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The gravity g′ at depth d is given by g′ = g(1 − d/R) where g is acceleration due to gravity on the surface of the Earth, d is depth and R is the radius of the Earth. If the density decreased linearly with increasing radius from a density ρ 0 at the center to ρ 1 at the surface, then ρ ( r ) = ρ 0 − ( ρ 0 − ρ 1 ) r / R , and the ...
Gravity gradiometry is the study of variations in the Earth's gravity field via measurements of the spatial gradient of gravitational acceleration. The gravity gradient tensor is a 3x3 tensor representing the partial derivatives, along each coordinate axis , of each of the three components of the acceleration vector ( g = [ g x g y g z ] T ...
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.
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]
In addition to Poynting, measurements were made by C. V. Boys (1895) [25] and Carl Braun (1897), [26] with compatible results suggesting G = 6.66(1) × 10 −11 m 3 ⋅kg −1 ⋅s −2. The modern notation involving the constant G was introduced by Boys in 1894 [12] and becomes standard by the end of the 1890s, with values usually cited in the ...
For example, the equation above gives the acceleration at 9.820 m/s 2, when GM = 3.986 × 10 14 m 3 /s 2, and R = 6.371 × 10 6 m. The centripetal radius is r = R cos( φ ) , and the centripetal time unit is approximately ( day / 2 π ), reduces this, for r = 5 × 10 6 metres, to 9.79379 m/s 2 , which is closer to the observed value.
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After converting to SI units, Cavendish's value for the Earth's density, 5.448 g cm −3, gives G = 6.74 × 10 −11 m 3 kg –1 s −2, [24] which differs by only 1% from the 2014 CODATA value of 6.67408 × 10 −11 m 3 kg −1 s −2. [25] Today, physicists often use units where the gravitational constant takes a different form.