Gee

:This article is about the unit of acceleration. GEE is also the name of a WWII radio navigation device built and implemented by the RAF for use in night bombing. For the Latin alphabet letter, see G.

Variations of Earth's gravity

The actual acceleration of a body at the Earth's surface depends on the location at which it is measured, smaller at lower latitudes, for two reasons.

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The first is that the rotation of the Earth imposes an additional acceleration on the body that opposes gravitational acceleration. The net downward force on the body is therefore offset by a centrifugal force that acts upwards, reducing its weight. This effect on its own would result in a range of values of g from 9.789 m/s² at the equator to 9.823 m/s² at the poles.

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The second reason is the Earth's equatorial bulge, which causes objects at the equator to be further from the planet's centre than objects at the poles. Because the force due to gravitational attraction between two bodies (the Earth and the object being weighed) varies inversely with the square of the distance between them, objects at the equator experience a weaker gravitational pull than objects at the poles.

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The combined result of these two effects is that g is 0.052 m/s² more, hence the force due to gravity of an object is 0.5% more, at the poles than at the equator.

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If the terrain is at sea level, we can estimate g, at a height h in the air above it:

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:g=9.780 318 4 left( 1+A {sin}^2 L-B {sin}^2 2L ight) -3.086 imes 10^{-6}h

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where

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:g = acceleration in m/s²

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:A = 0.005 302 4

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:B = 0.000 005 9

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:L = latitude

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:h = height in meters above sea level

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The last term, 3.086 × 10-6 s-2 (0.3086 mGal/m in non-SI units; to use those units in the formula above the other constants need to be modified as well), is the free air correction: gravity decreases with height, at a rate which near the surface of the Earth is such that linear extrapolation would give zero gravity at a height of one half the radius of the Earth, i.e. the rate is 9.8 m/s² per 3200 km.

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For flat terrain above sea level a term is added, for the gravity due to the extra mass; for this purpose the extra mass can be approximated by an infinite horizontal slab, and we get 2πG times the mass per unit area, i.e. 4.2 × 10-10 m3 s-2 kg-1 (0.000,042 mGal/(kg/m²)) (the Bouguer correction). For a mean rock density of 2.67 kg/cm³ this gives 1.1 × 10-6 s-2 (0.11 mGal/m). Combined with the free-air correction this means a reduction of gravity at the surface of ca. 2 µm/s2 (0.20 mGal) for every meter of elevation of the terrain. (The two effects would cancel at a surface rock density of 4/3 times the average density of the whole Earth.)

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For the gravity below the surface we have to apply the free-air correction as well as a double Bouguer correction. With the infinite slab model this is because moving the point of observation below the slab changes the gravity due to it to its opposite. Alternatively, we can consider a spherically symmetrical Earth and subtract from the mass of the Earth that of the shell outside the point of observation, because that does not cause gravity inside. This gives the same result.

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Local variations in both the terrain and the subsurface cause further variations; the gravitational geophysical methods are based on these: the small variations are measured, the effect of the topography and other known factors is subtracted, and from the resulting variations conclusions are drawn. See also physical geodesy and gravity anomaly.

Related Topics:
Geophysical - Physical geodesy - Gravity anomaly

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