Gravitational Constant

gravitational constant (G), physical constant denoted by G and used in calculating the gravitational attraction between two objects. In Newton’s law of universal gravitation, the attractive force between two objects (F) is equal to G times the product of their masses (m₁m₂) divided by the square of the distance between them (r²); that is, F = Gm₁m₂/r². The value of G is (6.6743 ± 0.00015) × 10⁻¹¹ m³ kg⁻¹ s⁻².

It must be pointed out that G occupies a rather anomalous position among the other constants of physics. In the first place, the mass M of any celestial object cannot be determined independently of the gravitational attraction that it exerts. Thus, the combination GM, not the separate value of M, is the only meaningful property of a star, planet, or galaxy. Second, according to general relativity and the principle of equivalence, G does not depend on material properties but is in a sense a geometric factor. Hence, the determination of the constant of gravitation does not seem as essential as the measurement of quantities like the electronic charge or Planck’s constant.

The gravitational constant G was first measured in 1797–98 by the English scientist Henry Cavendish. He followed a method prescribed, and used an apparatus built, by his countryman the geologist and astronomer John Michell, who had died in 1793.

The apparatus featured a torsion balance: a wooden rod was suspended freely from a thin wire, and a lead sphere weighing 0.73 kg (1.6 pounds) hung from each end of the rod. A much larger sphere, weighing 158 kg (348 pounds), was placed at each end of the torsion balance. The gravitational attraction between each larger weight and each smaller one drew the ends of the rod aside along a graduated scale. The attraction between these pairs of weights was counteracted by the restoring force from a twist in the wire, which caused the rod to move from side to side like a horizontal pendulum.

Cavendish and Michell did not conceive of their experiment as an attempt to measure G. The formulation of Newton’s law of gravitation involving the gravitational constant did not occur until the late 19th century. The experiment was originally devised to determine Earth’s density, which Cavendish determined to be 5.48 grams per cubic centimetre—close to the modern value of 5.51 grams per cubic centimetre. This leads to a value for G of about 6.7 × 10⁻¹¹ m³ kg⁻¹ s⁻². Since the late 19th century, refinements of the Cavendish experiment have been used for determining G.