Newton's Gravitational Constant |

**In General**
> s.a. newtonian gravitation; theories of gravity.

* __History of measurements__: 1687, Newton guessed
its value to within 2%; 1798, Cavendish and Michell measured it to within 1%; 1895, C V Boys at
Clarendon Laboratory measured it to within 0.1%; 2000, Measurements by Gundlach & Merkowitz
of the Eöt-Wash Group with 10^{−5} relative error.

* __Value__: *G*
= 6.67390 × 10^{−11}
N·m^{2}/kg^{2}
± 0.0014% (2000 value, from torsional balance experiment at the University of Washington);

* __2001__: *G* =
6.67559 × 10^{−11}
N·m^{2}/kg^{2}
± 41 ppm (BIPM-Birmingham team of Terry Quinn et al);

* __2004__: *G*
= (6.675 ± 0.007) × 10^{−11}
N·m^{2}/kg^{2}
(using a superconducting gravimeter, Bologna);

* __2005__: *G*
= 6.6723(9) × 10^{−11}
N·m^{ 2}/kg^{2}
in the HUST experiment;

* __2006__: *G*
= 6.674252(109)(54) × 10^{−11}
N·m^{2}/kg^{2},
with beam balance;

* __2008__: CODATA value (6.67428
± 0.00067) × 10^{−11}
N·m^{2}/kg^{2};

* __2009__:
*G* = 6.67349(18) × 10^{−11}
N·m^{2}/kg^{2}
with time-of-swing method;

* __2010__:
*G* = 6.67234(14) × 10^{−11}
N·m^{2}/kg^{2}
from the change in spacing between two free-hanging pendulum masses;

* __2013__:
*G* = 6.67545(18) × 10^{−11}
N·m^{2}/kg^{2} from
new International Bureau of Weights and Measures (BIPM) measurements using two methods.

* __2014__: Serious disagreement between different
measurements of *G* is a sign of problems with the theory and/or experiments.

* __2018__: New experiments give the
smallest uncertainty yet, *G* = 6.674184 (11.64 ppm) and 6.674484 (11.61 ppm)
× 10^{−11}
N·m^{2}/kg^{2}.

* __Status__: It is difficult to measure because
in the lab gravity is weak, and in astronomy it appears in the combination *GM*; The
best values come from modern versions of the Cavendish experiment, although some geophysical
data seem to contradict them.

@ __General references__: de Sabbata et al ed-04;
Wilczek PT(01)jun [smallness].

@ __Status of measurements__:
Milyukov et al G&C(08);
Milyukov & Fan G&C(12);
Horstman & Trimble a1811 [history, 1686 to 2016].

@ __And the dilaton__: Zee PRL(79);
Nieh PLA(82);
> s.a. conformal invariance.

@ __Other origin__:
Townsend PRD(77) [spacetime structure];
Damour MST(99)gq [significance];
> s.a. emergent gravity [entropic].

> __Online resources__:
see Wikipedia page.

**Measurements**

* __Methods__: In the lab, it
can be measured with a torsion balance, in static/compensation mode or in
dynamic mode, or with an electronic balance.

@ __General references__: Anderson et al EPL(15)-a1504 [correlation of results with the length of the day];
news sn(15)apr [discrepancy not understood].

@ __Torsion balance__: Kuroda PRL(95);
Gundlach et al PRD(96);
Luo et al PRD(99) [torsion pendulum period];
Gundlach & Merkowitz PRL(00)gq;
Schwarzschild PT(00)jul;
Quinn et al PRL(01);
Armstrong & Fitzgerald PRL(03);
Fitch et al AJP(07)apr [automation];
Kuznetsov et al G&C(07);
Luo et al PRL(09),
Tu et al PRD(10) [time-of-swing method];
Quinn et al PRL(13).

@ __Space-based__: Sanders & Gillies RNC(96);
Alexeev et al G&C(99)gq/00,
Metr-gq/01,
Melnikov gq/00 [SEE];
Swain a1405 [using a purely gravitational oscillator];
Feldman et al CQG(16)-a1605
+ CQG+ [proposal].

@ __Other measurements__: Gillies Met(87) [index];
Hubler et al PRD(95) [lake];
Schurr et al PLA(98),
PRL(98),
Schlamminger et al PRL(02),
PRD(06) [beam balance];
Baldi et al PRD(05) [superconducting gravimeter];
Lamporesi et al PRL(08) [cold-atom interferometry];
Parks & Faller PRL(10) [simple-pendulum experiment];
Pitkin EPL(15)-a1505 [on correlation with observed periodic variations in the length of the day];
Armata et al PRA(17)-a1707 [using an optomechanical cavity];
Li et al Nat(18)aug
+ news sn(18)sug [using two independent methods];
Kawasaki a1903 [precision displacement sensors].

Measured values of the gravitational constant. Credit: S Schlamminger / Nature 2018

**Running / Scale Dependence in Quantum Theory**
> s.a. asymptotic safety; dark
matter [alternative]; renormalization of quantum gravity.

* __Idea__: 2005, Some
non-perturbative studies of quantum gravity suggest that the effective
*G* might slowly increase with distance; In cosmology, this may work
as an alternative to dark matter and be related to the expansion acceleration.

@ __General references__: Greensite PRD(94)gq/93 [in quantum gravity, universe not in an eigenstate of *G*];
Dou & Percacci CQG(98)ht/97;
Reuter ht/00;
Hamber & Williams PRD(05)ht [vacuum polarization, effective field equations],
PRD(07)ht/06 [static isotropic];
López Nacir & Mazzitelli PRD(07)ht/06 [and non-integer powers of \(\square\)];
Robbers et al PRL(08);
Calmet et al PRD(08)-a0803 [without extra dimensions];
Jalalzadeh & Darabi IJMPA(10)-a1010 [one-loop correction in FLRW models];
Anber & Donoghue PRD(12)-a1111 [no useful and universal definition];
Nagy et al JHEP(12)-a1203 [infrared fixed point];
Frampton & Karl a1304 [at very short distances];
Codello et al PRD(14)-a1304 [consistent closure of RG flow];
Falls PRD(15)-a1501 [gauge-independent beta function];
Solodukhin PRD(15)-a1502 [due to fields of various spins];
Moffat a1505 [modified gravitational theory];
Smolin CQG(16)-a1507 [*G* and Λ as conjugate dynamical variables];
Chen et al a2008 [quantum corrections];
> s.a. unimodular gravity.

@ __And observations / phenomenology__:
Reuter & Weyer JCAP(04),
EAS(06)ap/05-proc [astrophysical distances];
Reeb a0901-proc [and standard model, GUTs];
Rodrigues et al PoS-a1301 [inside galaxies];
Moffat a1507 [in astrophysics and cosmology].

**Other Issues and Generalizations**
> s.a. variation of newton's gravitational constant.

@ __References__: Deffayet & Woodard JCAP(09) [distorted constant, and cosmology].

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