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Concept# Gravitational constant

Summary

The gravitational constant (also known as the universal gravitational constant, the Newtonian constant of gravitation, or the Cavendish gravitational constant), denoted by the capital letter G, is an empirical physical constant involved in the calculation of gravitational effects in Sir Isaac Newton's law of universal gravitation and in Albert Einstein's theory of general relativity.
In Newton's law, it is the proportionality constant connecting the gravitational force between two bodies with the product of their masses and the inverse square of their distance. In the Einstein field equations, it quantifies the relation between the geometry of spacetime and the energy–momentum tensor (also referred to as the stress–energy tensor).
The measured value of the constant is known with some certainty to four significant digits. In SI units, its value is approximately This can also be rendered as 6.674X10-11 N*m2/kg2.
The modern notation of Newton's law involving G was introduced in the 1890s by C. V. Boys. The first implicit measurement with an accuracy within about 1% is attributed to Henry Cavendish in a 1798 experiment.
According to Newton's law of universal gravitation, the magnitude of the attractive force (F) between two point-like bodies is directly proportional to the product of their masses, m1 and m2, and inversely proportional to the square of the distance, r, directed along the line connecting their centers of mass:
The constant of proportionality, G, in this non-relativistic formulation is the gravitational constant. Colloquially, the gravitational constant is also called "Big G", distinct from "small g" (g), which is the local gravitational field of Earth (equivalent to the free-fall acceleration). Where is the mass of the Earth and is the radius of the Earth, the two quantities are related by:
The gravitational constant appears in the Einstein field equations of general relativity,
where G_μν is the Einstein tensor, Λ is the cosmological constant, g_μν is the metric tensor, T_μν is the stress–energy tensor, and κ is the Einstein gravitational constant, a constant originally introduced by Einstein that is directly related to the Newtonian constant of gravitation:
The gravitational constant is a physical constant that is difficult to measure with high accuracy.

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