The Universal Gravitational Constant G

The constant $G$ appearing in Newton's law of gravitation, $F = Gm_1m_2/r^2$, is called the universal gravitational constant. Its currently accepted value is

and, exactly as its name suggests, this same numerical value applies everywhere in the universe, for every pair of masses, at every distance -- it is one of the small handful of truly universal constants of nature, alongside constants such as the speed of light.

From $F = Gm_1m_2/r^2$, the dimensional formula of $G$ works out to $[G] = [M]^{-1}[L]^3[T]^{-2}$, obtained by rearranging $G = Fr^2/(m_1m_2)$ and substituting the dimensions of force, distance and mass.

$G$ is also notoriously difficult to measure accurately, precisely because the gravitational force between any two ordinary, laboratory-sized masses is extraordinarily small -- far smaller than the everyday forces (friction, air currents, electrostatic effects) that would easily swamp it in a naive experiment. The first successful measurement was made by Henry Cavendish in 1798, using a sensitive torsion balance: two small masses are fixed to the ends of a light rod, itself suspended by a very fine torsion fibre, and two much larger masses are then brought close to the small ones. The tiny gravitational attraction between the large and small masses twists the fibre through a small angle before the fibre's own restoring torque brings it to a new equilibrium; carefully calibrating how much torque corresponds to a given angle of twist lets $G$ be worked out from the measured deflection, the known masses, and the known separation -- the same basic method, refined considerably, is still used in modern determinations of $G$ today. …