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An approximate value for gravity at a distance r from the center of the Earth can be obtained by assuming that the Earth's density is spherically symmetric. 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 ...
The value of ɡ 0 defined above is a nominal midrange value on Earth, originally based on the acceleration of a body in free fall at sea level at a geodetic latitude of 45°. Although the actual acceleration of free fall on Earth varies according to location, the above standard figure is always used for metrological purposes.
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 m 3 kg −1 s −2. [1] The modern notation of Newton's law involving G was introduced in the 1890s by C. V. Boys.
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 ...
rad/s is the diurnal angular speed of the Earth axis, and km the radius of the reference sphere, and the distance of the point on the Earth crust to the Earth axis. [3] For the mass attraction effect by itself, the gravitational acceleration at the equator is about 0.18% less than that at the poles due to being located farther from the mass ...
For several objects in the Solar System, the value of μ is known to greater accuracy than either G or M. The SI unit of the standard gravitational parameter is m 3 ⋅s −2. However, the unit km 3 ⋅s −2 is frequently used in the scientific literature and in spacecraft navigation.
The gravity gradient (variation with height) above Earth's surface is about 3.1 μGal per centimeter of height (3.1 × 10 −6 s −2), resulting in a maximal difference of about 2 Gal (0.02 m/s 2) from the top of Mount Everest to sea level. [6]
At a fixed point on the surface, the magnitude of Earth's gravity results from combined effect of gravitation and the centrifugal force from Earth's rotation. [2] [3] At different points on Earth's surface, the free fall acceleration ranges from 9.764 to 9.834 m/s 2 (32.03 to 32.26 ft/s 2), [4] depending on altitude, latitude, and longitude.
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