Big G is among the hardest numbers in physics to pin down
Gravity holds galaxies together, yet in a laboratory it is feeble next to the other fundamental forces. That weakness makes its governing constant, G, notoriously tough to measure. Physicists know it to only about four significant digits, roughly 6.6743 times ten to the minus 11 in SI units.
In Newton's law, G is the factor linking the pull between two bodies to the product of their masses divided by the square of the distance between them. In Einstein's general relativity it reappears inside a related constant, kappa, that ties the curvature of spacetime to the matter and energy within it. It is nicknamed Big G to tell it apart from small g, the acceleration of falling objects at Earth's surface, which follows from G, Earth's mass and its radius.
Newton's law, published in the 1680s, implied the constant but never calculated it. He wondered in the Principia about detecting gravity's strength through a pendulum pulled sideways by a large hill, and judged the effect too tiny to see. Pierre Bouguer and Charles Marie de La Condamine attempted such a measurement in 1738 on their Peruvian expedition; Bouguer later claimed only that it proved Earth was not hollow, as Edmond Halley and others had proposed. The Schiehallion experiment in Scotland, finished in 1776, first succeeded in weighing Earth's average density, which is equivalent to finding G. Charles Hutton's 1778 result, 4.5 times the density of water, came in about 20% low.
Henry Cavendish's 1798 experiment is credited with the first measurement accurate to within about 1%, which is why G is sometimes called the Cavendish constant. The letter itself, in the modern form of Newton's law, was introduced in the 1890s by C. V. Boys.
Because G is so uncertain, astronomers often sidestep it. The product of G and a body's mass, called the standard gravitational parameter, is known far more precisely than either factor and feeds into formulas for escape velocity, gravitational lensing and Kepler's laws. From 1964 until 2012 the astronomical unit was even defined through a gravitational formula, before being fixed as an exact length.
Source: Gravitational constant
