmol-Russia, 18, 216, 10.1134/S0202289312030061 · DOI
  10. Richarz, 1897, The gravitation constant and the mean density of the Earth, Nature, 55, 296, 10.1038/055296a0 · DOI
  11. Hubler, 1995, Determination of the gravitational constant with a lake experiment: new constraints for non-Newtonian gravity, Phys Rev D, 51, 4005, 10.1103/PhysRevD.51.4005 · DOI
  12. Boys, 1895, On the Newtonian constant of gravitation, Philos Trans R Soc A, 186, 1
  13. Braun, 1897, Die Gravitations-Konstante, die Masse und mittlere Dichte der Erde nach einer neuen experimentellen Bestimmung, Denkschriften der Academie der Wissenschaft zu Wien, Mathematische und Naturwissenschaftliche Klasse, 64, 187
  14. Cohen, 1973, The 1973 least-squares adjustment of the fundamental constants, J Phys Chem Ref Data, 2, 663, 10.1063/1.3253130 · DOI
  15. Cohen, 1987, The 1986 adjustment of the fundamental physical constants, Rev Mod Phys, 59, 1121, 10.1103/RevModPhys.59.1121 · DOI
  16. Mohr, 2000, CODATA recommended values of the fundamental physical constants: 1998, Rev Mod Phys, 72, 351, 10.1103/RevModPhys.72.351 · DOI
  17. Mohr, 2005, CODATA recommended values of the fundamental physical constants: 2002, Rev Mod Phys, 77, 1, 10.1103/RevModPhys.77.1 · DOI
  18. Mohr, 2008, CODATA recommended values of the fundamental physical constants: 2006, Rev Mod Phys, 80, 633, 10.1103/RevModPhys.80.633 · DOI
  19. Heyl, 1930, A redetermination of the constant of gravitation, J Res Natl Bur Stand, 5, 1243, 10.6028/jres.005.074 · DOI
  20. Heyl, 1942, A new redetermination of the constant of gravitation, J Res Natl Bur Stand, 29, 1, 10.6028/jres.029.001 · DOI
  21. Luther, 1982, Redetermination of the Newtonian gravitational constant G, Phys Rev Lett, 48, 121, 10.1103/PhysRevLett.48.121 · DOI
  22. Michaelis, 1995, A new precise determination of Newton’s gravitational constant, Metrologia, 32, 267, 10.1088/0026-1394/32/4/4 · DOI
  23. Fizgerald, 1995, Newton’s gravitational constant with uncertainty less than 100 ppm, IEEE Trans Instrum Meas, 44, 494, 10.1109/19.377890 · DOI
  24. Walesch, 1995, The gravitational force at mass separations from 0.6 m to 2.1 m and the precise measurement of G, IEEE Trans Instrum Meas, 44, 491, 10.1109/19.377889 · DOI
  25. Karagioz, 1996, Measurement of the gravitational constant with a torsion balance, Meas Tech, 39, 979, 10.1007/BF02377461 · DOI
  26. Bagley, 1997, Preliminary results of a determination of the Newtonian constant of gravitation: a test of the Kuroda hypothesis, Phys Rev Lett, 78, 3047, 10.1103/PhysRevLett.78.3047 · DOI
  27. Karagioz, 1998, Gravitational constant measurement using a four-position procedure, Gravit Cosmol-Russia, 4, 239
  28. Schwarz, 1998, A free-fall determination of the Newtonian constant of gravity, Science, 282, 2230, 10.1126/science.282.5397.2230 · DOI
  29. Schurr, 1998, Gravitational constant measured by means of a beam balance, Phys Rev Lett, 80, 1142, 10.1103/PhysRevLett.80.1142 · DOI
  30. Luo, 1998, Determination of the Newtonian gravitational constant G with a nonlinear fitting method, Phys Rev D, 59, 042001, 10.1103/PhysRevD.59.042001 · DOI
  31. Gundlach, 2000, Measurement of Newtons constant using a torsion balance with angular acceleration feedback, Phys Rev Lett, 85, 2869, 10.1103/PhysRevLett.85.2869 · DOI
  32. Quinn, 2001, A new determination of G using two methods, Phys Rev Lett, 87, 111101, 10.1103/PhysRevLett.87.111101 · DOI
  33. Armstrong, 2003, New measurements of G using the measurement standards laboratory torsion balance, Phys Rev Lett, 91, 201101, 10.1103/PhysRevLett.91.201101 · DOI
  34. Hu, 2005, Correction of source mass effects in the HUST-99 measurement of G, Phys Rev D, 71, 127505, 10.1103/PhysRevD.71.127505 · DOI
  35. Schlamminger, 2006, Measurement of Newton’s gravitational constant, Phys Rev D, 74, 082001, 10.1103/PhysRevD.74.082001 · DOI
  36. Luo, 2009, Determination of the Newtonian gravitational constant G with time-of-swing method, Phys Rev Lett, 102, 240801, 10.1103/PhysRevLett.102.240801 · DOI
  37. Tu, 2010, New determination of the gravitational constant G with time-of-swing method, Phys Rev D, 82, 022001, 10.1103/PhysRevD.82.022001 · DOI
  38. Parks, 2010, Simple pendulum determination of the gravitational constant, Phys Rev Lett, 105, 110801, 10.1103/PhysRevLett.105.110801 · DOI
  39. Quinn, 2013, Improved determination of G using two methods, Phys Rev Lett, 111, 101102, 10.1103/PhysRevLett.111.101102 · DOI
  40. Quinn, 2014, The BIPM measurements of the Newtonian constant of gravitation, G, Philos Trans R Soc A, 372, 20140032, 10.1098/rsta.2014.0032 · DOI
  41. Rosi, 2014, Precision measurement of the Newtonian gravitational constant using cold atoms, Nature, 510, 518, 10.1038/nature13433 · DOI
  42. Prevedelli, 2014, Measuring the Newtonian constant of gravitation G with an atomic interferometer, Philos Trans R Soc A, 372, 20140030, 10.1098/rsta.2014.0030 · DOI
  43. Newman, 2014, A measurement of G with a cryogenic torsion pendulum, Philos Trans R Soc A, 372, 20140025, 10.1098/rsta.2014.0025 · DOI
  44. Quinn, 2000, Measuring big G, Nature, 408, 919, 10.1038/35050187 · DOI
  45. Quinn, 2014, Don’t stop the quest to measure big G, Nature, 505, 455, 10.1038/505455a · DOI
  46. Schlamminger, 2014, A cool way to measure big G, Nature, 510, 478, 10.1038/nature13507 · DOI
  47. Gibney, 2014, Rivals join forces to nail down big G, Nature, 514, 150, 10.1038/514150a · DOI
  48. Schlamminger, 2018, Gravity measured with record precision, Nature, 560, 562, 10.1038/d41586-018-06028-6 · DOI
  49. Li, 2018, Measurements of the gravitational constant using two independent methods, Nature, 560, 582, 10.1038/s41586-018-0431-5 · DOI
  50. Parks, 2019, Erratum: simple pendulum determination of the gravitational constant [Phys Rev Lett 2010; 105], Phys Rev Lett, 122, 199901(E), 10.1103/PhysRevLett.122.199901 · DOI
  51. de Boer, 1984, Precision Measurement and Fundamental Constants II (National Bureau of Standards Special Publication 617)
  52. Chen, 1993, Gravitational Experiments in the Laboratory, 10.1017/CBO9780511563966 · DOI
  53. Gillies, 1997, The Newtonian gravitational constant: recent measurements and related studies, Rep Prog Phys, 60, 151, 10.1088/0034-4885/60/2/001 · DOI
  54. Luo, 2000, Status of measurement of the Newtonian gravitational constant G, Class Quantum Grav, 17, 2351, 10.1088/0264-9381/17/12/307 · DOI
  55. Speake, 2005, Newton’s constant and the twenty-first century laboratory, Philos Trans R Soc A, 363, 2265, 10.1098/rsta.2005.1643 · DOI
  56. Hu, 2006, Determination of the gravitational constant G, Front Phys China, 1, 449, 10.1007/s11467-006-0039-3 · DOI
  57. Tu, 2011, Precise determination of Newtonian gravitational constant G (in Chinese), Sci Sin Phys Mech Astron, 41, 691, 10.1360/132011-104 · DOI
  58. Liu, 2018, Progress on the precision measurement of the Newtonian gravitational constant G (in Chinese), Acta Physica Sinica, 67, 160603, 10.7498/aps.67.20181381 · DOI
  59. Wu, 2019, Progress in precise measurements of the gravitational constant, Ann Phys, 531, 1900013, 10.1002/andp.201900013 · DOI
  60. Rose, 1969, Determination of the gravitational constant G, Phys Rev Lett, 23, 655, 10.1103/PhysRevLett.23.655 · DOI
  61. Gundlach, 1996, New technique for measuring Newton’s constant G, Phys Rev D, 54, R1256, 10.1103/PhysRevD.54.R1256 · DOI
  62. Gundlach, 1999, A rotating torsion balance experiment to measure Newton’s constant, Meas Sci Technol, 10, 454, 10.1088/0957-0233/10/6/307 · DOI
  63. Kuroda, 1995, Does the time-of-swing method give a correct value of the Newtonian gravitational constant?, Phys Rev Lett, 75, 2796, 10.1103/PhysRevLett.75.2796 · DOI
  64. Schurr, 1991, A new method for testing Newton’s gravitational law, Metrologia, 28, 397, 10.1088/0026-1394/28/5/004 · DOI
  65. Kleinevoß, 1999, Absolute measurement of the Newtonian force and a determination of G, Meas Sci Technol, 10, 492, 10.1088/0957-0233/10/6/313 · DOI
  66. Fitzgerald, 1994, A method to measure Newton’s gravitational constant, Metrologia, 31, 301, 10.1088/0026-1394/31/4/003 · DOI
  67. Fitzgerald, 1999, The measurement of G using the MSL torsion balance, Meas Sci Technol, 10, 439, 10.1088/0957-0233/10/6/305 · DOI
  68. Armstrong, 2002, Proceedings of the Ninth Marcel Grossmann Meeting on General Relativity, 1779, 10.1142/9789812777386_0382 · DOI
  69. Newman, 1999, On determining G using a cryogenic torsion pendulum, Meas Sci Technol, 10, 445, 10.1088/0957-0233/10/6/306 · DOI
  70. Bantel, 2000, High precision measurement of torsion fibre internal friction at cryogenic temperatures, J Alloy Compd, 310, 233, 10.1016/S0925-8388(00)01010-0 · DOI
  71. Kuroda, 1999, Anelasticity in G experiments, Meas Sci Technol, 10, 435, 10.1088/0957-0233/10/6/304 · DOI
  72. Li, 2014, G measurements with time-of-swing method at HUST, Philos Trans R Soc A, 372, 20140141, 10.1098/rsta.2014.0141 · DOI
  73. Yang, 2009, Direct measurement of the anelasticity of a tungsten fibre, Phys Rev D, 80, 122005, 10.1103/PhysRevD.80.122005 · DOI
  74. Luo, 2000, Thermoelastic property of the torsion fiber in the gravitational experiments, Rev Sci Instrum, 71, 1524, 10.1063/1.1150489 · DOI
  75. Luo, 2001, Precise determination of separation between spherical attracting masses in measuring the gravitational constant, Chin Phys Lett, 18, 1012, 10.1088/0256-307X/18/8/305 · DOI
  76. Guo, 2004, Measurement of eccentricity of the centre of mass from the geometric centre of a sphere, Chin Phys Lett, 21, 612, 10.1088/0256-307X/21/4/006 · DOI
  77. Tian, 2004, Correlation method in period measurement of a torsion pendulum, Rev Sci Instrum, 75, 1971, 10.1063/1.1753095 · DOI
  78. Liu, 2008, Measurement of density inhomogeneity for glass pendulum, Chin Phys Lett, 25, 4203, 10.1088/0256-307X/25/12/005 · DOI
  79. Liu, 2009, Measurement of density inhomogeneity for source masses in time-of-swing method of measuring G, Chin Phys Lett, 26, 010403, 10.1088/0256-307X/26/1/010403 · DOI
  80. Liu, 2009, Precision measurement of distribution of film thickness on pendulum for experiment of G, Chin Phys Lett, 26, 090402, 10.1088/0256-307X/26/9/090402 · DOI
  81. Li, 2010, Effect of local magnetic field in G measurement with time-of-swing method, Chin Phys Lett, 27, 070401, 10.1088/0256-307X/27/7/070401 · DOI
  82. Li, 2016, Research on supporting mounts of spheres in measurement of gravitational constant G, Rev Sci Instrum, 87, 034504, 10.1063/1.4944475 · DOI
  83. Quan, 2014, Feedback control of torsion balance in measurement of gravitational constant G with angular acceleration method, Rev Sci Instrum, 85, 014501, 10.1063/1.4861189 · DOI
  84. Xue, 2014, Preliminary determination of Newtonian gravitational constant with angular acceleration feedback method, Philos Trans R Soc A, 372, 20140031, 10.1098/rsta.2014.0031 · DOI
  85. Nolting, 1999, A value for G from beam-balance experiments, Meas Sci Technol, 10, 487, 10.1088/0957-0233/10/6/312 · DOI
  86. Schlamminger, 2002, Determination of the gravitational constant with a beam balance, Phys Rev Lett, 89, 161102, 10.1103/PhysRevLett.89.161102 · DOI
  87. Schlamminger, 2002, Determination of the gravitational constant using a beam balance
  88. Schurr, 1998, Measurement of the gravitational constant G by means of a beam balance, Phys Lett A, 248, 295, 10.1016/S0375-9601(98)00699-9 · DOI
  89. Nolting, 1999, Determination of G by means of a beam balance, IEEE Trans Instrum Meas, 48, 245, 10.1109/19.769574 · DOI
  90. Nolting, 2000, Determination of the gravitational constant G by means of a beam balance, Euro Phys News, 31, 25
  91. Schlamminger, 2014, Reflections on a measurement of the gravitational constant using a beam balance and 13 tons of mercury, Philos Trans R Soc A, 372, 20140027, 10.1098/rsta.2014.0027 · DOI
  92. Parks, 2014, A simple pendulum laser interferometer for determining the gravitational constant, Philos Trans R Soc A, 372, 20140024, 10.1098/rsta.2014.0024 · DOI
  93. Lamporesi, 2007, Source masses and positioning system for an accurate measurement of G, Rev Sci Instrum, 78, 075109, 10.1063/1.2751090 · DOI
  94. Bertoldi, 2006, Atom interferometry gravity-gradiometer for the determination of the Newtonian gravitational constant G, Eur Phys J D, 40, 271, 10.1140/epjd/e2006-00212-2 · DOI
  95. Fixler, 2007, Atom interferometer measurement of the Newtonian constant of gravity, Science, 315, 74, 10.1126/science.1135459 · DOI
  96. Lamporesi, 2008, Determination of the Newtonian gravitational constant using atom interferometry, Phys Rev Lett, 100, 050801, 10.1103/PhysRevLett.100.050801 · DOI
  97. Bantel, 1998, Anelastic behavior of a torsion pendulum with a CuBe fiber at low temperature and implications for a measurement of the gravitational constant
  98. Cross, 2009, Systematic error sources in a measurement of G using a cryogenic torsion pendulum

Cited by

Sorted by citations

Authors
Xue, C., Liu, J.-P., Li, Q., Wu, J.-F., Yang, S.-Q., Liu, Q., Shao, C.-G., Tu, L.-C., Hu, Z.-K., & Luo, J.
Affiliations
  • Sun Yat-sen University (CN)
  • TianQin Research Center for Gravitational Physics & School of Physics and Astronomy, Sun Yat-sen University (Zhuhai Campus), Zhuhai 519082, China
  • Huazhong University of Science and Technology (CN)
  • MOE Key Laboratory of Fundamental Physical Quantities Measurement & Hubei Key Laboratory of Gravitation and Quantum Physics, PGMF and School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
Corresponding author
  • Yang, Shan-Qing
  • Luo, Jun
Venue
National Science Review
Published
2020-07-22
Volume
7
Issue
12
Pages
1803-1817
ISSN
  • 2053-714X (ISSN-L)
  • 2095-5138
OpenAlex
W3043914808
Cited by
60
References
0
Citations by year
2026: 6 · 2025: 14 · 2024: 12 · 2023: 8 · 2022: 7 · 2021: 10 · 2020: 3
FWCI
4.27
Type
journal article
Language
en
Open access
Locations
  • National Science Review (publishedVersion, cc-by)
  • PubMed Central (publishedVersion, cc-by)
  • PubMed (publishedVersion)
Funders
  • National Natural Science Foundation of China (91536223, 11722542, 11325523, 11605295)
  • National Basic Research Program of China (2010CB832801)
Topics
  • Physical Sciences › Physics and Astronomy › Instrumentation › Scientific Measurement and Uncertainty Evaluation
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
  • Physical Sciences › Engineering › Mechanical Engineering › Advanced Measurement and Metrology Techniques
Keywords
gravitational constant, Newtonian gravity, precision measurement, fundamental physical constants, CODATA 2018

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review