Gravitational constant

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The gravitational constant, denoted G, is an empirical physical constant involved in the calculation of the gravitational attraction between objects with mass. It appears in Newton's law of universal gravitation and in Einstein's theory of general relativity. It is also known as the universal gravitational constant, Newton's constant, and colloquially Big G.[1] It should not be confused with "little g" (g), which is the local gravitational field (equivalent to the free-fall acceleration[2]), especially that at the Earth's surface; see Earth's gravity and Standard gravity.

According to the law of universal gravitation, the attractive force (F) between two bodies is proportional to the product of their masses (m1 and m2), and inversely proportional to the square of the distance (r) between them:

The constant of proportionality, G, is the gravitational constant.

The gravitational constant is perhaps the most difficult physical constant to measure to high accuracy.[3] In SI units, the 2006 CODATA-recommended value of the gravitational constant is:[4]

with relative standard uncertainty 1 part in 104.

Contents

Dimensions, units and magnitude

The dimensions assigned to the gravitational constant in the equation above — length cubed, divided by mass and by time squared (in SI units, metres cubed per kilogram per second squared) — are those needed to balance the units of measurements in gravitational equations. However, these dimensions have fundamental significance in terms of Planck units: when expressed in SI units, the gravitational constant is dimensionally and numerically equal to the cube of the Planck length divided by the Planck mass and by the square of Planck time.

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