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·m2/kg2 ± 0.0014% (2000 value, from torsional balance experiment at the University of Washington);
* 2001: G = 6.67559 × 10−11 N·m2/kg2 ± 41 ppm (BIPM-Birmingham team of Terry Quinn et al);
* 2004: G = (6.675 ± 0.007) × 10−11 N·m2/kg2 (using a superconducting gravimeter, Bologna);
* 2005: G = 6.6723(9) × 10−11 N·m 2/kg2 in the HUST experiment;
* 2006: G = 6.674252(109)(54) × 10−11 N·m2/kg2, with beam balance;
* 2008: CODATA value (6.67428 ± 0.00067) × 10−11 N·m2/kg2;
* 2009: G = 6.67349(18) × 10−11 N·m2/kg2 with time-of-swing method;
* 2010: G = 6.67234(14) × 10−11 N·m2/kg2 from the change in spacing between two free-hanging pendulum masses;
* 2013: G = 6.67545(18) × 10−11 N·m2/kg2 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·m2/kg2.
* 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.

* 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].

measurements of G
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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