Editing Gravitational constant (section)

=== Modern value ===
[[Paul R. Heyl]] (1930) published the value of {{val|6.670|(5)|e=−11|u=m<sup>3</sup>⋅kg<sup>−1</sup>⋅s<sup>−2</sup>}} (relative uncertainty 0.1%),<ref>{{cite journal |first=P. R. |last=Heyl |author-link=Paul R. Heyl |title=A redetermination of the constant of gravitation |journal= Bureau of Standards Journal of Research|volume=5 |issue=6 |year=1930 |pages=1243–1290|doi=10.6028/jres.005.074 |doi-access=free }}<!--Also  https://archive.org/details/redeterminationo56124heyl, and a shorter version at https://europepmc.org/articles/PMC1085130--></ref> improved to {{val|6.673|(3)|e=−11|u=m<sup>3</sup>⋅kg<sup>−1</sup>⋅s<sup>−2</sup>}} (relative uncertainty 0.045% = 450&nbsp;ppm) in 1942.<ref>P. R. Heyl and P. Chrzanowski (1942), cited after Sagitov (1969:715).</ref>

However, Heyl used the statistical spread as his standard deviation, and he admitted himself that measurements using the same material yielded very similar results while measurements using different materials yielded vastly different results. He spent the next 12 years after his 1930 paper to do more precise measurements, hoping that the composition-dependent effect would go away, but it did not, as he noted in his final paper from the year 1942.

Published values of {{mvar|G}} derived from high-precision measurements since the 1950s have remained compatible with Heyl (1930), but within the relative uncertainty of about 0.1% (or 1000&nbsp;ppm) have varied rather broadly, and it is not entirely clear whether the uncertainty has been reduced at all since the 1942 measurement. Some measurements published in the 1980s to 2000s were, in fact, mutually exclusive.<ref name=gillies/><ref name=codata2002>{{cite journal|first1=Peter J. |last1=Mohr |first2=Barry N. |last2=Taylor |title=CODATA recommended values of the fundamental physical constants: 2002 |journal=Reviews of Modern Physics |year=2012 |volume=77 |issue=1 | pages=1–107 |url=http://www.atomwave.org/rmparticle/ao%20refs/aifm%20refs%20sorted%20by%20topic/other%20rmp%20articles/CODATA2005.pdf |access-date=1 July 2006 |doi=10.1103/RevModPhys.77.1 |bibcode=2005RvMP...77....1M |citeseerx=10.1.1.245.4554 |url-status=dead |archive-url=https://web.archive.org/web/20070306174141/http://www.atomwave.org/rmparticle/ao%20refs/aifm%20refs%20sorted%20by%20topic/other%20rmp%20articles/CODATA2005.pdf |archive-date=6 March 2007|arxiv=1203.5425 }} Section Q (pp. 42–47) describes the mutually inconsistent measurement experiments from which the CODATA value for {{mvar|G}} was derived.</ref> Establishing a standard value for {{mvar|G}} with a relative standard uncertainty better than 0.1% has therefore remained rather speculative.

By 1969, the value recommended by the [[National Institute of Standards and Technology]] (NIST) was cited with a relative standard uncertainty of 0.046% (460&nbsp;ppm), lowered to 0.012% (120&nbsp;ppm) by 1986. But the continued publication of conflicting measurements led NIST to considerably increase the standard uncertainty in the 1998 recommended value, by a factor of 12, to a standard uncertainty of 0.15%, larger than the one given by Heyl (1930).

The uncertainty was again lowered in 2002 and 2006, but once again raised, by a more conservative 20%, in 2010, matching the relative standard uncertainty of 120&nbsp;ppm published in 1986.<ref>{{Cite journal|url = http://physics.nist.gov/cuu/pdf/RevModPhysCODATA2010.pdf|title = CODATA recommended values of the fundamental physical constants: 2010|date = 13 November 2012|journal = Reviews of Modern Physics |doi = 10.1103/RevModPhys.84.1527|bibcode=2012RvMP...84.1527M|arxiv = 1203.5425 |volume=84 |issue = 4|pages=1527–1605|last1 = Mohr|first1 = Peter J.|last2 = Taylor|first2 = Barry N.|last3 = Newell|first3 = David B.|s2cid = 103378639|citeseerx = 10.1.1.150.3858}}</ref> For the 2014 update, CODATA reduced the uncertainty to 46&nbsp;ppm, less than half the 2010 value, and one order of magnitude below the 1969 recommendation.

The following table shows the NIST recommended values published since 1969:
[[File:Gravitational constant historical.png|thumb|350px|Timeline of measurements and recommended values for ''G'' since 1900: values recommended based on a literature review are shown in red, individual torsion balance experiments in blue, other types of experiments in green.]]
{|class=wikitable
|+Recommended values for ''G''
!scope="col"| Year
!scope="col"| ''G'' <br />{{bracket|10{{sup|−11}}&nbsp;m{{sup|3}}⋅kg{{sup|−1}}⋅s{{sup|−2}}}}
! scope="col"|Relative standard uncertainty
!scope="col"| Ref.
|-
!scope="row"|1969
| {{val|6.6732|(31)}}  || 460&nbsp;ppm || <ref>{{cite journal | last1=Taylor | first1=B. N. | last2=Parker | first2=W. H. | last3=Langenberg | first3=D. N. | title=Determination of ''e''/''h'', Using Macroscopic Quantum Phase Coherence in Superconductors: Implications for Quantum Electrodynamics and the Fundamental Physical Constants | journal=Reviews of Modern Physics | publisher=American Physical Society (APS) | volume=41 | issue=3 | date=1969-07-01 | issn=0034-6861 | doi=10.1103/revmodphys.41.375 | bibcode=1969RvMP...41..375T | pages=375–496}}</ref>
|-
!scope="row"|1973
| {{val|6.6720|(49)}}  || 730&nbsp;ppm || <ref>{{cite journal | last1=Cohen | first1=E. Richard | last2=Taylor | first2=B. N. | title=The 1973 Least-Squares Adjustment of the Fundamental Constants | journal=Journal of Physical and Chemical Reference Data | publisher=AIP Publishing | volume=2 | issue=4 | year=1973 | issn=0047-2689 | doi=10.1063/1.3253130 | bibcode=1973JPCRD...2..663C | pages=663–734| hdl=2027/pst.000029951949 | hdl-access=free }}</ref>
|-
!scope="row"|1986
| {{val|6.67449|(81)}} || 120&nbsp;ppm || <ref>{{cite journal | last1=Cohen | first1=E. Richard | last2=Taylor | first2=Barry N. | title=The 1986 adjustment of the fundamental physical constants | journal=Reviews of Modern Physics | publisher=American Physical Society (APS) | volume=59 | issue=4 | date=1987-10-01 | issn=0034-6861 | doi=10.1103/revmodphys.59.1121 | bibcode=1987RvMP...59.1121C | pages=1121–1148}}</ref>
|-
!scope="row"|1998
| {{val|6.673|(10)}} || 1500&nbsp;ppm || <ref>{{cite journal | last1=Mohr | first1=Peter J. | last2=Taylor | first2=Barry N. | title=CODATA recommended values of the fundamental physical constants: 1998 | journal=Reviews of Modern Physics | volume=72 | issue=2 | year=2012 | issn=0034-6861 | doi=10.1103/revmodphys.72.351 | bibcode=2000RvMP...72..351M | pages=351–495| arxiv=1203.5425 }}</ref>
|-
!scope="row"|2002
| {{val|6.6742|(10)}} || 150&nbsp;ppm || <ref>{{cite journal | last1=Mohr | first1=Peter J. | last2=Taylor | first2=Barry N. | title=CODATA recommended values of the fundamental physical constants: 2002 | journal=Reviews of Modern Physics | volume=77 | issue=1 | year=2012 | issn=0034-6861 | doi=10.1103/revmodphys.77.1 | bibcode=2005RvMP...77....1M | pages=1–107| arxiv=1203.5425 }}</ref>
|-
!scope="row"|2006
| {{val|6.67428|(67)}} || 100&nbsp;ppm || <ref>{{cite journal | last1=Mohr | first1=Peter J. | last2=Taylor | first2=Barry N. | last3=Newell | first3=David B. | title=CODATA recommended values of the fundamental physical constants: 2006 | journal=Journal of Physical and Chemical Reference Data | volume=37 | issue=3 | year=2012 | issn=0047-2689 | doi=10.1063/1.2844785 | bibcode=2008JPCRD..37.1187M | pages=1187–1284| arxiv=1203.5425 }}</ref>
|-
!scope="row"|2010
| {{val|6.67384|(80)}} || 120&nbsp;ppm || <ref>{{cite journal | last1=Mohr | first1=Peter J. | last2=Taylor | first2=Barry N. | last3=Newell | first3=David B. | title=CODATA Recommended Values of the Fundamental Physical Constants: 2010 | journal=Journal of Physical and Chemical Reference Data | volume=41 | issue=4 | year=2012 | pages=1527–1605 | issn=0047-2689 | doi=10.1063/1.4724320 | bibcode=2012JPCRD..41d3109M | arxiv=1203.5425 }}</ref>
|-
!scope="row"|2014
| {{val|6.67408|(31)}} ||  46&nbsp;ppm || <ref>{{cite journal | last1=Mohr | first1=Peter J. | last2=Newell | first2=David B. | last3=Taylor | first3=Barry N. | title=CODATA Recommended Values of the Fundamental Physical Constants: 2014 | journal=Journal of Physical and Chemical Reference Data | volume=45 | issue=4 | year=2016 | pages=1527–1605 | issn=0047-2689 | doi=10.1063/1.4954402 | bibcode=2016JPCRD..45d3102M | arxiv=1203.5425 }}</ref>
|-
!scope="row"|2018
| {{val|6.67430|(15)}} ||  22&nbsp;ppm || <ref>Eite Tiesinga, Peter J. Mohr, David B. Newell, and Barry N. Taylor (2019), "[http://physics.nist.gov/constants The 2018 CODATA Recommended Values of the Fundamental Physical Constants]" (Web Version 8.0). Database developed by J. Baker, M. Douma, and [[Svetlana Kotochigova|S. Kotochigova]]. National Institute of Standards and Technology, Gaithersburg, MD 20899.</ref>
|-
!scope="row"|2022
| {{val|6.67430|(15)}} ||  22 ppm || <ref>{{citation |author1=Mohr, P. |author2=Tiesinga, E. |author3=Newell, D. |author4=Taylor, B. |date=2024-05-08 |title=Codata Internationally Recommended 2022 Values of the Fundamental Physical Constants |work=NIST |url=https://www.nist.gov/publications/codata-internationally-reconmmended-2022-values-fundamental-physical-constants |access-date=2024-05-15 }}</ref>
|-
|}
In the January 2007 issue of ''[[Science (journal)|Science]]'', Fixler et al. described a measurement of the gravitational constant by a new technique, [[atom interferometry]], reporting a value of {{nowrap|1={{math|''G''}} = {{val|6.693|(34)|e=−11|u=m<sup>3</sup>⋅kg<sup>−1</sup>⋅s<sup>−2</sup>}}}}, 0.28% (2800&nbsp;ppm) higher than the 2006 CODATA value.<ref>{{cite journal |first1=J. B. |last1=Fixler |first2=G. T. |last2=Foster |first3=J. M. |last3=McGuirk |first4=M. A. |last4=Kasevich |s2cid=6271411 |title=Atom Interferometer Measurement of the Newtonian Constant of Gravity |date=5 January 2007 |volume=315 |issue=5808 |pages=74–77 |doi=10.1126/science.1135459 |journal=Science |pmid=17204644 |bibcode=2007Sci...315...74F }}</ref> An improved cold atom measurement by Rosi et al. was published in 2014 of {{nowrap|1={{math|''G''}} = {{val|6.67191|(99)|e=−11|u=m<sup>3</sup>⋅kg<sup>−1</sup>⋅s<sup>−2</sup>}}}}.<ref>
{{cite journal
 |last1=Rosi |first1=G.
 |last2=Sorrentino |first2=F.
 |last3=Cacciapuoti |first3=L.
 |last4=Prevedelli |first4=M.
 |last5=Tino |first5=G. M.
 |title=Precision measurement of the Newtonian gravitational constant using cold atoms
 |journal=Nature |volume=510 |issue=7506  |date=26 June 2014 |pages=518–521
 |url=http://www2.fisica.unlp.edu.ar/materias/FisGral2semestre2/Rosi.pdf |url-status=live
 |archive-url=https://ghostarchive.org/archive/20221009/http://www2.fisica.unlp.edu.ar/materias/FisGral2semestre2/Rosi.pdf
 |archive-date=2022-10-09
 |doi=10.1038/nature13433 |pmid=24965653  |arxiv=1412.7954
 |s2cid=4469248
 |bibcode=2014Natur.510..518R
}}</ref><ref>
{{cite journal
 |last1=Schlamminger |first1=Stephan
 |title=Fundamental constants: A cool way to measure big G
 |journal=Nature |volume=510 |issue=7506 |pages=478–480
 |date=18 June 2014
 |url=https://www.nature.com/articles/nature13507.pdf
 |archive-url=https://ghostarchive.org/archive/20221009/https://www.nature.com/articles/nature13507.pdf
 |archive-date=2022-10-09
 |url-status=live
 |doi=10.1038/nature13507 |doi-access=free
 |bibcode=2014Natur.510..478S |pmid=24965646
}}</ref> Although much closer to the accepted value (suggesting that the Fixler ''et al.'' measurement was erroneous), this result was 325&nbsp;ppm below the recommended 2014 CODATA value, with non-overlapping [[standard uncertainty]] intervals.
<!-- 6.67191(99) vs. 6.67408(31) [2014], a difference of 0.00217(104). Also *barely* not overlapping with the
2010 interval, 6.67384(80) [2010] (differences 0.00193(127) and 0.00024(86)).
This doesn't mean anything beyond "2-sigma effect" until the experiment is repeated.
-->

As of 2018, efforts to re-evaluate the conflicting results of measurements are underway, coordinated by NIST, notably a repetition of the experiments reported by Quinn et al. (2013).<ref>{{cite journal |author1=C. Rothleitner |author2=S. Schlamminger |title=Invited Review Article: Measurements of the Newtonian constant of gravitation, G |journal=Review of Scientific Instruments |volume=88 |issue=11 |pages=111101 |id=111101 |year=2017 |doi=10.1063/1.4994619 |pmid=29195410 |pmc=8195032 |quote=However, re-evaluating or repeating experiments that have already been performed may provide insights into hidden biases or dark uncertainty. NIST has the unique opportunity to repeat the experiment of Quinn et al. [2013] with an almost identical setup. By mid-2018, NIST researchers will publish their results and assign a number as well as an uncertainty to their value.|bibcode=2017RScI...88k1101R |doi-access=free }} Referencing:
* {{cite journal |author1=T. Quinn |author2=H. Parks |author3=C. Speake |author4=R. Davis |title=Improved determination of G using two methods |journal=Phys. Rev. Lett. |volume=111 |issue=10 |pages=101102 |id=101102 |year=2013 |doi=10.1103/PhysRevLett.111.101102 |pmid=25166649 |bibcode=2013PhRvL.111j1102Q |url=https://www.bipm.org/utils/en/pdf/PhysRevLett.111.101102.pdf |access-date=4 August 2019 |archive-date=4 December 2020 |archive-url=https://web.archive.org/web/20201204172116/https://www.bipm.org/utils/en/pdf/PhysRevLett.111.101102.pdf |url-status=dead }}
The 2018 experiment was described by {{cite conference |author=C. Rothleitner |url=https://www.bipm.org/cc/CODATA-TGFC/Allowed/2015-02/Rothleitner.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://www.bipm.org/cc/CODATA-TGFC/Allowed/2015-02/Rothleitner.pdf |archive-date=2022-10-09 |url-status=live |title=Newton's Gravitational Constant 'Big' G – A proposed Free-fall Measurement |conference=CODATA Fundamental Constants Meeting, Eltville – 5 February 2015 }}</ref>

In August 2018, a Chinese research group announced new measurements based on torsion balances, {{val|6.674184|(78)|e=−11|u=m<sup>3</sup>⋅kg<sup>−1</sup>⋅s<sup>−2</sup>}} and {{val|6.674484|(78)|e=−11|u=m<sup>3</sup>⋅kg<sup>−1</sup>⋅s<sup>−2</sup>}} based on two different methods.<ref>{{cite journal|first=Qing |last=Li |s2cid=52121922 |display-authors=etal |title=Measurements of the gravitational constant using two independent methods |journal=Nature |volume=560 |issue=7720 |pages=582–588 |year=2018 |doi=10.1038/s41586-018-0431-5|pmid=30158607 |bibcode=2018Natur.560..582L }}.
See also: {{cite news|url=https://www.techexplorist.com/physicists-precise-measurement-ever-gravitys-strength/16643/ |title=Physicists just made the most precise measurement ever of Gravity's strength |date=31 August 2018 |access-date=13 October 2018 }}</ref> These are claimed as the most accurate measurements ever made, with standard uncertainties cited as low as 12&nbsp;ppm. The difference of 2.7{{px1}}[[standard deviation|''σ'']] between the two results suggests there could be sources of error unaccounted for.