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.

* __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];
Milyukov et al G&C(08),
Milyukov & Fan G&C(12) [status of measurements].

@ __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].

@ __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 a1707 [using an optomechanical cavity].

**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];
> 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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4 jul 2017