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The measured value of the constant is known with some certainty to four significant digits. In SI units, its value is approximately 6.6743 × 10 −11 N⋅m 2 /kg 2. [1] The modern notation of Newton's law involving G was introduced in the 1890s by C. V. Boys.
Although the actual acceleration of free fall on Earth varies according to location, the above standard figure is always used for metrological purposes. In particular, since it is the ratio of the kilogram-force and the kilogram, its numeric value when expressed in coherent SI units is the ratio of the kilogram-force and the newton, two units ...
The gravity depends only on the mass inside the sphere of radius r. All the contributions from outside cancel out as a consequence of the inverse-square law of gravitation. Another consequence is that the gravity is the same as if all the mass were concentrated at the center. Thus, the gravitational acceleration at this radius is [14]
A conventional standard value is defined exactly as 9.80665 m/s² (about 32.1740 ft/s²). Locations of significant variation from this value are known as gravity anomalies. This does not take into account other effects, such as buoyancy or drag.
Other units include the cgs gal (sometimes known as a galileo, in either case with symbol Gal), which equals 1 centimetre per second squared, and the g (g n), equal to 9.80665 m/s 2. The value of the g n is defined as approximately equal to the acceleration due to gravity at the Earth's surface, although the actual acceleration varies slightly ...
The General Conference on Weights and Measures fixed the value of standard gravity at precisely 9.80665 m/s 2 so that disciplines such as metrology would have a standard value for converting units of defined mass into defined forces and pressures. Thus the kilogram-force is defined as precisely 9.80665 newtons.
The standard gravitational parameter μ of a celestial body is the product of the gravitational constant G and the mass M of that body. For two bodies, the parameter may be expressed as G ( m 1 + m 2 ) , or as GM when one body is much larger than the other: μ = G ( M + m ) ≈ G M . {\displaystyle \mu =G(M+m)\approx GM.}
One g is the force per unit mass due to gravity at the Earth's surface and is the standard gravity (symbol: g n), defined as 9.806 65 metres per second squared, [5] or equivalently 9.806 65 newtons of force per kilogram of mass. The unit definition does not vary with location—the g-force when standing on the Moon is almost exactly 1 ⁄ 6 that