Gravitational constant

The gravitational constant G is a fundamental physical constant which appears in Newton's law of gravitation and in Einstein's theory of general relativity.

In terms of metric units, the constant of gravitation is approximately:

G = 6.673 × 10^-11 m³ s^-2 kg^-1

This small number is the attraction in newtons of two objects of mass 1 kg each, at a distance of 1 m apart (between two objects of 1000 kg each, 1 m apart, the force is ca. 6.7 × 10^-5 N, approximately equal to the pull of Earth's surface gravity on a 6.8 mg mass).

Only the first two digits are known to be correct. Thus, the gravitational constant is among the least precisely determined physical constants. Equally uncertain is the mass of the sun. The position of the planets are known far more accurately, and also the product of G and the mass of the sun. Therefore calculations in celestial mechanics are carried out using the unit of solar mass rather than the standard SI unit kg.

G was first measured by Henry Cavendish (Philosophical Transactions 1798). He used a horizontal torsion beam with lead balls whose inertia (in relation to the torsion constant) he could tell by timing the beam's oscillation. Their faint attraction to other balls placed alongside the beam was detectable by the deflection it caused.

The gravitational constant plays a fundamental role in Einstein's equation of general relativity. In combination with Planck's constant and the speed of light in a vacuum, it is possible to create a system of units known as Planck units in which the gravitational constant, Planck's constant and the speed of light all take the numerical value 1.