Newton's constant

Newton's constant
User:Dna-Dennis · CC BY 3.0 · source
Name	Newton's constant
Quantity	gravitational constant
SI	6.67430×10^−11 m^3 kg^−1 s^−2 (2018 CODATA)
Dimension	M^−1 L^3 T^−2

Newton's constant is the empirical coupling constant that sets the strength of the inverse-square law of gravitation in classical mechanics and appears as the coupling parameter in relativistic gravitation. It enters the laws formulated by Isaac Newton and later by Albert Einstein and provides the scale that relates mass, length, and time in gravitational interactions. Because it is both small and difficult to measure, Newton's constant plays an outsized role in precision tests carried out by institutions such as National Institute of Standards and Technology, Cavendish Laboratory, and Laboratoire Kastler Brossel.

Definition and value

Newton's constant appears in Newton's law of universal gravitation and is denoted by G in the equations of Isaac Newton and later in the field equations of Albert Einstein. The conventional SI value recommended by Committee on Data for Science and Technology and CODATA is 6.67430×10^−11 m^3 kg^−1 s^−2, with a relative standard uncertainty that has been the subject of international metrology work at International Bureau of Weights and Measures, National Physical Laboratory (United Kingdom), and Physikalisch-Technische Bundesanstalt. Historically, values reported by experiments at institutions such as Queen Mary University of London and University of Zürich have varied, motivating coordinated efforts among laboratories including Harvard University and Massachusetts Institute of Technology.

Historical development

The empirical determination of the gravitational coupling began with the torsion balance experiment by Henry Cavendish at the Cavendish Laboratory in 1798, which yielded the first laboratory estimate of the Earth’s density and thereby of the constant used in Isaac Newton’s law. Later refinements were made by researchers at Princeton University and by instrument builders such as John Michell and experimenters influenced by the work of Charles-Augustin de Coulomb and James Clerk Maxwell. In the 20th century, measurements at institutions including Niels Bohr Institute, Royal Society, and Institute for Advanced Study confronted systematic challenges that paralleled developments in precision metrology by groups at National Bureau of Standards and Laboratoire National de Métrologie et d'Essais.

Role in Newtonian gravity and units

In classical mechanics, Newton's gravitational law uses the constant G to relate the force between two point masses; this law was central to the celestial mechanics of Johannes Kepler and the orbital calculations of Edmond Halley. The constant fixes the scale that converts mass units such as the kilogram (established by International Prototype of the Kilogram) and length units such as the metre (defined by the Bureau International des Poids et Mesures) into forces measured with instruments developed at places like the Royal Observatory, Greenwich. G also appears in the definition of derived quantities such as the gravitational potential energy used in studies at Cambridge University and in the formulation of escape velocity in works associated with Hermann Bondi and Arthur Eddington.

Relation to general relativity and gravitational theories

In the Einstein field equations of Albert Einstein, Newton's constant sets the coupling between spacetime curvature and the stress–energy tensor, replacing the Newtonian description used by Isaac Newton. G, together with the speed of light c, appears in combinations that define the Planck units, which were introduced by Max Planck and later used by researchers such as Paul Dirac and Richard Feynman to explore quantum gravity. Alternative theories of gravitation proposed by Hermann Weyl, Theodor Kaluza, and Jordan–Brans–Dicke theory modify or reinterpret the role of G, while modern approaches including Loop quantum gravity and string theory seek to derive or explain its value from deeper principles.

Experimental measurements and uncertainties

Precision measurements of G have been performed with torsion balances, atom interferometry, and beam-balance methods at laboratories such as Stanford University, Wuhan University, BIPM, and University of Zürich. Discrepancies among determinations reported by teams at University of Washington, National Institute of Standards and Technology, and Moscow State University have led to intensive scrutiny by committees of International Council for Science and working groups at CODATA. Atom interferometry experiments influenced by techniques developed at Massachusetts Institute of Technology and University of California, Berkeley offer complementary systematic uncertainties, while proposed space-based tests associated with missions like MICROSCOPE and concepts studied at European Space Agency aim to reduce environmental noise and test for spatial or temporal variations.

Cosmological and astrophysical implications

Although Newton's constant is measured in terrestrial experiments, its value is central to astrophysical calculations performed by teams at Max Planck Institute for Astrophysics, Harvard–Smithsonian Center for Astrophysics, and NASA. G enters estimates of stellar structure used in models by Subrahmanyan Chandrasekhar and Hans Bethe, compact object masses for Karl Schwarzschild and Jocelyn Bell Burnell-related pulsar work, and in calculations of the dynamics of galaxies that prompted propositions of Vera Rubin and Fritz Zwicky regarding dark matter. In cosmology, G appears in the Friedmann equations employed by Alexander Friedmann and Georges Lemaître to describe expansion, and it sets the scale in contexts studied by Max Tegmark and Alan Guth regarding inflation and large-scale structure.

Theoretical significance and attempts at unification

The smallness of Newton's constant relative to couplings in Paul Dirac-era electrodynamics motivated speculative ideas by Paul Dirac and later work by Steven Weinberg seeking naturalness explanations. Efforts to unify gravity with the Standard Model of particle physics by researchers at CERN, Perimeter Institute, and Institute for Advanced Study include approaches in string theory developed by Edward Witten and alternatives such as asymptotic safety advanced by Steven Weinberg (physicist). The appearance of G in Planck-scale combinations relates it to ongoing attempts by John Schwarz and Leonard Susskind to derive coupling constants from higher-dimensional or quantum-geometric frameworks.

Category:Physical constants