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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.
For example, the Earth's mean specific gravity (5.515) is far higher than the typical specific gravity of rocks at the surface (2.7–3.3), implying that the deeper material is denser. This is also implied by its low moment of inertia ( 0.33 M R 2 , compared to 0.4 M R 2 for a sphere of constant density).
The component due to the Earth's rotation can then be included, if appropriate, based on a sidereal day relative to the stars (≈366.24 days/year) rather than on a solar day (≈365.24 days/year). That component is perpendicular to the axis of rotation rather than to the surface of the Earth.
Based on this, Hutton's 1778 result is equivalent to G ≈ 8 × 10 −11 m 3 ⋅kg −1 ⋅s −2. Diagram of torsion balance used in the Cavendish experiment performed by Henry Cavendish in 1798, to measure G, with the help of a pulley, large balls hung from a frame were rotated into position next to the small balls.
The above equation describes the Earth's gravitational potential, not the geoid itself, at location ,,, the co-ordinate being the geocentric radius, i.e., distance from the Earth's centre. The geoid is a particular equipotential surface, [ 27 ] and is somewhat involved to compute.
It is a generalisation of the vector form, which becomes particularly useful if more than two objects are involved (such as a rocket between the Earth and the Moon). For two objects (e.g. object 2 is a rocket, object 1 the Earth), we simply write r instead of r 12 and m instead of m 2 and define the gravitational field g(r) as: